From 09b58ac6433459a1ecbe983fa515aa6f4756966a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Laurent?= <francois.laurent@posteo.net>
Date: Tue, 28 Sep 2021 17:37:11 +0200
Subject: [PATCH] StatsModels TP

---
 notebooks/images/heteroskedasticity.png  |  Bin 0 -> 35925 bytes
 notebooks/scipy_cours.ipynb              |   97 +-
 notebooks/statsmodels_TP.ipynb           |  486 ++++
 notebooks/statsmodels_TP_solutions.ipynb | 2567 ++++++++++++++++++++++
 notebooks/statsmodels_cours.ipynb        | 1274 ++++++++---
 5 files changed, 4110 insertions(+), 314 deletions(-)
 create mode 100644 notebooks/images/heteroskedasticity.png
 create mode 100644 notebooks/statsmodels_TP.ipynb
 create mode 100644 notebooks/statsmodels_TP_solutions.ipynb

diff --git a/notebooks/images/heteroskedasticity.png b/notebooks/images/heteroskedasticity.png
new file mode 100644
index 0000000000000000000000000000000000000000..564346faf591e500f8026a5cd25e65aee5f0a888
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diff --git a/notebooks/scipy_cours.ipynb b/notebooks/scipy_cours.ipynb
index 1b23c75..0f98bfd 100644
--- a/notebooks/scipy_cours.ipynb
+++ b/notebooks/scipy_cours.ipynb
@@ -148,18 +148,19 @@
     "We will merely review statistical tests:\n",
     "\n",
     "* Student $t$ tests\n",
-    "    * compare a sample against the population mean\n",
-    "    * compare two independent samples\n",
-    "    * compare paired samples\n",
+    "    * compare a sample mean against the population mean\n",
+    "    * compare means of two independent samples\n",
+    "    * compare the means of paired samples\n",
     "* analyses of variance (one-way)\n",
-    "    * compare more than two groups\n",
+    "    * compare more than two group means\n",
     "* tests for other tests' assumptions\n",
     "    * normality tests\n",
     "    * homoscedasticity tests\n",
     "* $\\chi^2$ tests for discrete variables\n",
     "    * goodness-of-fit test\n",
     "    * homogeneity and independence tests\n",
-    "* correlation coefficients"
+    "* correlation coefficient and linear regression\n",
+    "* effect sizes and test power"
    ]
   },
   {
@@ -192,7 +193,9 @@
     "Always good to get a reminder about [general considerations](https://www.coursera.org/learn/stanford-statistics/home/welcome), __prior to data collection__ and analysis.\n",
     "\n",
     "* Sampling from the population,\n",
-    "* identifying the sources of variability, etc."
+    "* identifying the sources of variability,\n",
+    "* checking the assumptions of a test are met,\n",
+    "* etc."
    ]
   },
   {
@@ -217,7 +220,9 @@
     "\n",
     "However, because experimental designs are often complex and involve multiple treatments and additional sources of variability, most studies also involve multiple tests, that are usually carried out after a so-called *omnibus* test.\n",
     "\n",
-    "In addition, every statistical test makes various assumptions that in turn needs to be checked. As a consequence, every statistical analysis involves a series of tests and procedures.\n",
+    "In addition, every statistical test makes various assumptions that in turn needs to be checked.\n",
+    "\n",
+    "As a consequence, reaching a conclusion about the data usually involves a series of tests and procedures.\n",
     "\n",
     "<table style=\"text-align:left;\"><tr><th>\n",
     "Example worflow adapted from...?\n",
@@ -282,27 +287,6 @@
     "]]>"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "e4db04ef",
-   "metadata": {
-    "heading_collapsed": true,
-    "hidden": true
-   },
-   "source": [
-    "### Replicability"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "05a435dd",
-   "metadata": {
-    "hidden": true
-   },
-   "source": [
-    "Not covered: tools and resources to support code and data management practices, some of which are provided by the Python ecosystem."
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "d6b0c2ee-4f6b-49db-8c26-dd64aede72fb",
@@ -1067,7 +1051,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 153,
+   "execution_count": 5,
    "id": "b00250f8",
    "metadata": {
     "hidden": true
@@ -1079,7 +1063,7 @@
        "46.485710784313724"
       ]
      },
-     "execution_count": 153,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1115,7 +1099,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 154,
+   "execution_count": 6,
    "id": "e60ba8f3",
    "metadata": {
     "hidden": true
@@ -1199,7 +1183,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 145,
+   "execution_count": 7,
    "id": "7e3b5520",
    "metadata": {
     "hidden": true
@@ -1213,7 +1197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 151,
+   "execution_count": 8,
    "id": "d6bbb149",
    "metadata": {
     "hidden": true
@@ -1225,7 +1209,7 @@
        "0.945200708300442"
       ]
      },
-     "execution_count": 151,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1237,7 +1221,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 152,
+   "execution_count": 9,
    "id": "1341b01d",
    "metadata": {
     "hidden": true
@@ -1249,7 +1233,7 @@
        "0.011092083467945555"
       ]
      },
-     "execution_count": 152,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1277,7 +1261,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 197,
+   "execution_count": 10,
    "id": "62f75d44",
    "metadata": {
     "hidden": true
@@ -1289,7 +1273,7 @@
        "1.9599639845400545"
       ]
      },
-     "execution_count": 197,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1314,7 +1298,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 155,
+   "execution_count": 11,
    "id": "a2a23163",
    "metadata": {
     "hidden": true
@@ -1337,7 +1321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 156,
+   "execution_count": 12,
    "id": "99fe274d",
    "metadata": {
     "hidden": true
@@ -1355,6 +1339,39 @@
     "print(f'{sample_mean:.2f} ± {1.96 * sem:.2f} years old on average')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "ddef9204",
+   "metadata": {
+    "hidden": true
+   },
+   "source": [
+    "`scipy` actually offers a more straightforward way to computing confidence intervals:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "a7d15497",
+   "metadata": {
+    "hidden": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(45.535126163333835, 47.43629540529361)"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "stats.norm(sample_mean, sem).interval(1 - alpha)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "52848e98",
diff --git a/notebooks/statsmodels_TP.ipynb b/notebooks/statsmodels_TP.ipynb
new file mode 100644
index 0000000..d876b1a
--- /dev/null
+++ b/notebooks/statsmodels_TP.ipynb
@@ -0,0 +1,486 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d5065981",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from matplotlib import pyplot as plt\n",
+    "import seaborn as sns\n",
+    "from scipy import stats\n",
+    "from patsy import dmatrices\n",
+    "import statsmodels.api as sm\n",
+    "import statsmodels.formula.api as smf\n",
+    "from statsmodels.stats import diagnostic\n",
+    "from statsmodels.stats.multitest import multipletests\n",
+    "from statsmodels.stats.outliers_influence import OLSInfluence"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4ddd8902",
+   "metadata": {},
+   "source": [
+    "# Multi-way ANOVA"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c4680b9",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Load the `titanic.csv` data file, insert the natural logarithm of `1+Fare` as a new column in the dataframe (*e.g.* with column name `'LogFare'`), and plot this new variable as a function of `Age`, `Pclass` and `Sex`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2d4fa47",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ae476b31",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b32ced14",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Fit a linear model to these data to explain our synthetic variable `LogFare` as a function of `Age`, `Pclass` and `Sex`.\n",
+    "\n",
+    "Treat `Pclass` and `Sex` as factors.\n",
+    "\n",
+    "Print an ANOVA table."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24492fad",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0ad3c464",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ded672e8",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Let us ignore the not-normal residuals and play with post-hoc tests instead.\n",
+    "\n",
+    "Split the ANOVA for levels of `Pclass` and `Sex`, perform all pairwise comparisons if it make sense, and correct for multiple comparisons.\n",
+    "\n",
+    "We are not interested in the significance of the slope of `Age` for the different levels of the factors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "00ace9f5",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9f6645bb",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a863196",
+   "metadata": {},
+   "source": [
+    "# Linear model with multiple variables"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ef97cb7f",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Load the `mi.csv` file and plot the variables `Temperature`, `HeartRate` and `PhysicalActivity`.\n",
+    "\n",
+    "We will try to «explain» `Temperature` from `HeartRate` and `PhysicalActivity`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c66b1c3b",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4bdeea0c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "358d3903",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f3003272",
+   "metadata": {
+    "hidden": true
+   },
+   "source": [
+    "The `PhysicalActivity` variable exhibit a long-tail distribution. This is usually undesirable for an explanatory variable, because we cannot densely sample a large part of its domain of possible values, and therefore a model based on the data cannot be reliable.\n",
+    "\n",
+    "We will proceed to transforming `PhysicalActivity` using a simple natural logarithm. `log` is undefined at $0$ and tends to the infinite near $0$, which renders its straightforward application to `PhysicalActivity` inappropriate. Therefore we will also add $1$ to the `PhysicalActivity` measurements prior to applying `log`.\n",
+    "\n",
+    "Plot again the temperature versus the transformed `PhysicalActivity` variable and compare the skewness of the transformed versus raw variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34dff28d",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16e7787e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7887928e",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "To appreciate the increased robustness of a linear model using the transformed variable compared to the raw variable, design a simple univariate linear regression of `Temperature` as response variable, and draw the Cook's distance of all the observations in regard of this model:\n",
+    "* first with the raw `PhysicalActivity` as explanatory variable,\n",
+    "* second with the transformed `PhysicalActivity` as explanatory variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9ed6879",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1044c8c6",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "49408adc",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Make a linear model of `Temperature`  as response and `HeartRate` and `PhysicalActivity` (or its transformed variant) as explanatory variables.\n",
+    "\n",
+    "Make two such models, one with interaction and one without. How would you choose between the two models?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b977a53",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## A (with nested Q&A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b891fa3e",
+   "metadata": {
+    "hidden": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c469b3d5",
+   "metadata": {
+    "hidden": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "475eb53d",
+   "metadata": {
+    "hidden": true
+   },
+   "source": [
+    "### Q\n",
+    "\n",
+    "To get a better intuition about the log-likelihood, plot it (with a dot plot) for different models, with one variable, with two variables, with and without interaction.\n",
+    "\n",
+    "Feel free to introduce one or two extra explanatory variables such as `BMI`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f7a51e03",
+   "metadata": {
+    "hidden": true
+   },
+   "source": [
+    "### A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3a4295ad",
+   "metadata": {
+    "hidden": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2474a218",
+   "metadata": {},
+   "source": [
+    "# White test for homoscedasticity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1bf04c2f",
+   "metadata": {},
+   "source": [
+    "To keep things simple, let us use the `'Heart + PhysicalActivity'` or `'Heart + logPhysicalActivity'`.\n",
+    "\n",
+    "## Q\n",
+    "\n",
+    "Inspect the residuals plotting them versus each explanatory variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "77c0d822",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4d7f9d1f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "20fdd05b",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "We will further inspect the residuals for heteroscedasticity, using the [White test](https://itfeature.com/heteroscedasticity/white-test-for-heteroskedasticity).\n",
+    "\n",
+    "`statsmodels` features an implementation of this test, but the [documentation](https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.het_white.html) is scarce on details.\n",
+    "Try to apply the `het_white` function, but do not feel ashamed if you fail."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34e7a050",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5de56d54",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98ca812e",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Instead, we will implement this test, as an application of polynomial regression.\n",
+    "\n",
+    "The algorithm is simple. First part:\n",
+    "\n",
+    "* take the squared residuals as a response variable,\n",
+    "* take the same explanatory variables as in the original model, plus all their possible interaction terms, plus all their values squared,\n",
+    "* fit a linear model to these data."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ebf1176",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "46c53e4e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "46bd2a33",
+   "metadata": {},
+   "source": [
+    "## Q\n",
+    "\n",
+    "Second part:\n",
+    "* get the coefficient of determination $R^2$,\n",
+    "* get the sample size $n$,\n",
+    "* set the number $k$ of degrees of freedom as the number of predictors (intercept excluded),\n",
+    "\n",
+    "The test is:\n",
+    "$$\n",
+    "H_0: nR^2 \\sim \\chi_{k}^2\n",
+    "$$\n",
+    "$$\n",
+    "H_A: nR^2 > \\tt{Critical Value}(\\chi_{k}^2, 1-\\alpha)\n",
+    "$$\n",
+    "\n",
+    "You do not necessarily need to compute the critical value. Just note the test is one-sided.\n",
+    "\n",
+    "Compute the statistic $nR^2$ and the resulting $p$-value."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "374e25eb",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "08216a83",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": false,
+   "sideBar": false,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": false,
+   "toc_window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/statsmodels_TP_solutions.ipynb b/notebooks/statsmodels_TP_solutions.ipynb
new file mode 100644
index 0000000..8325700
--- /dev/null
+++ b/notebooks/statsmodels_TP_solutions.ipynb
@@ -0,0 +1,2567 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "4e16caf7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from matplotlib import pyplot as plt\n",
+    "import seaborn as sns\n",
+    "from scipy import stats\n",
+    "from patsy import dmatrices\n",
+    "import statsmodels.api as sm\n",
+    "import statsmodels.formula.api as smf\n",
+    "from statsmodels.stats import diagnostic\n",
+    "from statsmodels.stats.multitest import multipletests\n",
+    "from statsmodels.stats.outliers_influence import OLSInfluence"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "358dce7a",
+   "metadata": {},
+   "source": [
+    "# Multi-way ANOVA"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a1face9f",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Load the `titanic.csv` data file, insert the natural logarithm of `1+Fare` as a new column in the dataframe (*e.g.* with column name `'LogFare'`), and plot this new variable as a function of `Age`, `Pclass` and `Sex`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "965cc75c",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "7eb30cc9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>PassengerId</th>\n",
+       "      <th>Survived</th>\n",
+       "      <th>Pclass</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Sex</th>\n",
+       "      <th>Age</th>\n",
+       "      <th>SibSp</th>\n",
+       "      <th>Parch</th>\n",
+       "      <th>Ticket</th>\n",
+       "      <th>Fare</th>\n",
+       "      <th>Cabin</th>\n",
+       "      <th>Embarked</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Braund, Mr. Owen Harris</td>\n",
+       "      <td>male</td>\n",
+       "      <td>22.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>A/5 21171</td>\n",
+       "      <td>7.2500</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
+       "      <td>female</td>\n",
+       "      <td>38.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>PC 17599</td>\n",
+       "      <td>71.2833</td>\n",
+       "      <td>C85</td>\n",
+       "      <td>C</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3</td>\n",
+       "      <td>1</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Heikkinen, Miss. Laina</td>\n",
+       "      <td>female</td>\n",
+       "      <td>26.0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>STON/O2. 3101282</td>\n",
+       "      <td>7.9250</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
+       "      <td>female</td>\n",
+       "      <td>35.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>113803</td>\n",
+       "      <td>53.1000</td>\n",
+       "      <td>C123</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Allen, Mr. William Henry</td>\n",
+       "      <td>male</td>\n",
+       "      <td>35.0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>373450</td>\n",
+       "      <td>8.0500</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   PassengerId  Survived  Pclass  \\\n",
+       "0            1         0       3   \n",
+       "1            2         1       1   \n",
+       "2            3         1       3   \n",
+       "3            4         1       1   \n",
+       "4            5         0       3   \n",
+       "\n",
+       "                                                Name     Sex   Age  SibSp  \\\n",
+       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
+       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
+       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
+       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
+       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
+       "\n",
+       "   Parch            Ticket     Fare Cabin Embarked  \n",
+       "0      0         A/5 21171   7.2500   NaN        S  \n",
+       "1      0          PC 17599  71.2833   C85        C  \n",
+       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
+       "3      0            113803  53.1000  C123        S  \n",
+       "4      0            373450   8.0500   NaN        S  "
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv('data/titanic.csv')\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "17f37d48",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(891, 12)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "31c6e99b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df['LogFare'] = np.log(1+df['Fare'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "e5b46f36",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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3lgu4dIuChVwJsxkVo8mwIwA+dvg4RpMRZEo6tg/GsZQr1fxOLt3Sh1PzWWSK7qieEHaNlKuGeh/+sVQE51eKIFaeLEwG7BlNAFjdBEQ3+KQlg1UVVN5GKyWdz0D83AmMAUt5DXc/Mtn0vVQv9DJd0LCQU2EyVnMF4K3NM5cuQjVYRTmPWkJ8vC+MdEGvGFu6oOP56WXHR+Ke8L2TXiuesyCTh982Hz98HMOJMLKqISaCFtLTNv6NYrsMktnrtWOnCzr6owryquGbFPbFR1/D5x89gXSRO0TTRR2ff/QEvvjoa1XHMTWfA2MMmmGipHHhSeCa8EpBQ65kYDQZxmgqCiKCbjAs5zWcms85D+qJuSx0o9Js4/5Obj8wgbAiY7w/isu2pDDeH0VYkZ1ztR25z55dwoV0Ec+eXcJyXkUiIoPAhToBGIyH8Imb9gJY3QTEBCATEA3JVe333kYrNowxJ1taIn5NmsWbuJcIKxhOhJ3QSztpLapUH6fX/7NcUJFVDRimyWs/ESpKNfj5i/7fc+dB1vWIhXhYsCIT7n/iFAD/EiH2pAe05jkL4ofx+i8Mk2Epr+H0Yr6jWckbkZ4W/BslWzBIZq9fM+tMUUdYkXyden/82I9W1W5h1vvVMEwThqVNM5T/lwn4/iduRF8sVJEoNJ8tQSLAYK6uVJKEC5lSxX7d30m9c/Vz5BY0E6mwjKt3DGJrfwxX7xisMMF4JxPb5GOYDJMzaUxZk5FbUJ1dyiPizYhD2fTUKtylir9469UIK7IzwZd0E2A8ic3GK1C9wjBd0CFLhLAiY+94H/aMpdAfCzkC1M/562q45iARnJ4FfiVC3JNeK56zIM3YvRPMXMa6v8z17XrmriXVjAO+F+hpU89Gyhasl9nbqFO01OD7ABCWZejm6o5cYZk/jF6TlGpp3+7mJFv6IpheLtb8TmqdazVH7lxOwxO/6R966E0eCssSSrrBJ60q/YW9PYg1g4tGBlg1/fnEt3ukdUqEd5zxsIxERHb8J8BqgdpodzE/fxFh9YRWr2idm1Y8Z0Hu3yD313rVkup1v2E9elrjb1UNnF4gZDk/TZM3GjEt+0QzTtGqmky1XVnve01SskQwPRqrIku4dCxZ8Z3ccs3FuPfxqbZqUG7NesdQjJtBavQX9vYgVqh8qgZjIAkYiIfwyfe9uW3j/OKtVyMkyzVNfF5t2zZNVesE5qedD8b5RFCtaN2u4ThPpHPdWybj79tjXutzFuT+XXV/Eb+/3KvM9a4ltVGrjPa0xg/0RmvAVhDEKeomLBFUb21ii2qaTL1Vgldj3TkUx0JOhSxRRZ2dT71/b9MRIRMjCZyYzVZ15AYhSH9h7zaRkIzBsIR00cBYKrIuJQeClDm4/cAEPnb4OM4tF7jJA4BuMAwnFN/aRn7aeTIawo9dOoLvTM75Ovr9SoQMRConvbU+Z0HuX+/12DWSwFy2ZDnbW1fHqRbd0sqy3fS84N8sNNrM+tdv3I0/fPTEqve3pCKOJpNXddz9yKQTAWJUmSjc73sFgF9pCfffG40I+cRNe8sRJgaPWnE7coMQpL9wtW12j61vNmsQgUoAwGCtsiT0xWQMxEK+tY2aqZlzcO8YPnfLVW2tsxP0/m30/mo1rch56AWE4O8RGn2gbW3ODuc0TYbRZBhjfWXhpxsmTi/ksXM4joFYCNNLBd99yVJ1c1I9wdWoBnVw7xh+f41CKIhNulv8Q/Xi1u99fAp9sRDG+2POe3lVx2Aigkd+o/YE1Yifut0r52aLuNUbV6vj/rvlvmg3olbPJsGvXsuJCxmAgD1jKQDAi+dWfIVFKiLjhd+5qWXHXY86MUE0xfXWJv3GWK+WTzNtO5upD9SLiVPtqrfU6fuiUUSRth7G++C1uvKm30NyeiGHbQMx9MXCAICpuSwKqgHb0h+kgFozx7V7xNpJOetRZbRT1BKoQSZFv23ms0XkSoZvtm8zE22vVu8Uxec4zQh+YerpArwO0FPzWfzw9CLGUmEMJyItCSk7uHcMt0wvV2Tybk1FoLiiQ0aSEZxbLiAsEXaPJR0hvZQrOaUPgghpr7C75ZqL8eTUIqaX8khGeFy5ZrKq53rHA8egm0DJMANlHLeKVmu99RzbQcxgXtODX/a0O7u1mfpKvZoBv1kcse2g7eGcRCQT0bNE9I12H6tX8YaQZYo6JOJp9a0KKXtschaHj53DaCqCN4+nMJqKoGRwk4EdPqfIhIF4CLtGElgpaAhbWZxuIX3PkZM4vZCtmknplzl6+Ng53H5gAt//xI0YiIfRHwtVPddMQUO6ZCCvGVAk7li758jJmhnHraCZCqn1qBcaGCQxyhtK6c2e9ma3EoBzy8WKHsb1nJO9mgG/URI4O8F6aPx3AngFQN86HKsnaTRJx6YRDdVPqwN4PPhAPOzYMz/1/ssrzAaqYTrbuoX0SDLqW2SsXq0ev3MFY8irBiZn0k4iFQGQSIJEPP78f35vquZKo15donp/b1brrbXfehppNUfieF8YV37mW84+37N3FAB31pZ004nLB1Znt473RzG9VMCFTBGpqFLVOekt+JcraVB15oRa9sUU7Bz2DxXuFjaLI7YdtFXjJ6JtAN4P4P52HqfXaTRJB2hcQ62m1WVLupNQ5C374P2Md0Kyi4zlVD1wrR7vuUpE0HjlAkfor4Ix5DWj6rnaXb0KVVYJ9f5e6/rU0nrr7beeRuqXGPX2Hf146PkZZ5+5ko6vPXcekzMrvhq9/V3Y90oqGsLFA1EwhqrJVt57R5EIS3kdBc1wvt/ZjIobJoaqnns3sJkSOFtNuzX+LwD4zwBS1TYgotsA3AYAO3bsaPNwuhOv5pKKKpjLquiL+SfpAI1rqNsH4z4JNMqqBLBapZ/DsuR8FqhSZMyq1WM7jIFKYec9V61K0ph7CtBM7miudq73P3EKEgGKxMdlrxLuf+IU7njvpXX/bl+fRuO36+03iEbqDVe88jPfqtgnA584Vgo6tg2u1uhl4iUp3Nmtiizhmh2DVR2c3nunpJuQqVyfyb43npxaxB1Vz747WK8Ezl6MeqpF2wQ/EX0AwCxj7BkiOlhtO8bYfQDuA4DL3vI2dui+pzp+cde7v6uf4/XmK8cxk1arhpQ16tjyliFWDRNzWRU/f11Zq6tX+tk7IZV0XkvFXbJhS18EZ5cKOHEh41s22BvPzQiQYdfI4fuwhb7JTKdy5nCi+rnmVK4du3EXIav3d6A5s4HffhnjlVBtZ7jbsR0kNNC7T/ua2NeBa/QMM+kSVgpaU9mtfuY2ReblEfaO9znn0e02/vViI9bvaafG/y4ANxPRTwKIAugjoq8yxn6h2gfeWC5gm2c5v94Xt96X3MxNEGSftuN1hyV0nnl9peaytVEN9ckpHjljNx6x7bhurc6rCY4kuaafKxmWkEni568bcgSZX5Ex1TB5whfBt2wwUKmlXfbbDzsZqTYl3YDJAN3khcS2pBREPGYY97kmwrJjprBxFyGr93d7TI0mGHn3a/cvIKDCsd2I+cG7T7tshXvsXo2+0bhz773jXckBwknqplejnmrRNsHPGPtNAL8JAJbG/7FaQp9vV305v17U+5KbuQnasc9GNdSzS3kMJyKOMAdWa3V+q4jhRASKVJksZE8U9oTmHsNijsfouzuD1ToXv9o8EhEu25LEwx89UPU47nP98P5duOfISegm90GYVn0fuwhZvb/bNGo28O5Xt9TyMU9ZjEbuYe8+bXnfX8Ps1+i4vfdOX0zBbEZFKlr9GJuZjRg22lXVOSVXdiLQmYtbz8nXjBOwHfts1LEVJPSt0fA4vzEkI3KFvbneuXzipr0YjIeqNlkJcq53vPdS3HnjbsRCMnSTH+/OG3c79vt6f28W734BYMxTFqPRe9i7z0REwc+8bSv2jve3zIHpvZ47h5O488bd2DWSFE5SHzZi2GhXZe72bb+M/dh//rLz2puFtx4OlnrZgM1kC7Zjn41id7ZyV2BMRhR8ztXQJEiWbb1r3mzmaC+lyFdDZJJuTLo9s7mZzN2u0vgZQ9Xa5O1IsPGjXhvEIG0S12OfzeCu8gi2uvy+VxP0JnAFuebNnIu7Rr03pLRZOtFFab2+R8H6shHDRrtK498ycTlL3vo5RyO97k0DAElOaGE8LK+yHYckwmAiEngVEGTVUE8DbUZDrZdA9BsPHsNDz884537zleP4/K3XNHgFq9OOlUo1Oq3Bt0pDa6Z+UivOvd11mzrFRguJ7BZ6vkhbZOsetuM/3AOJeDKPyYCheAgXDcTwykwaEhEu6o85zarTBRXTywXsHE4EesA7tWSrd1w7EcgOtbSdj62wQ9s0WuWx2c90A60wuXi/M3eNnJFkpG33jve489kS5rKqU8uo28wMQel2c0kv0/OmHoCnnqs6c+KWlwsaiAhRhTs/7aQhALiQKSEkSYHbpPnVTlF1A3c8+GxbTQL1ara4E4Ekkqz/+fu1aMSc0YyDar2cWq02y7Si9oxfk3OJeNmKdrbkW4+6TZ1gs7Q07BW6TvCbrDLu254ARlMRgPEsQ7f9dEsDlQi9AsGv5EA7/Ab1BFFOrYwxB1YnGHlp1OfRDt9ErbEFFeTt8N20YsKqV64CaC7qrN61addx18paJ+deLQTX7TRrsQkcx09EMQA7GGOvNnWkwMfh/3vPJxUNYSRlOMlE2wbjTuKJm1oPuDdxxa/kgLcdYStskfWSrRJhGTlVB2MGGOPXgAhIhKt/PUFi/2uVRw7akq/RpKZGE9zakRzTiuJd7UhyCnJtvKU1DJNBt+6JyZl01VIb7aQVmau93tJwPf0TpslgMAbDtH6s5vS6yZy/6QaDaW3TDIEEPxH9FIDPAQgD2EVEbwNwF2Ps5qaOWgvPeUgEJ6kkJMv44q1Xrgo/rPWAu7+wVETBilXcKhaSfUsOeNsRtiKDuJ4ges/eUXztufPlS8D4dbCrMvpRL6nE72FtNIsUaDw56N7Hp6DqBhaylTWBqgnydiTHNNvmz007kpyCTHLe0hqa9TzwaqX+pTbaTSsmZ79nIF3QEJLIKW/Rrc7eVkx8hsmgmyZME1yoG9WF+3r4XYNq/J8BcB2AxwCAMfYcEe2q9YFmkCUCWc5NXpRLhkTk21QaqP+Ae7+wgmaAAIQkvk+/kgMX0rXLCjdDvXHOpFUMxBSki7pz7n1RBTNpteo+62lQnUozf+1CGumiDgnEC4gZDAs5FbqRbuo8qlFPA1tr8S7vd7ZzOIlD1w41tGLyEmSS85bW8JaZ8Cu10W5aMTl7r2cyoqCoGTi9mIdhMsxnS/jY4eMVeSXdQrVn6X9+70e4YfdwWXiblYLc/brbCCr4NcbYClVm1rb8bGQi7BpJwC95CACen15e9bB7B+PeJl3QIEuoqDOeiipOo2rfFYNpIhGS8NIbK44QHk6EoLqqSDaz7KsliM5agsQbPVPrwaq3iuhUmrldWlmyJBYRX7qqrpLLtVZhQTTpVhXN8n6P431hfGdyzrcOPgBcuW1gTVFWQSY5b2mNyZm0E+nVqQJq2wfjOL2QXVXnqdF6/e5n4KbPfw8FzYRMXEFgJrCc1/DZh1/pmOC3hbRtQrFNK6cXcuiLKtAMEzwFhkEi4PRCDueWCh0Z61oJKvhfIqKfByAT0R7wci3/3OrBXDQQw1gqGrhF38cOHwcB6IuFMBAL4fQC38YOuXtjqQATgCIRFGm19umniS/nSljI686YTAbMZTVs6+e23WaFTq3Johmt16+i54f371rTPoOM2xtT7n0NAGCA6aq9Y5oMBdXA/ruPIBmWsZBTne/MuwrbZu3z3sen8NtffxGpCDetuDOHm1nN+J3H4WPnnO9xcmYFT07pkAlQZHLq4A/GFVw8EF8Xkx/QvgJqjSor7u3BGC6kS5AlqqjXf+jaoaqfqXeMUwt5bs5yKQjMZDi10NoJrZqJxX7P/bdqJpYtqSgWcqUK53RRMzHeF2vpWBvlh1OLePDpswiN7nxro58NGtXzEQBXACgB+GsAKwA+2ujB6jGXKTnaLwCEZMLMShGvXshgNlMCwCrC2rIlHSsFzdnmQppvY4fc2ampXAgRJIlgMoalgu5EJzw/vQygrNVlSnx1QbCcrNb7iwU+GTQTllYvcqWZ6Bm/VoqHj52ruU93/9wgkRnecXtbL55e4K9PzZdbMZZ0E6moAkXibQHt6ydbAvb0Yh5Lec3pGBUPK+iLhTCYiOD7n7gRtx+YwOFj5zCbKUIm4MRsFifncpAJznU7MZtpKELE7/r/8WM/gqobzve4Yn2/BuMrRHuBstLCMMogGaDe7y0VVWAyOKWw/e6NehE3jUZOebefz6qAVTzPNjeNJsN4cmqx6WM0i2kyaIaJomYgV9KRLmpYzqtYyJYwmyni/EoB00t5vL6Qx6n5HM5YWvn5lQJm00Us5EpYzqvIFnXkVR2qbkI3zZp29Vuv3Q7d5H4dBv6/bjLceu32lp5bI/xwahH3HDmBhVwJYKZe/xOV1NX4iUgG8A+MsXcD+C/NDDIoumk6N82p+Rx3cpIrwscK57TRDL4k0wyjbHdiQNHahiyV07SWZ3wpB0hUfRVhmySY8w8nb2ms7Whm3YwzstF9eldQQTRY7zG8rRfdse2jKd6KcTAewlJew7bBGGIhGSdnsyAibHH1iJWIT/K2b8V9/dzHnJrL8hLPDJjPqpgYTToPa0EzAq9m/K6VbprWuPk2bjOsN5zYjqYZSYZbZmLJqzpeemMFHzt8HHvGUs737f3evKWw6/mx/L7XRldI3u0Nqx+zIhEmrAvmNTc1egx3VVaAgTGunV8ymsBKXqvQyt2aeicSTq+bGMKd2IMHnz6LmXQB430x3HrtdlzXhg5lJmPWpGYgW9KRK+nIq3ySy6k6siX++7demkFeNVaVXQlKXcHPGDOIyCSifsbYSpPHCYRE5GhXpkvYu9FdT6jp+p1cE4RhMkzOpMEYc5xjtv1OJiAaklclx9g9ZGsxEAthPlPCueUiAHIyiIM0s65nb2/UGdnoPr39c6s9mO7luneS88aU+8WYjyQj0A3TMdkxAINxBfPZEt5YKTirAM0wHIHqthe7z8up7Q8+mU/NZa0evajrF6h1HgAQkaUKJcKN+14CuIKhGwamlwrYM1a9Y1m9pj2piMKbpkiEdJEraQXVwOmFbIWw9rsXqjlygwjcRv093u3DsgTNMCu+Zz/fhP0ZWzhHFAmvL+aQKWqrnJ4f2r8L//2br1QUDeyLhfAf3rWLa7FdxnUTQ3UFvWGyVcI6W9KRs37PqzpyJVuIV76XtQR7vmS03nnqQ1AbfxbAC0T0bQA5+03GWNsDC+wZzX0x7HC6irnBJwzUAFaVfQB4yObkTBq6wSeGvEsIycSX+97jhmRqqJm1m3bEMDfqcAvy8Hu1R+8k57U3V7M/2/WUGHik1mJOgyJLkCXimpu1rT1pzKyUsJBVcclvfRMAkC1q2D6UQFiWoNsON5PHLhO4XVgzTLyxXIBqMCTCMq7YmsIdDz6LnGogokjQdAMGK2vyZxYLeNNQebLuj4ewmNMce7vtQHUG7sK+FwxWmVTnrXg6ny3hIw8cw7bBODIl3RH0/ZY/4+Rs1lmNukkXdIz3Vw95rTW5+H2vumHi2OtLTphk0mruEvT+896vI8kwzi4WwAC8cn4FskRIRBR89D17MJcpwTAZxlK8Xla2qEMzTIRkCcmIjIsHEpjLcEFu26TPpwvY2hfDT191EZ49u1KhRb86k8bv/sPLKGgGYiEZP/f2bfjgO3f6jtNvn81o4nY3ObdAtn/Pl3RkXe+Vte/V2/l9t63AntgTERkJ6/+puRx0kyEsS3ijiX0GFfx/Z/2sO36z3yszGSTCMiRY2hlgedvLmIwLtpDMe5KuFDREZBlFzQBkgkyADuYIeVni2xmM/85YuWyE7FpPeVvfBTHLBHHqNep8u2FiCE9NLTjnrBkG8qqBQ9f69y0OMvnc+/gUNKMcg2/3cz2zWKkZEky8cn4FkhWuCWbglfMrUCQJkZDEnXTzOeim6dSpNzwPBaEsaBkA1WCIKPx4ywUd6XMrIGsStrdXTR5VEZLtEgZ88sgWdTx5asnZd75KxvOZxTxkiRCSeUnqXzt4iWNCSUYUqLqJom763nNE3CE2mylro599+BUs5VQn21wzGIoATs5mcNl4H07OZlHSTSxk1ZpaXE418PpiHtNLBccm7l4lTC/loVkToHdySRc0ZIsaNINHrkngq+KQLDmmn3RBc44fC8mOn+CX37kTuZIOgzH86XdP4q+eOoO8aiAsS1AkYCgZQUTh2zPw54Cx8k+uZCBT5Cuvqy7ux3Nnl3nzGAI0w8RCzsQH3toPoGyTViRCX1TBQq6ER16+gDtv3OMI6r/659P4i6fOQCJAlngntr946gwAOMLfLegTYQWLuRISEQWxkITz6QJ+/x9fxU9duRUXD8aRU/UK4cx/N5z33UK8XSGX0ZCERERB0hbcEaVCiPOQcsX6ka3tyu8nIwrC3v6enuvZDIEEP2PsL5rae4OYlg3Pbj3n911IBLx5PIWCZqCgGTAMfpMTlW37EZlwqSv0zS4q9r4vPI4Ts1nLc4vVKwbrDQkMey/iN6xtXnBrtfWaWXtpNN8giP39b55+fZUwYdb7fiGHQSafE7MZrOQ1SBJBlgiq5q/BmAxO6ClD+XdY9n4wIKRIUGQJulndnLJ3vA8vvbFifxQSSZCJwYAJEzzSRwafFBgAYvw9O2SUMSCsSCi6juE103ixzX2EyvBMu1BeSOaRKyXdCksFnLaPhudcTs7lHMWBUL6fNJNfk1KVScT3elg/3ki1V2fS0MzKyLSiZjqTS76kYzGv8cgoGbBiEzAUVWAwrhHGwzJCsoRUNITzK2XteveWJC6ki6sErm6aKOlAQjOg6ibyqonhRAhDibK5rKAZePDps47QfvbsCobiIeRUw9H4E2EZz55dwQcBPPj0WSgSOU55ewL66lNncPFgDDlVxwNPn3WuhqMUMIa/+sHrOLWQxxvLBZxayDnf7wWTT8LLhUrf5p8/eSbgVa+ORLwJjq1h28I6ab0Xd2nfCdd7tuC2PyM3KZjr4fY7gKSGOykGzdzdA+B/ALgcvH8uAIAx1tJC44okOVr02cV8Rey3jS104mEFI8kw5rMqSILjNAQDxvvLYVZurTZT0nHxQBTzWRWq1e3JfmDth6QvFsJivmwCSEUVzGZK0Cwt19s8PCi1bPjNhCeeS/Ob3p1awVj5fb/j13Mgq7rJY5gNtmoFxTOdDatyKMMVW/sxNZcFA3/IJ0a5iemFc1yQ2zHPbtxC2WTlbd3n4Z4o7Lj1F63topbQ0MyyRk8NurciisS1zlio4vo+ObWIVERGuqg72bKAvZrk18NkwO6R8grJ0RL97JGel/UmJICbEWfSRYABW6wuXvbca5jMiZSy39eMspJkjw/gmnm2pGMwHgbAJ8dMUcd9v+hfwPFvnpm2hL7kOh8T2ZKBv//Ifhz6X0+hL1oWFYwxhGXCueU8Ti/kkC8ZOL2YQ1SRkIpKMF1ZqJMX0vjU11/Ey+dXQETW3ywlD8D0chEf/MoPK8Zjei6UbjI89tpcrYu3isF4qEJwV2jRFYK70oRifyYakuDJW+o6bL/D1z9y+oVGPxt0pvgzAP8VwOcBvBvAL6MNBd4mRhNOud9LfuubUCSraBtb9UwB4P1gs1boZs4wEA3JThy2X1q9be6whZRbm7ffy6s6hhMRDCYimF7KYzAeRq6kQzMZmAnf5uFrJajzzW0OqiZEagmXeg5kk5nwmWtX7dsWMH7O3fK+GhsbebZxK0qSZfKxcwPcFLXqhex8j2ON13t9X7uQRk41EJL46lG30+fBlQJZIgxEQvjk+97sfEaRrdUHc51Ak4z1hRENydCtCVP1mMYYKhal/D3GQxtliV+3iZEkzi7loRsmNNd34o45tx2QjqNR1R3TmHvSJXAT1G997QVkizoWc6o1ubCK7/Y//PnRuuf2TycXXGcRDPfllCTC+94yjiOTs4iFJEhW0tdiXnUmwu2DcUgSQdUNjCSj+MN/e1XgY21Gggr+GGPsO0REjLEzAD5DRM8A+HS7BpawHFIRy8Ria5tugTCfLUE1GLYNRrHDU//Dz/4etP7Kp95/edVoGKB28/BmCGJ/95qDzi0VHN8GuewM8XBlfHsjSCRBIv7w+0225Wbo/LWfc9dt8vDi/Zv7NRfsZdPIcCLsbBeSJciMa7z2Sq2KH7aOVm2Zh2Rp1fX1ZhyHZAJ3QxPG+6K+K6SJ4ThOzOZgegaiEKDqRuU4a4wrGZIQDykwTcaP79o2LJOz8jVZWTArEpBTde5nMRlkIizkVOs132Z6Ke/4rZYLGn7ynu8HdkDaQ3jKFatfC3vYElGF3fnyrX1403AcKwUNR88sQZEIEUWyatIAH3zHm/COS4aQiCj4u6Nn8Zc/eN3xE9irmF98xw588J07Mb1YqEikkq08H1kmhBRCUeOKSyfj63uFoIK/REQSgBNE9OsAzgFoa3nAD+/fhXuOnIRums6NAMZr2NhCeimvIRGWMbNSrIhssUsyeGmm/sp6lD4IYn/3moPGUhFcsByNbi35V9bQ5i+sSJBVnuhGBKgat7UDXOh4v4NUVMFcVnWSiwqaUVPyhxVybOeKRAjZk7pmwASgm3zikonbuO19pqI8B6E/FkIsJOO1C5kKM2CtycaLaTL0JUKrrm9YkZAv6TBgOkKHGNAXV/D1X9/vxJSfWy7wCokmwy+/awJ3f2sSOVV3hHaICFv67AStMGYzaoUg866oFAJkRcJctsS1dGvCtR3q7vBl9+JGN2FFXNnfD89Kd5N3+Wgyxeo5PtWuXywk4f1XbkUirGAhq+L49DIyRQ3DiQhuumIc104MWTZvGWFFwtOnlmrGutuO2Zl0AdsG4qv+/ovv2gUiwt88M+0b1XPrtdtxz5ETKGgGopbm3xcLYTAWQqaotzW+fqMRVPDfCSAOHk78u+Dmnl9q16AA4I73XopT81k89PwMNIMvtfduieONlZIT1SNLViy+5YzUTYb5jArNyFTdr9fc8djkLJ6cWqwqONajnGwQ+7t3Ahrri4IxhrmsCkki33aOjbJnLFURIhoLywAYijqDbvIy0e/ZO4qZtOokF90wwevbzGb4dxK2HLp25IdddA8oO0yBcqKKXYK6L6Lg+c/8BIDV7Qttf4r9HhEhpjDYPj0GICQBOuMaJwBEFQJjPOHPjrqRCEjFFFzUH8cvXL8Dl46nML2Uh2mC10oCQ7ZUdk72xxRs7Y/j9Hy2Ihqk/LuBfW8awvGzy8iUNEQUGVv6IlBkCSZ41EuFOcgHncHJGq4k2FQmEyEWLoe9xkIyJkYS2D4cRyLMo0Lq2bh/4cs/gKabWMprjtVqMB5CWJHwqwd3BxoHUD/WPUgs/AffubNq+KZfItWvHdy9roKeiFxZ/eSYHvl9vPpvBACe197tQPD9G/+o5xju/cIVWNEgNQU/Ef0jY+zHGWNPE9FvMsb+B7h9vy1kijoO3fdURbLLzuG404LuxFweY6kwdgzxRhtT8zlIABSSrPECJrFV9tFqVIumuWV62ak/kwzLSDdYRGwt1JqA/OL2r58YDhxdVA975THer1Rtj2cLZQZgOa/ixGwGo6mIY2qbmstBkuDYyt225ohL4y9HbfD/veV5//eH38EdzZZj9XuTs04CEDNNFDxfsa3cEnEhm1MZRhIKtvRFUNBMaAbDT191EbYNxZArGXj1QgbPvr6MrCXMNcPESoGn5NsROQXNxFx2BT/7p08Gun4FzcSyda/UI6zwqBd3REg8XI4acYf+JV1ORztaJBlpnQNya18MC7kSRpKVUTvDiUiNT60fbmH4zt0jeNeeEev96sKWqIqg9XlfourC1fvZjUI9jd9dEP7fgEf2tI03lgvYZtX6ODmbhW4yJMIKKFwly5YBJvjy3R01EZaDfUF+0TRzVh2XbYMxp4gYA7cLB43bBxqLyw8Szumt016tUNZaaDTs1PsdxcMKIiEJhmFCkQklK4kKsMMVCQTma+fPqjqGkxGcW87jk3/3PG77F5dg79YUciUdT59ewt8+c9bJt1BrzOvuOX8+p2M+V9amv/LPp1tynWwk4iuF8b6IFe7nHyESj6wW6CG55bERTVNpQuHRW4bJ8O/escMJla6nzUpUKUirabFuDRY++7OF60YUtt1EPcHfdAALEUUBPA4gYh3nMGPsv9b6jGqY+NGckxiMsEyYz5bQFwtBNeyWi+Us25DEH3RFJkcLDskSVIMFau7gZ7/PFHXoZmVpAwAYiIfx8EcPACgXxaqVpt/qLlRPTvGqo3ZnJrvEdCvqsjNml6MFjr2+iBfPLSOnGljOq3j69AKuftMgGGP4o++eRFHVMV/iY9BNO6mp6IRaDsZ4H4HhqIIhOYSzS9wOLRGvE+S+oZIRmUeUMG4G+tF8zsrlAO76h5fXeFarkS2TWLUwv4Q7mcaTKXnXQy9hernoVJS0I1wUAj77r69sekxVtU6yhKlHyEpUDmD1E5L1hK37tb2vXSMJjPdH19S4RtBb1BP8E0T0EPi9ZP/uUKcDVwnAjYyxLBGFADxBRA8zxp4KOjieuMNVOAlAyeQDsRt8GAyQJGC8P+qYg+ayKsZS4UAC189+X9JNJ5LIpl5nq7UWxTq7lEe/5TAF+GwbUSScXcyhoHLzw5nFHAbj4YokGsYYzizkrFA75spgZo6T0BZQDOV4dHsbHiprm14Y/uz7p/DXT591nJE51cCfPDaFY68v463bBvDCuWWoeqUuYIKbOE7OZir6Jc948gkMezAusqXKUMxa2ZMELnAlKkfgAFiV6GdHlDDGAAK+/EvXImkJ94gS3DTiFbwzmRJkCZAkyRHCMBmmlwvoi4UgubeX4AhzW6DbArdCM25Tck8zrLVxjaC3qCf4f9r1++ca2THjEiVrvQxZPw2vIOzyCfYHFTvtEvwB2tofdQqC5VUDY6mw08SinsD1i6bhxaLKQhjg4ZsX9cdQ1Az8yWM/giwBEUWGyfj/hqnjj757Em/d1g8GVDRucJ/H6YUszlrRGm6BPJKI4NxyrsKxaNc5Ob/CGz2MJaM4NZ9Fuqg7Drg+q/fqfKZY6Xz0qydS5f28UyyqXPvI8ASMPzm1WFGC149a8f9+hCRCPCIjU9TLIanggjsWlrAlFcOnf+pyJCIKPvP1l7CYV3kYHwELWdWJYFEkwK7QwE1B5eiZiZEk3rZ9wHGg2UJXorITWKqmJXsmCHJt736PiCps4wJBL1BT8DPGvreWnVslnZ8BsBvAHzPGfuCzzW0AbgMAuW91j9ntAzEs5flDPpIIIa8ajqljtC8Cw2T44393DRhj+MCXnkC/R+AqEuHMQg4zK0UwlDNSGWO4ZCyJX3/3JXjgh2d5Knt/DD9/7QgeefkCVgoaoiEJRc2EbjL8zNUX443lAs4scqGuu44RkgnTS3mnYqRf44aCZmBLKlYxNsYYirqJy7YkcHya1zkB8VVHUTOxc5jw5/90GjlVx4VMESuukDwGYKWo4/lzy/jxL3y/iW+nMSJKuZqlO+rAUqyRiikYTkTwE5dvwb5dQ040SSwk46tPncHfHp1GXjMQD8vYf8kw5rIazq/weitvrPDa+1x7Z8gUDfzi9Vuwb+cQiICPvGc3fufvX4bBGGKKjIF4CLppQtVNqAZDPCyBmSYYCLppQpEkRMM8Q/cDX3qiJf1c3WWE3THme0YTa7+4AsE6Q0HqWxPRC1itra8AOArgvzHGFlZ/quLzAwC+BuAjjLEXq20X2bqHbf2lL5Q/B+A7/+nHAAD/8f8c9xWmIVlCXzSE8+kCskUd8bCEwfjq6IRGMvnc8cbe2GB7HFFFcsoX5FUDqWgIv/yunbzO+rk0vjM562iZdt+Ai/pjkCRUaOftascZC8kuB6Pbrq2Uo0c8RaN++2sv+taXIQCXbknh9cUc/zvjmrXtZ9g+lMBXfvlaJ6PSth/bHZtqmVcO3fcUTs1nV/kudo0kK6KVvCGe1cofTy/lkXB1+aoWndQoj03O4uOHjzs+ILt0x+93YY9YweaCiJ5hjPnX46hC0Dj+h8GrHP+19fpW8Lj+GQB/DuCnan2YMbZMRN8FcBOAqoLfi93zFOCRB3d/axIX0kWnfndY4c5czTDRF1VgGCYWclzrHoiHHW3dm8mn6qZPk4NyfexXZzI4t1xAtqShqJn4yj+dwl8+dRq5koGlvMrNE56xXsiU8F/+X+1TO7WQq/l3G7cp4vKL+pAIK3hyasGyIQOwTBJ2BdEv/Nu3VRSNsotDuSewiCLjA1duxTt3j3Dbs8R9Jfx3LqC/N3kBf//ChVXjSUV4gs6Wvihet1rjERFMcJPKr797N/pcDettIfzahTQ0gyGsSBXNRvxq5Y+OlvMB0wW1oqywX29lL97eA5rJWtpo/uDeMfz+LVc17ABtpj9zN9Cr4xYEI6jgfy9j7BrX6xeI6Bhj7Boi+gW/DxDRKHiT9mUiigH4lwDuDjqwgaiM9755vOI9buu3nJFgyJcMJCM8VpybIXg6+FJeR6ZkICLLGE6G8eV/OoUvffek08VGa8Ag3UhsdkSRPIkyMuKeCJLKyBH++5e+cxLpooZ4WHZszd6Vyk996QmUdKNcSAvcGZoIy3jXnhHIRPjnk/P4wqNnML3M8w8WLa13JBlBuqjhi0dOYiQZqfoAP3t2pco14EZ02xbPbKcwW10izXZ+q7rh22zklunlil633pr/6YKGs4sFgIAL6SLmsyXc8cAxhEOyU9e+ntP+7FIeMlXWYmqme9YXH31tVU/jRnImWtUUfr3p1XELghNU8MtEdB1j7IcAQETXArBtLtVywbcC+AvLzi8B+BvG2DdqHUQiHm5HBBR1hk899CKGEmEwxuvyVJhFLIdeumQgXVpdqEs3efnalWJ9oU2AozGnCxp0kzlhhZJl0uiPhfFv9m3zmE4qhbjSYGw2N4UQ/r8Du/AH334NmskQs/wKDMCvHrwEO4bikCXC7QcmcM+RkzCtrmI8goZw27+YwEgygscmZ3H3t15FSCYMxcM4OZeFbjAkoyHY1UzrddyatkoAOJYZyx+imVzQX8gUQUR401DMaZvo3acd0bSQ1SGBryZ008SFdAlEwD1HTmI0GUZ/jDvgvY1t3ljOwwSgWGYjZgJpzUBIM7DVqrpaT4NPhmWrTy85EWDnlovY3YA93i7TLBF3IBc0A/ccOQkAgbOjm6m6CnRe22523ILeIajg/zCArxBRElxOpgF8iIgSqJLUxRh7HsDVjQzGZKyiwxEAq4F6bWTLdGGbRyKKhOsnhivqYiddKeruJgeJiIxoSHY++7N/8k/IlnRuq7YiRDTDREnT8TNXX1x1DES8OJUkkTMeRZKc320h/8SJOdz//VM4MZupMIPcum97Rc2gGyaG8Gf/fBp3/cPLzsN/85XjFSUsrnvTAJ6cWsTf3H0E6YKGRER2BGq93rbAas1ueolHEPm5fVYKGhjj3czmMiWcWy5Ytd4lTC8VHLPMaxfSSEYUJ0qIjLJ5JiLzzN2FnIqIIqMvFlrV2EZnXNDaCU5EAIzKxCxgdZcpt3B09weAaxJrJBno/idOWUJfstoG8tIP9xw5iSu3DQQSgEG6Y/n5Kty+hPlMCR8/fHxdfQnrUZ9K0FmCNmJ5GsBbiajfeu22CfxNKwdk1xYHeIIPAPzKwd3426NnkSvZbfK4ME0XVKwUDYz3RSsicNxdfRrFW6WRiAtRzWToi4W4Filz4S5bNYJky05ej8cmZ3HXN17xNYOcWy44zke/pbbdoMMuYbGQK+GHZ5YxmgxjJBnBzEoRBdVARJGRioYC9Un1anYEfxt6RKaKRjb2eZd0Azmr4bNtllF1E0u58irL3h8BACNIxN+xE/OAysY2l/32w74Ntd3vpAsazi0XoUj+pghv34WwLGG8L4JsqXqhMi851YBi9XlwR2IZJsOH/vIoLh1L4hM37a0pjL15IvXGDQB3PzKJpbwGWSIosgTGgKW8hrsfmWyr4HevMtIFDbphOi00gdbXpxJ0lkC2CSLqJ6I/BPAdAN8hoj+wJ4FWQuCaXthqllEyTFwymsL73jKOXzlwCX8QAIQUXvgqpCj4sT0jWMyp+NEcT2S66fItVYU+WcI6JEuIWZEtfbEQhhJhjKYi2NofQzQkOVKmrDgSoiEZI8kIBhNh9EV5k4doiHc2CpqIYwvaTJGbQRSJfzZd0BGSCfc+PlWxXTysOGaabElHpqg776ULvIRFxupHEFF41pDd33QkGYHJ+GqIZzzrq2oM2bXbp+ayvDl9lXGPpniUlCOQrTh/WwtngGOWMa0yGt59MXC/zEgibGXqmr7jmhhJONFSPMmMd8wKycRbAFomJ4Cbiezr475+2wfjUKweC3vH+zAxmoQiSw0JrkSY52nYNerd5yMTcGo+h08/9JLTKtGP2w9MQDNYxbhNy1756oUMryqrG864AfD6U05WLTmJYVPzwQIDqmFnm++/+wgO3fdUxbhtRWPWKpeSiMiYy6qYyxSr3jtrPaagswQ19XwFPBrn56zXHwRvzvKzrR5QudkGg26Ua2uvqszXH8M12wfwyEszGEnyJhZF3cQ/vjKLfTuHcOCyUce80ohWfumWvtXF0BKhqk3MG8FeQtv9bAE+uXgbg/gttQ2r2fhLb6w4vg4J5UbxknXtiroBxhgUmTAQD2E0GalaYygZljF5IYt6TC8XsfOT/wAAiCk8e9XbfCVInfeL+mNWhzMVugm8+EYaALCtP4J7H5/Cb3/9RaQiCsIyoWD5OXgGLBBVJMxlSgjLvFyCBIbTC2XTQ1whpzjf7Qcm8Kt/fayi9248LK/qmua1pY/38UqjXNsn3yAA25xnmAwhmfCxv30OSwXdiTS7+cpxfP5WHgfhrX2kG6ZjPrR9Dws5FbqRrnndTKukRi3zUC2fgF9T+I8dPo7PWeYj78rPToDMlYyG6lN5r61wEHcvQQX/JYyxf+16/TtE9FzLByNL1gPHBeOukQTef9VWR4D/7Nu34d9cu92JDT9031OIhWXnhg1bjaG/+oPX8f6rLmpqDNUqVLaiGqe99A/LEnSjnAjkbQziV0rCaYzCyiYZW9TKVu0YZjBEw7LzsLobyvjRjM22oAN9Ed4W0d06MQipqILXZlZW2eunV0qYy6nYM5bCQq6Eom7y7msgmFbDjqFEGIosQTN4B6mSZx95nUHO89XO15+bXtVwPa8a+Ppz01ULzr1yfgVPTumQJS7cq/UKloic72w+XcSKK7DAMBm+9tx5AMcqhL99zCs/8y3eKtFlRjRNVtFbYNdwHCfnciCr8CDvBMbLTvsJUD8B+/HDxzGcCCOrGtg+GMfZxRyW85rj7GYmsJzX8NmHX8HBvWO+isZwIgJF0pyOeI0iHMTdTVDBXyCi/YyxJwCAiN4FoNDqwUgEXDKadITtB67citv+8pmqmkwQ59kNE0NOieUgERJBauM3iz2ppKIKFnIqX/YzrGoM4ldKwm7I4WuOsUwvkkTYMRjDI7/xY4HGk61V5tIDWbMNA4+kCpL452WloMEnAAsAL9Jmm7BkiZyuXrp1jWZWilBknj2sm/7HzlizwdePn/f9+9ePn8fnb+W/ewWT7XPhHcYkMMYHajt4NavHgGaaCEkSRlMRZ8Xh9hkzBjz0/IxzHDdhRUJBNZxVLbO+t7BStrh+8n1vrtDOTcYgAbh4MO4bneU9D8NkWMpryJR07B5NYjZTxPRyEYpVZ8geLzMZTlnjb7bnRK2VhnAQdzdB4w9/BcAfE9FpIjoN4I8A3N7qwdjN1sdSUdxyzcU4fOycY3e0NR23nXD7YNyJMQfKzjMC145OL2Rxz5GTODWfrboPPw7uHcMDt12P73/iRjxw2/Ut01AO7h3DXTdfgV0jSfRH+YqiP87NSO6s0oN7x3DLNRdjLsObzsxlSiDwaBcnicuFYZl2Lh6IroqKaimuA68EzG1wE0R7dPfxVQ3eDctkJkoGN3UFiZitlg3tfv/sUr4iC9zbH8DdX/iigSjCTvE3YGt/BHINs2G1YnN7xlIYSYWdpumKRBhJhbFnLOVsc3DvGD53y1W4evsgxvuiCMkStrvCZwGsMgu6z2MuU+I9ik3mTBTA6qgoN15fRBCbvtcv4H22vM8mIBzE3UTQqJ7jAK4ioj7rdZqIPgrg+VYOxt1s/dB9T9VdKno1Y6/Tz+0AHU1Fu2K5GaQK4mOTszh87FxFg5NMSfd9eCXiZheAx9SPuSIx6tl+vZUt3TgaqQ+yxKN8Lvmtb9asqNkM3j6+tqnDrmZp2vauNeLVcu1r4S5fbPcXTkVDSI2HMJcpIq/y3s9jqShOzed8r1+1SSGoGdGbhTybKVb8vZZZ0O5J7O6DbNdZcq803HWGmlnl1jPlBGknKugcQU09ALjAd738jwC+0MrBuDtw2an8brxLxYN7x3DL9LKTXWkyhpFEyNGO3NpjtX20giAJN40k5fg9VGEJvmaSkISKRvH2gxXEufaOnYN48tSS7xi8Qt/9+uYreUZ1PCQhU81242E4Hqq7DWMMfTEFsxkVqaiCiCLh3HLRaa1oJ9WFJfg2Y7lh16B1LAUL+dWhm8Px8u3uFUx9UQXLBd1ZYdimLXeP57Ai47M/e6Vz/X7jwWP42nPnV10r+/p4aUbA1hOg3r/LxFuQuiuGDsZDWMipIHBTqCJJGIyH8Imb9laMrRFlqJ4pp50mU8HaaUjwewieDRMQdweu+SxP5SciR5B7l4pezfjkbBZLeR3xsIa+WGiV9ui3j7USRMA2GuHg91BpPoKOAOiMfCMvAjnXSEI8JFU05ZZQ6TTemgrjfEb1jVrZNhjH5EzGt6ib+72YQviDn3sbAC5I0z6Nv2WJn8fO4SQOXTvkJLPtGUvizEIeJcNAWCKMpiJIRUN4bWalYiK8YdcgHrj9nQCAP/i5q/ErXz2Koqt3QFQh/MHPlfMJvYLpzVv7K6J6vP2F/QQXvw7H8NDzM77Xx49GBWw9Aer9+66RBOayJSgyVUxYH3n37ooEwbUK4SB+AVHjv3tZi+BveV1JonLHqy1Wjf0zC3kr0oJXQ3SH5HmFmzf93609+mnFrSCIgA2yjTeBJlfSoOrMmbhMK5on6rLnFjXeIu/sUgFvrBQx3heucK5569X4ZdmOpiIViU6JsIyVoo7RVKRqaKC9KlvIltyJsU7o5UBMgWbCqXFzUX8EH/rLozXNQhf1R31j/wfiYbzvLeNOfZ9YiEdupWJhTCQjyJR0x4nv7or2vreMu4Q4r7PjFUKtEEyfv/UaX0duK6k3zuenl/HSGyvOuVabsNbaqc3N7Qcm8LHDx3FuueBMesmIsipktlHWWq6iFeUuOl0yYz2o12w9A38BTwBirR6Mu8kF4ASr8FR7Wj0Qr2bsTf/3ao/tWG4GiV6ot413RZAv6VjMa5CsxCW3qaqkG+XQThd2KOHfP/9Np9+AY7NmgGaUs2xnVgqYz5SgmTzLNqRIvJetYSKXNRCusjLxjvPcUsER+M44GLBU0LFrJIEdIRmnF3KYvFA7+YjAE6WGExGcXsjih6cXnYzk2UwRh4+dwy3XXOx8jwmrmJ1qmBiIhXBqnn9mLBV27UPFaDKMHUPcyXj42LnApRZ6Cb+aQg89P4M7b9yNO94bvKBcM1jpNlUL9jXKWmP/W5E7sFnyD+o1YknV+nurMV3G0vlsCbJEiFkZmMDqgmB+y013+r9NKzUdL0GWvPW2uffxKWiGgYUsTxozTOaEW5lWzDgxA6rp73B1O2K9oY6rbPWAUwrAmU/sz1rx5JrB8OqFjFMbv1rooH1cIiCq8JVIUePOz2qOTzchmUe3EIB0QcdIMlrVIf/NF85jMBEBA/DGShFxV/5Gpsg/U2sfc5ki7njwWfTFQhtKi3PXFAL4iks3Tdz/xKnAxeSa4d7Hp9AXC2G8v6z/rTVwwm9lPJ8N/r21Indgs+QfNFZOss0wBiekrKSbACuXCwBWa9LNhKG1miBjqLfNidkMZtMl5FVuirLLHhCRU3IgpMhVRlAfryZW0syK+jOaaaLoasBil2CwM0tPXOA+fW/ooF30jIfaM6eVJFDuzFULmXiUjmGVcAD8HfK6YeLEXNYJHcypOhZyKtJWSKn3M97X6YKGhZyKnKo3FNbbCyUHcqoBbxCRRGhvWC9W3wvA2gMnvPvMFDXMZ1TkVSPQ99aKMbXjvLqRrhL8Fw3EMJaKYqXAa9OPpMIV8ct+zqO7br7C+cxYKrqmLkvNEGQM9bbJq4bTs9Zt7XKvgAqWmSYiS4gqjX1tUc+NzFAZxhmSJV6jyEVJN6GZZkVmqTc2O6pIvAG5FTeuuCWQuzJmFez+t0D5XG1/htshfyFTQkiSnDpF9upiPlvy/Yz3tb1dVJF9a/v4US9OvZ00MuHYNYXcmIy/307aEafv3edcpgQQD0cN8r21YkybJf9gLc7dlpOKKo6Jxn7w6sUBd0PkQJAx1NpG1a1GJ84/HMZQURZBlspVQ2UqNzivl0TrvZFXUeXzjJUjfAC+cvn44eM4t1SAbvJ4ccMEr58Dnkjm/mw9CprhzA0mAyZn0lbIIcNwotIhnwzLTp0iIoAYUGK80FsqqmAuq6IvpqwKCbVXj4TVq8cTs5kKh3DDUVFovSOwURvzh/fvwj1HTkI3TScXwWT8/XbSjjh97z6LugHJ08y+lvbdijFtlvyDrtL4J2cyjobTDdr8eiFLktNsvJaSbJhAUTe4Hb2Fx1dkqhDaNkRYlSnLAIDKZh4nqsfjca53LhX7c+1DIkLMqjdkZy3HQxJWinrZfGRNSHYI6K6RJO68cTd2Dicdp/6dN+7GrpFk1dXjQq6ETFGvqtEHWfLbtfOffX0JMysFPPv6Ej5++PiaVgV+lVlrabl3vPdS3HnjbsRCMnSTj5E7dttn3wfas9r27jMRVjCcCDvlu4Ha2ncrxrRZ5E5XafyKRKs0nI12wW3cmqLk0t692KYfbymBVgbT2s5zd+VPZh/L8rvY41WsSqcGGAwrszXkcsCfW8pj0aonLxGg6izQUCUCLh6Igwg4u5gHs95TddOp/OndT0k38cZKkZePYCZeOp9BTuUVJW+YGKq5elzMaRiMh6pq9EGc9n618xeyKn71r49hKBFeVfHTHWrZSP2pejbmK7cN4IqL+p19Aqi6kmmUWiuadjyf7n0GXfVX+3wrxrBRoWaKbbWLgR172b/4+P1O6YFG+pt2O+4HKBmWsWD1w42FZEzNZSuSqHqZfitBa73uqojVm8Ft57YTyLYNRAEiXwHMGMNQIlyRw6AQkFa5eSGiSDBNEyC+f2ZlDe8dTzkNWOymMXYfZN0woVkDectFfTi3nMeSTwaxBDgd2lJRpaK7ll2iwT3hzGeLyJUM38gWt2nIbtBzIV2CTACskuTJiOKUYG4E775twbueGrD93FQLx25nzP1a9r2euQBE9AxjbF9Dn+lGwc8Yw0qh+ZKw3Yb3AbL74W4b5MW3Gi1vLChjC6RqhGQeX64ZDFv6IhhJRlDQDLy+mIdpMiiyxHsiaKZjPnNPJu56RrIEjCYjCCsy7rr5Ctz+1WeguqKhbAjAWy7ur1hBeWsfRUN2SC3DnrEkHv7oAQD+gnw2ozp5DV7h650oTlzIoGj5NCKKdQzGsHs0Ebhqq43fJNRNSlk7J6a17Hu9J8xmBH9X2fhtNoIX3R2ZcceDz0LVDcduy3u48kYiQui3Fm9bXdnW2AEs5dRyxUrGTVV2lqAt9Hn2cfmxcJreWA7lTLHcLS0ZlqpmN7o/64dp8l7OuskwOZNx/ALeyqyzGRV9URmjKf9uY15fRMlVyY+s5kMSwSnB3AhrDW1sdzhso/6Q9dp3O8fVKrpO8HciFr/VeEMBvXHnzAxm9xY0jncB626w7m54Ys8Qdg6DF78QSZ3x+PjXF/M49vpS9X4GAbzaqmFWHMN2LLvrT715PAUCkC0ayBTLZbDdwtcv/BDg81lRM1DSjaYrqK4ltHE9wmHbGXO/ln33Qi5AVwl+w2QbwovunfG9cefuR8mroQqqQ7T6epmsvm/E9xpbM0RIqp8X4f24naJQ0s2KaCy3ps+sXsGew/miSHA0Qu+94+2lDFQKX29yoDuVws7XMBgwmgzXPEc/1pIguR5abztj7tey717IBWib4Cei7UT0XSJ6mYheIqI7633msvFUSxufdArvjD+ailQ0GLeFgB2aKAgGY6sFaEmvfQEZmFMfPySXG8+DyHKA8h/J2b5yMvEvrU8Y74860VgRRUY0xH/s7V+ZySASkhGSqu2jjETkaITee8eOYbd7KXuFrzf8MBKSKyYhAs/5cIeyBmUtoY3rofW2M3N/LfvuhooC9WhnOKcO4D8xxo4RUQrAM0T0bcbYy208ZlfgDQVMRUMYSRlO82ouiBjCcmWlzY0wB/RHFd42cA0noxA3q9hs64/g2l1DTvljiYCITOiPh7GQU32botvY9efjMRlb+6JOCWseJy47UT2xsOxE9egmzxGIWQ5Yd7tHiXhHrlQ0hOFECHNZzUme0i2H8GBcwcUDXOtLFzQMJ8LIqQZmMyX0RWUs5DTHcSwT9y+4NUL3vdMXC6GkG8ir1Rufu8MP9999BHISFdFKI8kwsqXV0UVBaDa0MUg47FojX9pZ838t++6FXgTrFtVDRF8H8EeMsW9X22bfvn3s6NGj6zKedlLPq++uqOjOtrQTby7/1CPIu7JagfLCQCJX43WLkEw1hV8tJPCV1muzWd7YPMBnIoqEV//b+2pGfdgZkLOZIkyrDSBj3KzhF7r6M2/bWrOOvRv7uDMrRegGQ8mo3J+tYRMRLuqP+j549SJW6kVi2duXNAPpou7UxumLytg2mPDdp31M3WB4Y6UACQQGnrQ21se1aQBrigjplkices9AN4SKbhS6NqqHiHYCuBrAD9bjeJ2m3hK5Xrblr/zYBBfwKP8A/MuyzQqOcANvvbhzOM7jwwlO8hQAnrWaDOPN46sLrRKAr/z7a/HwRw/gy7+4D3vHU85kJMH/5iAAv3bwEgC1l7T2Ndg5FIfBeAXOrf0RbB2IIR6SnPHJEjUk9IGyGcHuyat4bCm8rAPhzht3V+2bXG857v0Odw7FMRgPQZaoYvv/9q/eiuc/8xP40X//SWztj+LigUo7rtu8YR9TkfmERBI3Fe0aSTj3x1ozR7vFzFDvPHoh8mUj03aNn4iSAL4H4PcYY3/n8/fbANwGADt27Hj7mTNn2jqeXuGLj77mtJRMhLmteKVoQCYCkd2LliEkAZeN960yK9RKdqm1/PRu4018+vD+XRXlAJrZ51qXvV6NX5IIql4udCdLFKhsQaPjqrd9EG271deiFefVCfbffQQDsVBF1NVGy99ZL7ougYuIQgC+AeBbjLE/rLf9RjH1tIPHJmfxscPHuf3c6ngUlggXDcSqCvqNim0mUHUDCzmVv8mAkVQYIVnumLlAmC+C0y0mqY1AM4K/bc5d4lP5lwG8EkToC2pzcO8YPnfLVV2vya0HbueZbqShGgxhRcLO4WRHr0kvOPW6hc1SBbNbaZvGT0T7AXwfwAsoJ0b+FmPsm9U+IzR+QTU2Qx/UzUYvmKR6ga4z9TSKEPwCP4QJRSCoTtdG9QgEa0FEgAgErUUIfkHX0wu1TwSCXkIIfkHX0wu1TwSCXkIIfkHX0y1JSQLBRqGrWi8K1sZGjXwRYZICQWsRgn+D4I58cdc/t3sX9zqboQ+qQLBeCFPPBkFEvggEgqAIwb9BEJEvAoEgKELwbxBE5ItAIAiKEPwbBBH5IhAIgiIE/wZhrXXcBQLB5kFE9WwgROSLQCAIgtD4BQKBYJMhBL9AIBBsMoTgFwgEgk2GEPwCgUCwyRCCXyAQCDYZQvALBALBJkMIfoFAINhkCMEvEAgEmwwh+AUCgWCTIQS/QCAQbDKE4BcIBIJNRtsEPxF9hYhmiejFdh1DIBAIBI3TTo3/zwHc1Mb9CwQCgaAJ2ib4GWOPA1hs1/4FAoFA0Bwdt/ET0W1EdJSIjs7NzXV6OAKBQLDh6bjgZ4zdxxjbxxjbNzo62unhCAQCwYan44JfIBAIBOuLEPwCgUCwyWhnOOcDAJ4EcBkRTRPRh9p1LIFAIBAEp209dxljh9q1b4FAIBA0jzD1CAQCwSZDCH6BQCDYZAjBLxAIBJsMIfgFAoFgkyEEv0AgEGwyhOAXCASCTYYQ/AKBQLDJEIJfIBAINhlC8AsEAsEmQwh+gUAg2GQIwS8QCASbDCH4BQKBYJMhBL9AIBBsMoTgFwgEgk2GEPwCgUCwyRCCXyAQCDYZQvALBALBJkMIfoFAINhkCMEvEAgEmwwh+AUCgWCTIQS/QCAQbDKE4BcIBIJNhhD8AoFAsMlQ2rlzIroJwD0AZAD3M8Y+287jbTYem5zFvY9P4exSHtsH47j9wAQO7h3ruWO0gyDj9m5zw8QQnpxarPq6W869V78TQfdAjLH27JhIBvAagH8JYBrA0wAOMcZervaZffv2saNHj7ZlPBuNxyZn8emHXkJIJsRCMgqaAc1guOvmK1omBNbjGO0gyLi92yzkSpjNqBhNhjGSjKx63S3n3qvfiaB9ENEzjLF9jXymnaae6wCcZIxNMcZUAA8C+Ok2Hm9Tce/jUwjJhHhYARH/PyQT7n18qqeO0Q6CjNu7TbqgQyIgU9R9X3fLuffqdyLoLtop+C8GcNb1etp6rwIiuo2IjhLR0bm5uTYOZ2NxdimPWEiueC8WkjG9lO+pY7SDIOP2bqMaJiTi//u99ttHJ+jV70TQXXTcucsYu48xto8xtm90dLTTw+kZtg/GUdCMivcKmoFtg/GeOkY7CDJu7zZhWYLJ+P9+r/320Ql69TsRdBftFPznAGx3vd5mvSdoAbcfmIBmMORVHYzx/zWD4fYDEz11jHYQZNzebfpiCkwGpKKK7+tuOfde/U4E3UU7nbsKuHP3PeAC/2kAP88Ye6naZ4RztzHs6I7ppTy2tTmqp53HaAdBxu3dxo7iqfa6W869V78TQXtoxrnbNsEPAET0kwC+AB7O+RXG2O/V2l4IfoFAIGiMZgR/W+P4GWPfBPDNdh5DIBAIBI3RceeuQCAQCNYXIfgFAoFgkyEEv0AgEGwyhOAXCASCTUZbo3oahYjmAJzp9DhqMAJgvtODCIAYZ2sR42wtYpyt5TLGWKqRD7Q1qqdRGGNdnbpLREcbDZvqBGKcrUWMs7WIcbYWImo4Bl6YegQCgWCTIQS/QCAQbDKE4G+M+zo9gICIcbYWMc7WIsbZWhoeZ1c5dwUCgUDQfoTGLxAIBJsMIfgFAoFgkyEEfxWI6CtENEtEL7reGyKibxPRCev/wQ6PcTsRfZeIXiail4jozm4cpzWmKBH9kIiOW2P9Hev9XUT0AyI6SUT/h4jCXTBWmYieJaJvdOsYAYCIThPRC0T0nB3S16Xf/QARHSaiSSJ6hYhu6LZxEtFl1nW0f9JE9NFuG6c11t+wnqEXiegB69lq6B4Vgr86fw7gJs97nwTwHcbYHgDfsV53Eh3Af2KMXQ7gegC/RkSXo/vGCQAlADcyxq4C8DYANxHR9QDuBvB5xthuAEsAPtS5ITrcCeAV1+tuHKPNuxljb3PFm3fjd38PgEcYY3sBXAV+bbtqnIyxV63r+DYAbweQB/A1dNk4iehiAHcA2McYewt4yftb0eg9yhgTP1V+AOwE8KLr9asAtlq/bwXwaqfH6Bnv1wH8yx4YZxzAMQDvAM+MVKz3bwDwrQ6PbRv4A34jgG8AoG4bo2uspwGMeN7rqu8eQD+AU7ACSbp1nJ6x/TiAf+rGcaLcy3wIPAH3GwB+otF7VGj8jbGFMXbe+n0GwJZODsYNEe0EcDWAH6BLx2mZUJ4DMAvg2wB+BGCZMaZbm0yD39id5AsA/jMAu8v6MLpvjDYMwD8S0TNEdJv1Xrd997sAzAH4M8t8dj8RJdB943RzK4AHrN+7apyMsXMAPgfgdQDnAawAeAYN3qNC8DcJ41NrV8TCElESwP8F8FHGWNr9t24aJ2PMYHwpvQ3AdQD2dnZElRDRBwDMMsae6fRYArKfMXYNgPeBm/kOuP/YJd+9AuAaAH/KGLsaQA4ec0mXjBMAYNnGbwbwt96/dcM4LR/DT4NPqBcBSGC1SbouQvA3xgUi2goA1v+zHR4PiCgELvT/N2Ps76y3u26cbhhjywC+C74kHbD6MwN8QjjXqXEBeBeAm4noNIAHwc0996C7xuhgaX9gjM2C26OvQ/d999MAphljP7BeHwafCLptnDbvA3CMMXbBet1t43wvgFOMsTnGmAbg78Dv24buUSH4G+MhAL9k/f5L4Db1jkFEBODLAF5hjP2h609dNU4AIKJRIhqwfo+B+yJeAZ8AbrE26+hYGWO/yRjbxhjbCb7cP8IY+3foojHaEFGCiFL27+B26RfRZd89Y2wGwFkiusx66z0AXkaXjdPFIZTNPED3jfN1ANcTUdx6/u3r2dg92mlHSrf+gH/55wFo4FrLh8Dtvd8BcALAowCGOjzG/eBLz+cBPGf9/GS3jdMa65UAnrXG+iKAT1vvTwD4IYCT4MvrSKfHao3rIIBvdOsYrTEdt35eAvBfrPe78bt/G4Cj1nf//wAMduk4EwAWAPS73uvGcf4OgEnrOforAJFG71FRskEgEAg2GcLUIxAIBJsMIfgFAoFgkyEEv0AgEGwyhOAXCASCTYYQ/AKBQLDJEIJfIABARP+KiBgRdVU2sUDQDoTgFwg4hwA8Yf0vEGxohOAXbHqsWkf7wZP0brXek4joT6wa8t8mom8S0S3W395ORN+ziqN9y07pFwh6BSH4BQJe9OoRxthrABaI6O0Afha8LPflAD4IXlfIro30JQC3MMbeDuArAH6vE4MWCJpFqb+JQLDhOQRejA3gxdkOgT8bf8sYMwHMENF3rb9fBuAtAL7NS6VABi/tIRD0DELwCzY1RDQEXoXzrUTEwAU5A6926fsRAC8xxm5YpyEKBC1HmHoEm51bAPwVY+xNjLGdjLHt4B2jFgH8a8vWvwW8aBvAOzKNEpFj+iGiKzoxcIGgWYTgF2x2DmG1dv9/AYyDV2V9GcBXwVtFrjDGVPDJ4m4iOg5eEfWd6zZagaAFiOqcAkEViCjJGMsS0TB4ydt3MV5fXiDoaYSNXyCozjes5jFhAL8rhL5goyA0foFAINhkCBu/QCAQbDKE4BcIBIJNhhD8AoFAsMkQgl8gEAg2GULwCwQCwSbj/wfn/9YPutUutgAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.regplot(y='LogFare', x='Age', data=df);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "7cf9b21a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.boxplot(y='LogFare', x='Pclass', hue='Sex', data=df);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "154c1460",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Fit a linear model to these data to explain our synthetic variable `LogFare` as a function of `Age`, `Pclass` and `Sex`.\n",
+    "\n",
+    "Treat `Pclass` and `Sex` as factors.\n",
+    "\n",
+    "Print an ANOVA table."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ad89dec",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "39f58924",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model = smf.ols('LogFare ~ Age * C(Pclass) * C(Sex)', df).fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "bc136eb5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Pclass)</th>\n",
+       "      <td>318.183365</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>429.045083</td>\n",
+       "      <td>1.856872e-122</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>C(Sex)</th>\n",
+       "      <td>12.597516</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>33.973508</td>\n",
+       "      <td>8.516312e-09</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>C(Pclass):C(Sex)</th>\n",
+       "      <td>3.489752</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>4.705654</td>\n",
+       "      <td>9.331214e-03</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>12.274132</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>33.101391</td>\n",
+       "      <td>1.306440e-08</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Pclass)</th>\n",
+       "      <td>0.296834</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>0.400257</td>\n",
+       "      <td>6.703004e-01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Sex)</th>\n",
+       "      <td>1.421046</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>3.832335</td>\n",
+       "      <td>5.066866e-02</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Pclass):C(Sex)</th>\n",
+       "      <td>1.335653</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>1.801023</td>\n",
+       "      <td>1.658921e-01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>260.304489</td>\n",
+       "      <td>702.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                          sum_sq     df           F         PR(>F)\n",
+       "C(Pclass)             318.183365    2.0  429.045083  1.856872e-122\n",
+       "C(Sex)                 12.597516    1.0   33.973508   8.516312e-09\n",
+       "C(Pclass):C(Sex)        3.489752    2.0    4.705654   9.331214e-03\n",
+       "Age                    12.274132    1.0   33.101391   1.306440e-08\n",
+       "Age:C(Pclass)           0.296834    2.0    0.400257   6.703004e-01\n",
+       "Age:C(Sex)              1.421046    1.0    3.832335   5.066866e-02\n",
+       "Age:C(Pclass):C(Sex)    1.335653    2.0    1.801023   1.658921e-01\n",
+       "Residual              260.304489  702.0         NaN            NaN"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0e98e30e",
+   "metadata": {},
+   "source": [
+    "We can also have a look at the summary tables. This reveals that the residuals are not normally distributed."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "8d3ea24c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<caption>OLS Regression Results</caption>\n",
+       "<tr>\n",
+       "  <th>Dep. Variable:</th>         <td>LogFare</td>     <th>  R-squared:         </th> <td>   0.598</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.591</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   94.76</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Date:</th>             <td>Tue, 28 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>9.94e-131</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time:</th>                 <td>17:16:29</td>     <th>  Log-Likelihood:    </th> <td> -652.90</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>No. Observations:</th>      <td>   714</td>      <th>  AIC:               </th> <td>   1330.</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Residuals:</th>          <td>   702</td>      <th>  BIC:               </th> <td>   1385.</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Model:</th>              <td>    11</td>      <th>                     </th>     <td> </td>    \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "                  <td></td>                     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th>                         <td>    4.7381</td> <td>    0.181</td> <td>   26.121</td> <td> 0.000</td> <td>    4.382</td> <td>    5.094</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.2]</th>                    <td>   -1.4605</td> <td>    0.251</td> <td>   -5.810</td> <td> 0.000</td> <td>   -1.954</td> <td>   -0.967</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.3]</th>                    <td>   -2.0166</td> <td>    0.217</td> <td>   -9.277</td> <td> 0.000</td> <td>   -2.443</td> <td>   -1.590</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Sex)[T.male]</th>                    <td>   -0.3766</td> <td>    0.253</td> <td>   -1.487</td> <td> 0.137</td> <td>   -0.874</td> <td>    0.121</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.2]:C(Sex)[T.male]</th>     <td>    0.2608</td> <td>    0.338</td> <td>    0.771</td> <td> 0.441</td> <td>   -0.404</td> <td>    0.925</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.3]:C(Sex)[T.male]</th>     <td>    0.4762</td> <td>    0.295</td> <td>    1.615</td> <td> 0.107</td> <td>   -0.103</td> <td>    1.055</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age</th>                               <td>   -0.0071</td> <td>    0.005</td> <td>   -1.447</td> <td> 0.148</td> <td>   -0.017</td> <td>    0.003</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age:C(Pclass)[T.2]</th>                <td>   -0.0012</td> <td>    0.007</td> <td>   -0.166</td> <td> 0.868</td> <td>   -0.016</td> <td>    0.013</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age:C(Pclass)[T.3]</th>                <td>    0.0059</td> <td>    0.007</td> <td>    0.867</td> <td> 0.386</td> <td>   -0.007</td> <td>    0.019</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age:C(Sex)[T.male]</th>                <td>   -0.0044</td> <td>    0.006</td> <td>   -0.696</td> <td> 0.487</td> <td>   -0.017</td> <td>    0.008</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age:C(Pclass)[T.2]:C(Sex)[T.male]</th> <td>    0.0058</td> <td>    0.009</td> <td>    0.617</td> <td> 0.537</td> <td>   -0.013</td> <td>    0.024</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age:C(Pclass)[T.3]:C(Sex)[T.male]</th> <td>   -0.0106</td> <td>    0.009</td> <td>   -1.245</td> <td> 0.214</td> <td>   -0.027</td> <td>    0.006</td>\n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "  <th>Omnibus:</th>       <td>185.637</td> <th>  Durbin-Watson:     </th> <td>   1.920</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>2122.430</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Skew:</th>          <td>-0.817</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Kurtosis:</th>      <td>11.287</td>  <th>  Cond. No.          </th> <td>1.08e+03</td>\n",
+       "</tr>\n",
+       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.08e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary.Summary'>\n",
+       "\"\"\"\n",
+       "                            OLS Regression Results                            \n",
+       "==============================================================================\n",
+       "Dep. Variable:                LogFare   R-squared:                       0.598\n",
+       "Model:                            OLS   Adj. R-squared:                  0.591\n",
+       "Method:                 Least Squares   F-statistic:                     94.76\n",
+       "Date:                Tue, 28 Sep 2021   Prob (F-statistic):          9.94e-131\n",
+       "Time:                        17:16:29   Log-Likelihood:                -652.90\n",
+       "No. Observations:                 714   AIC:                             1330.\n",
+       "Df Residuals:                     702   BIC:                             1385.\n",
+       "Df Model:                          11                                         \n",
+       "Covariance Type:            nonrobust                                         \n",
+       "=====================================================================================================\n",
+       "                                        coef    std err          t      P>|t|      [0.025      0.975]\n",
+       "-----------------------------------------------------------------------------------------------------\n",
+       "Intercept                             4.7381      0.181     26.121      0.000       4.382       5.094\n",
+       "C(Pclass)[T.2]                       -1.4605      0.251     -5.810      0.000      -1.954      -0.967\n",
+       "C(Pclass)[T.3]                       -2.0166      0.217     -9.277      0.000      -2.443      -1.590\n",
+       "C(Sex)[T.male]                       -0.3766      0.253     -1.487      0.137      -0.874       0.121\n",
+       "C(Pclass)[T.2]:C(Sex)[T.male]         0.2608      0.338      0.771      0.441      -0.404       0.925\n",
+       "C(Pclass)[T.3]:C(Sex)[T.male]         0.4762      0.295      1.615      0.107      -0.103       1.055\n",
+       "Age                                  -0.0071      0.005     -1.447      0.148      -0.017       0.003\n",
+       "Age:C(Pclass)[T.2]                   -0.0012      0.007     -0.166      0.868      -0.016       0.013\n",
+       "Age:C(Pclass)[T.3]                    0.0059      0.007      0.867      0.386      -0.007       0.019\n",
+       "Age:C(Sex)[T.male]                   -0.0044      0.006     -0.696      0.487      -0.017       0.008\n",
+       "Age:C(Pclass)[T.2]:C(Sex)[T.male]     0.0058      0.009      0.617      0.537      -0.013       0.024\n",
+       "Age:C(Pclass)[T.3]:C(Sex)[T.male]    -0.0106      0.009     -1.245      0.214      -0.027       0.006\n",
+       "==============================================================================\n",
+       "Omnibus:                      185.637   Durbin-Watson:                   1.920\n",
+       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2122.430\n",
+       "Skew:                          -0.817   Prob(JB):                         0.00\n",
+       "Kurtosis:                      11.287   Cond. No.                     1.08e+03\n",
+       "==============================================================================\n",
+       "\n",
+       "Notes:\n",
+       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
+       "[2] The condition number is large, 1.08e+03. This might indicate that there are\n",
+       "strong multicollinearity or other numerical problems.\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ecf3bcd9",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Let us ignore the not-normal residuals and play with post-hoc tests instead.\n",
+    "\n",
+    "Split the ANOVA for levels of `Pclass` and `Sex`, perform all pairwise comparisons if it make sense, and correct for multiple comparisons.\n",
+    "\n",
+    "We are not interested in the significance of the slope of `Age` for the different levels of the factors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7a417d76",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "b81407bd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class1_model = smf.ols(data=df, formula='Fare ~ Age * C(Sex)', subset=df['Pclass']==1).fit()\n",
+    "class2_model = smf.ols(data=df, formula='Fare ~ Age * C(Sex)', subset=df['Pclass']==2).fit()\n",
+    "class3_model = smf.ols(data=df, formula='Fare ~ Age * C(Sex)', subset=df['Pclass']==3).fit()\n",
+    "female_model = smf.ols(data=df, formula='Fare ~ Age * C(Pclass)', subset=df['Sex']=='female').fit()\n",
+    "male_model = smf.ols(data=df, formula='Fare ~ Age * C(Pclass)', subset=df['Sex']=='male').fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "cafed8b7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((186, 4), (173, 4), (355, 4))"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class1_model.model.exog.shape, class2_model.model.exog.shape, class3_model.model.exog.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "7a8fb3ff",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Sex)</th>\n",
+       "      <td>4.043594e+04</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>6.627354</td>\n",
+       "      <td>0.010838</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>3.572113e+04</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>5.854608</td>\n",
+       "      <td>0.016520</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Sex)</th>\n",
+       "      <td>8.202655e+02</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.134440</td>\n",
+       "      <td>0.714299</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>1.110449e+06</td>\n",
+       "      <td>182.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                  sum_sq     df         F    PR(>F)\n",
+       "C(Sex)      4.043594e+04    1.0  6.627354  0.010838\n",
+       "Age         3.572113e+04    1.0  5.854608  0.016520\n",
+       "Age:C(Sex)  8.202655e+02    1.0  0.134440  0.714299\n",
+       "Residual    1.110449e+06  182.0       NaN       NaN"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(class1_model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "c5285b28",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Sex)</th>\n",
+       "      <td>9.143118</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.053774</td>\n",
+       "      <td>0.816901</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>1140.725330</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>6.709083</td>\n",
+       "      <td>0.010430</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Sex)</th>\n",
+       "      <td>7.201063</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.042352</td>\n",
+       "      <td>0.837197</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>28734.566043</td>\n",
+       "      <td>169.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                  sum_sq     df         F    PR(>F)\n",
+       "C(Sex)          9.143118    1.0  0.053774  0.816901\n",
+       "Age          1140.725330    1.0  6.709083  0.010430\n",
+       "Age:C(Sex)      7.201063    1.0  0.042352  0.837197\n",
+       "Residual    28734.566043  169.0       NaN       NaN"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(class2_model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "ed33eab1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Sex)</th>\n",
+       "      <td>553.194455</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>6.099022</td>\n",
+       "      <td>0.014001</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>1970.785958</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>21.728105</td>\n",
+       "      <td>0.000004</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Sex)</th>\n",
+       "      <td>896.982415</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>9.889317</td>\n",
+       "      <td>0.001804</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>31836.456663</td>\n",
+       "      <td>351.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                  sum_sq     df          F    PR(>F)\n",
+       "C(Sex)        553.194455    1.0   6.099022  0.014001\n",
+       "Age          1970.785958    1.0  21.728105  0.000004\n",
+       "Age:C(Sex)    896.982415    1.0   9.889317  0.001804\n",
+       "Residual    31836.456663  351.0        NaN       NaN"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(class3_model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "4652591d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# we could also make these additional model to treat the 'Age:Sex' interaction, but we are not interested in 'Age' alone (hence the hint about «pairwise»)\n",
+    "class3_female_model = smf.ols(data=df, formula='Fare ~ Age', subset=(df['Pclass']==3)&(df['Sex']=='female')).fit()\n",
+    "class3_male_model = smf.ols(data=df, formula='Fare ~ Age', subset=(df['Pclass']==3)&(df['Sex']=='male')).fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "ecfbec15",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Pclass)</th>\n",
+       "      <td>436677.926114</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>109.672659</td>\n",
+       "      <td>4.283604e-35</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>4564.359068</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>2.292698</td>\n",
+       "      <td>1.312222e-01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Pclass)</th>\n",
+       "      <td>5386.550285</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>1.352844</td>\n",
+       "      <td>2.603528e-01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>507660.125010</td>\n",
+       "      <td>255.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                      sum_sq     df           F        PR(>F)\n",
+       "C(Pclass)      436677.926114    2.0  109.672659  4.283604e-35\n",
+       "Age              4564.359068    1.0    2.292698  1.312222e-01\n",
+       "Age:C(Pclass)    5386.550285    2.0    1.352844  2.603528e-01\n",
+       "Residual       507660.125010  255.0         NaN           NaN"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(female_model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "27783db9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>df</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>C(Pclass)</th>\n",
+       "      <td>269207.914985</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>90.701809</td>\n",
+       "      <td>8.657391e-34</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age</th>\n",
+       "      <td>18986.128890</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>12.793652</td>\n",
+       "      <td>3.857634e-04</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Age:C(Pclass)</th>\n",
+       "      <td>11620.048872</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>3.915039</td>\n",
+       "      <td>2.062721e-02</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Residual</th>\n",
+       "      <td>663360.184028</td>\n",
+       "      <td>447.0</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                      sum_sq     df          F        PR(>F)\n",
+       "C(Pclass)      269207.914985    2.0  90.701809  8.657391e-34\n",
+       "Age             18986.128890    1.0  12.793652  3.857634e-04\n",
+       "Age:C(Pclass)   11620.048872    2.0   3.915039  2.062721e-02\n",
+       "Residual       663360.184028  447.0        NaN           NaN"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sm.stats.anova_lm(male_model, typ=2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce321919",
+   "metadata": {},
+   "source": [
+    "We won't include this last case, again, as we are not interested in the slope of `Age` for each level of `Pclass`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "d27e6f05",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>coef</th>\n",
+       "      <th>std err</th>\n",
+       "      <th>t</th>\n",
+       "      <th>P&gt;|t|</th>\n",
+       "      <th>Conf. Int. Low</th>\n",
+       "      <th>Conf. Int. Upp.</th>\n",
+       "      <th>pvalue-hs</th>\n",
+       "      <th>reject-hs</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>male-female [1st class]</th>\n",
+       "      <td>-19.279419</td>\n",
+       "      <td>32.487685</td>\n",
+       "      <td>-0.593438</td>\n",
+       "      <td>5.536250e-01</td>\n",
+       "      <td>-83.380352</td>\n",
+       "      <td>44.821514</td>\n",
+       "      <td>5.536250e-01</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>male-female [2nd class]</th>\n",
+       "      <td>0.432770</td>\n",
+       "      <td>4.806509</td>\n",
+       "      <td>0.090038</td>\n",
+       "      <td>9.283634e-01</td>\n",
+       "      <td>-9.055761</td>\n",
+       "      <td>9.921302</td>\n",
+       "      <td>9.283634e-01</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2-1 [female]</th>\n",
+       "      <td>-108.472618</td>\n",
+       "      <td>18.421076</td>\n",
+       "      <td>-5.888506</td>\n",
+       "      <td>1.224216e-08</td>\n",
+       "      <td>-144.749437</td>\n",
+       "      <td>-72.195799</td>\n",
+       "      <td>2.448432e-08</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3-1 [female]</th>\n",
+       "      <td>-119.359262</td>\n",
+       "      <td>15.928392</td>\n",
+       "      <td>-7.493491</td>\n",
+       "      <td>1.102750e-12</td>\n",
+       "      <td>-150.727213</td>\n",
+       "      <td>-87.991312</td>\n",
+       "      <td>3.308354e-12</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3-2 [female]</th>\n",
+       "      <td>-10.886644</td>\n",
+       "      <td>15.483529</td>\n",
+       "      <td>-0.703111</td>\n",
+       "      <td>4.826278e-01</td>\n",
+       "      <td>-41.378522</td>\n",
+       "      <td>19.605233</td>\n",
+       "      <td>4.826278e-01</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                               coef    std err         t         P>|t|  \\\n",
+       "male-female [1st class]  -19.279419  32.487685 -0.593438  5.536250e-01   \n",
+       "male-female [2nd class]    0.432770   4.806509  0.090038  9.283634e-01   \n",
+       "2-1 [female]            -108.472618  18.421076 -5.888506  1.224216e-08   \n",
+       "3-1 [female]            -119.359262  15.928392 -7.493491  1.102750e-12   \n",
+       "3-2 [female]             -10.886644  15.483529 -0.703111  4.826278e-01   \n",
+       "\n",
+       "                         Conf. Int. Low  Conf. Int. Upp.     pvalue-hs  \\\n",
+       "male-female [1st class]      -83.380352        44.821514  5.536250e-01   \n",
+       "male-female [2nd class]       -9.055761         9.921302  9.283634e-01   \n",
+       "2-1 [female]                -144.749437       -72.195799  2.448432e-08   \n",
+       "3-1 [female]                -150.727213       -87.991312  3.308354e-12   \n",
+       "3-2 [female]                 -41.378522        19.605233  4.826278e-01   \n",
+       "\n",
+       "                         reject-hs  \n",
+       "male-female [1st class]      False  \n",
+       "male-female [2nd class]      False  \n",
+       "2-1 [female]                  True  \n",
+       "3-1 [female]                  True  \n",
+       "3-2 [female]                 False  "
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def suffix_label(dataframe, label_suffix):\n",
+    "    dataframe.index = [ label + label_suffix for label in dataframe.index ]\n",
+    "    return dataframe\n",
+    "\n",
+    "comparisons = pd.concat([\n",
+    "    suffix_label(class1_model.t_test_pairwise('C(Sex)').result_frame, ' [1st class]'),\n",
+    "    suffix_label(class2_model.t_test_pairwise('C(Sex)').result_frame, ' [2nd class]'),\n",
+    "    suffix_label(female_model.t_test_pairwise('C(Pclass)').result_frame, ' [female]'),\n",
+    "])\n",
+    "comparisons"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "80024bdf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([False, False,  True,  True, False]),\n",
+       " array([8.61512929e-01, 9.28363378e-01, 4.89686469e-08, 5.51392265e-12,\n",
+       "        8.61512929e-01]))"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from statsmodels.stats.multitest import multipletests\n",
+    "corrected_rejections, corrected_pvalues, _, _ = multipletests(comparisons['P>|t|'])\n",
+    "corrected_rejections, corrected_pvalues"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b7b20012",
+   "metadata": {},
+   "source": [
+    "# Linear model with multiple variables"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "144b0584",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Load the `mi.csv` file and plot the variables `Temperature` vs `HeartRate` and `PhysicalActivity`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "35949307",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "47cf88a3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from matplotlib import pyplot as plt\n",
+    "import seaborn as sns\n",
+    "from scipy import stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "7a8dacd7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mi = pd.read_csv('../data/mi.csv', index_col=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "bea3243d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Age</th>\n",
+       "      <th>OwnsHouse</th>\n",
+       "      <th>PhysicalActivity</th>\n",
+       "      <th>Sex</th>\n",
+       "      <th>LivesWithPartner</th>\n",
+       "      <th>LivesWithKids</th>\n",
+       "      <th>BornInCity</th>\n",
+       "      <th>Inbreeding</th>\n",
+       "      <th>BMI</th>\n",
+       "      <th>CMVPositiveSerology</th>\n",
+       "      <th>...</th>\n",
+       "      <th>VaccineWhoopingCough</th>\n",
+       "      <th>VaccineYellowFever</th>\n",
+       "      <th>VaccineHepB</th>\n",
+       "      <th>VaccineFlu</th>\n",
+       "      <th>SUBJID</th>\n",
+       "      <th>DepressionScore</th>\n",
+       "      <th>HeartRate</th>\n",
+       "      <th>Temperature</th>\n",
+       "      <th>HourOfSampling</th>\n",
+       "      <th>DayOfSampling</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>22.33</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>3.0</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>94.9627</td>\n",
+       "      <td>20.13</td>\n",
+       "      <td>No</td>\n",
+       "      <td>...</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>66</td>\n",
+       "      <td>36.8</td>\n",
+       "      <td>8.883</td>\n",
+       "      <td>40</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>28.83</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>79.1024</td>\n",
+       "      <td>21.33</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>...</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>3</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>66</td>\n",
+       "      <td>37.4</td>\n",
+       "      <td>9.350</td>\n",
+       "      <td>40</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>23.67</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>117.2540</td>\n",
+       "      <td>22.18</td>\n",
+       "      <td>No</td>\n",
+       "      <td>...</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>4</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>62</td>\n",
+       "      <td>36.9</td>\n",
+       "      <td>8.667</td>\n",
+       "      <td>40</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>21.17</td>\n",
+       "      <td>No</td>\n",
+       "      <td>0.5</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>94.1796</td>\n",
+       "      <td>18.68</td>\n",
+       "      <td>No</td>\n",
+       "      <td>...</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>5</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>64</td>\n",
+       "      <td>36.0</td>\n",
+       "      <td>9.883</td>\n",
+       "      <td>40</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>26.17</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>1.5</td>\n",
+       "      <td>Female</td>\n",
+       "      <td>No</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>105.1250</td>\n",
+       "      <td>29.01</td>\n",
+       "      <td>No</td>\n",
+       "      <td>...</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>Yes</td>\n",
+       "      <td>No</td>\n",
+       "      <td>8</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>67</td>\n",
+       "      <td>36.7</td>\n",
+       "      <td>8.550</td>\n",
+       "      <td>81</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 43 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "     Age OwnsHouse  PhysicalActivity     Sex LivesWithPartner LivesWithKids  \\\n",
+       "1  22.33       Yes               3.0  Female               No            No   \n",
+       "2  28.83       Yes               0.0  Female              Yes            No   \n",
+       "3  23.67       Yes               0.0  Female              Yes            No   \n",
+       "4  21.17        No               0.5  Female               No            No   \n",
+       "5  26.17       Yes               1.5  Female               No            No   \n",
+       "\n",
+       "  BornInCity  Inbreeding    BMI CMVPositiveSerology  ...  \\\n",
+       "1        Yes     94.9627  20.13                  No  ...   \n",
+       "2        Yes     79.1024  21.33                 Yes  ...   \n",
+       "3        Yes    117.2540  22.18                  No  ...   \n",
+       "4         No     94.1796  18.68                  No  ...   \n",
+       "5        Yes    105.1250  29.01                  No  ...   \n",
+       "\n",
+       "   VaccineWhoopingCough  VaccineYellowFever  VaccineHepB  VaccineFlu  SUBJID  \\\n",
+       "1                   Yes                  No          Yes          No       2   \n",
+       "2                   Yes                  No          Yes          No       3   \n",
+       "3                    No                  No          Yes          No       4   \n",
+       "4                    No                  No          Yes          No       5   \n",
+       "5                   Yes                  No          Yes          No       8   \n",
+       "\n",
+       "   DepressionScore  HeartRate Temperature HourOfSampling DayOfSampling  \n",
+       "1              0.0         66        36.8          8.883            40  \n",
+       "2              0.0         66        37.4          9.350            40  \n",
+       "3              0.0         62        36.9          8.667            40  \n",
+       "4              1.0         64        36.0          9.883            40  \n",
+       "5              0.0         67        36.7          8.550            81  \n",
+       "\n",
+       "[5 rows x 43 columns]"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mi.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "d55877e4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.scatterplot(data=mi, x='PhysicalActivity', y='Temperature');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "62449fb6",
+   "metadata": {},
+   "source": [
+    "## Q"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c71d2a4c",
+   "metadata": {},
+   "source": [
+    "The `PhysicalActivity` variable is very asymmetric. This is usually undesirable for an explanatory variable, because we cannot densely sample a large part of its domain of possible values, and therefore a model based on the data cannot be reliable.\n",
+    "\n",
+    "We will proceed to transforming `PhysicalActivity` using a simple natural logarithm. `log` is undefined at $0$ and tends to the infinite near $0$, which renders its straightforward application to `PhysicalActivity` inappropriate. Therefore we will also add $1$ to the `PhysicalActivity` measurements prior to applying `log`.\n",
+    "\n",
+    "Plot again the temperature versus the transformed `PhysicalActivity` variable and compare the skewness of the transformed versus raw variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21e8879e",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "id": "0b8cac58",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.scatterplot(data=mi, x=np.log(1+mi['PhysicalActivity']), y='Temperature');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "04a941a5",
+   "metadata": {},
+   "source": [
+    "Note that one-liners such as the above expression will almost always be refactored.\n",
+    "We may need the transformed variable again, and therefore should reify it for future reference."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "b0cc612e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "logPA = np.log(1 + mi['PhysicalActivity'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "adf75983",
+   "metadata": {},
+   "source": [
+    "We may also append it to the dataframe, as a column, just like any other variable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "d357ea8a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "extended_mi = mi.copy()\n",
+    "extended_mi['logPA'] = logPA"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd32ce56",
+   "metadata": {},
+   "source": [
+    "We cannot compare the skewness of both variables with a single test.\n",
+    "\n",
+    "Instead, we can estimate their skewness and observe they dramatically differ:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "87455d20",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(4.715752340548497, 0.2806838326518803)"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "stats.skew(mi['PhysicalActivity']), stats.skew(logPA)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1067660f",
+   "metadata": {},
+   "source": [
+    "...although they both happen to be skewed if we perform individual skewness tests."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "645ef445",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SkewtestResult(statistic=23.77197168884431, pvalue=6.512720346815048e-125)"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "stats.skewtest(mi['PhysicalActivity'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "f5984bf0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SkewtestResult(statistic=3.242519136674468, pvalue=0.0011847799127530753)"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "stats.skewtest(logPA)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "478d1262",
+   "metadata": {},
+   "source": [
+    "Note we do not need the explanatory variable to be symmetric or normally distributed for a model to be valid.\n",
+    "The point is mainly to make our sample exhibit a good coverage (in a linear sense) of the domain of possible values for our predictors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c6d5225",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "To appreciate the increased robustness of a linear model using the transformed variable compared to the raw variable, design a simple univariate linear regression of `Temperature` as response variable, and draw the Cook's distance of all the observations in regard of this model:\n",
+    "* first with the raw `PhysicalActivity` as explanatory variable,\n",
+    "* second with the transformed `PhysicalActivity` as explanatory variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c47489e6",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "bf32c7e6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "model = smf.ols('Temperature ~ PhysicalActivity', mi).fit()\n",
+    "OLSInfluence(model).plot_index(threshold=0.01)\n",
+    "plt.axhline(0.5, color='r', linestyle=':', linewidth=1);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "ac8ab2cc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "model = smf.ols('Temperature ~ I(np.log(1+PhysicalActivity))', mi).fit()\n",
+    "OLSInfluence(model).plot_index(threshold=0.01);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3cd48b4f",
+   "metadata": {},
+   "source": [
+    "In the above example, we leveraged the expressiveness of `patsy` for Wilkinson formulae. The `I` «function» is a special symbol just like `C` for tagging a variable as categorical. `I` allows to evaluate a subexpression following the Python syntax instead of the Wilkinson formalism.\n",
+    "\n",
+    "Note for example that `1 + PhysicalActivity` does not take the same meaning in a Wilkinson formula as in Python.\n",
+    "\n",
+    "Alternatively, we can design the linear model in other ways:\n",
+    "* adding the transformed variable to the `mi` dataframe, as an extra column (with a different name),\n",
+    "* making the design matrix yourself, with the transformed variable as a column and the intercept as another column."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "177c2ec7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# already done\n",
+    "logPA = np.log(1 + mi['PhysicalActivity'])\n",
+    "extended_mi = mi.copy()\n",
+    "extended_mi['logPA'] = logPA\n",
+    "# \n",
+    "model = smf.ols('Temperature ~ logPA', extended_mi).fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "93e6b4ee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import statsmodels.api as sm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "d2ec65f0",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/flaurent/.local/lib/python3.8/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
+      "  x = pd.concat(x[::order], 1)\n"
+     ]
+    }
+   ],
+   "source": [
+    "y = mi['Temperature']\n",
+    "X = sm.add_constant(logPA)\n",
+    "model = sm.OLS(y, X).fit()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c39bd1c5",
+   "metadata": {},
+   "source": [
+    "Anyway, as can be seen in the plots above, we turned an influential observation (number 362 was above $0.5$) into a non-influential one, and similarly decreased the influence of several other points.\n",
+    "\n",
+    "A linear model of the transformed `PhysicalActivity` will indeed be more robust."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1c7871a2",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Make a linear model of `Temperature`  as response and `HeartRate` and `PhysicalActivity` (or its transformed variant) as explanatory variables.\n",
+    "\n",
+    "Make two such models, one with interaction and one without. How would you choose between the two models?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12d7e9a5",
+   "metadata": {},
+   "source": [
+    "## A (with nested Q&A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "82e9f8d6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<caption>OLS Regression Results</caption>\n",
+       "<tr>\n",
+       "  <th>Dep. Variable:</th>       <td>Temperature</td>   <th>  R-squared:         </th> <td>   0.102</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.099</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   46.01</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Date:</th>             <td>Tue, 28 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>1.17e-19</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time:</th>                 <td>17:16:31</td>     <th>  Log-Likelihood:    </th> <td> -179.89</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>No. Observations:</th>      <td>   816</td>      <th>  AIC:               </th> <td>   365.8</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Residuals:</th>          <td>   813</td>      <th>  BIC:               </th> <td>   379.9</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th> <td>   35.9204</td> <td>    0.074</td> <td>  485.671</td> <td> 0.000</td> <td>   35.775</td> <td>   36.066</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>HeartRate</th> <td>    0.0095</td> <td>    0.001</td> <td>    8.173</td> <td> 0.000</td> <td>    0.007</td> <td>    0.012</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>logPA</th>     <td>   -0.0515</td> <td>    0.015</td> <td>   -3.544</td> <td> 0.000</td> <td>   -0.080</td> <td>   -0.023</td>\n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "  <th>Omnibus:</th>       <td>43.500</td> <th>  Durbin-Watson:     </th> <td>   1.603</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  49.117</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Skew:</th>          <td> 0.591</td> <th>  Prob(JB):          </th> <td>2.16e-11</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Kurtosis:</th>      <td> 3.215</td> <th>  Cond. No.          </th> <td>    420.</td>\n",
+       "</tr>\n",
+       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary.Summary'>\n",
+       "\"\"\"\n",
+       "                            OLS Regression Results                            \n",
+       "==============================================================================\n",
+       "Dep. Variable:            Temperature   R-squared:                       0.102\n",
+       "Model:                            OLS   Adj. R-squared:                  0.099\n",
+       "Method:                 Least Squares   F-statistic:                     46.01\n",
+       "Date:                Tue, 28 Sep 2021   Prob (F-statistic):           1.17e-19\n",
+       "Time:                        17:16:31   Log-Likelihood:                -179.89\n",
+       "No. Observations:                 816   AIC:                             365.8\n",
+       "Df Residuals:                     813   BIC:                             379.9\n",
+       "Df Model:                           2                                         \n",
+       "Covariance Type:            nonrobust                                         \n",
+       "==============================================================================\n",
+       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
+       "------------------------------------------------------------------------------\n",
+       "Intercept     35.9204      0.074    485.671      0.000      35.775      36.066\n",
+       "HeartRate      0.0095      0.001      8.173      0.000       0.007       0.012\n",
+       "logPA         -0.0515      0.015     -3.544      0.000      -0.080      -0.023\n",
+       "==============================================================================\n",
+       "Omnibus:                       43.500   Durbin-Watson:                   1.603\n",
+       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               49.117\n",
+       "Skew:                           0.591   Prob(JB):                     2.16e-11\n",
+       "Kurtosis:                       3.215   Cond. No.                         420.\n",
+       "==============================================================================\n",
+       "\n",
+       "Notes:\n",
+       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model = smf.ols('Temperature ~ HeartRate + logPA', extended_mi).fit()\n",
+    "model.summary()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "faeab021",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<caption>OLS Regression Results</caption>\n",
+       "<tr>\n",
+       "  <th>Dep. Variable:</th>       <td>Temperature</td>   <th>  R-squared:         </th> <td>   0.102</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.099</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   30.78</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Date:</th>             <td>Tue, 28 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>7.55e-19</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time:</th>                 <td>17:16:31</td>     <th>  Log-Likelihood:    </th> <td> -179.70</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>No. Observations:</th>      <td>   816</td>      <th>  AIC:               </th> <td>   367.4</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Residuals:</th>          <td>   812</td>      <th>  BIC:               </th> <td>   386.2</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th>       <td>   35.8586</td> <td>    0.126</td> <td>  285.165</td> <td> 0.000</td> <td>   35.612</td> <td>   36.105</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>HeartRate</th>       <td>    0.0106</td> <td>    0.002</td> <td>    5.120</td> <td> 0.000</td> <td>    0.007</td> <td>    0.015</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>logPA</th>           <td>    0.0031</td> <td>    0.091</td> <td>    0.034</td> <td> 0.973</td> <td>   -0.176</td> <td>    0.182</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>HeartRate:logPA</th> <td>   -0.0009</td> <td>    0.002</td> <td>   -0.607</td> <td> 0.544</td> <td>   -0.004</td> <td>    0.002</td>\n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "  <th>Omnibus:</th>       <td>43.759</td> <th>  Durbin-Watson:     </th> <td>   1.601</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  49.451</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Skew:</th>          <td> 0.593</td> <th>  Prob(JB):          </th> <td>1.83e-11</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Kurtosis:</th>      <td> 3.217</td> <th>  Cond. No.          </th> <td>1.28e+03</td>\n",
+       "</tr>\n",
+       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.28e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary.Summary'>\n",
+       "\"\"\"\n",
+       "                            OLS Regression Results                            \n",
+       "==============================================================================\n",
+       "Dep. Variable:            Temperature   R-squared:                       0.102\n",
+       "Model:                            OLS   Adj. R-squared:                  0.099\n",
+       "Method:                 Least Squares   F-statistic:                     30.78\n",
+       "Date:                Tue, 28 Sep 2021   Prob (F-statistic):           7.55e-19\n",
+       "Time:                        17:16:31   Log-Likelihood:                -179.70\n",
+       "No. Observations:                 816   AIC:                             367.4\n",
+       "Df Residuals:                     812   BIC:                             386.2\n",
+       "Df Model:                           3                                         \n",
+       "Covariance Type:            nonrobust                                         \n",
+       "===================================================================================\n",
+       "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
+       "-----------------------------------------------------------------------------------\n",
+       "Intercept          35.8586      0.126    285.165      0.000      35.612      36.105\n",
+       "HeartRate           0.0106      0.002      5.120      0.000       0.007       0.015\n",
+       "logPA               0.0031      0.091      0.034      0.973      -0.176       0.182\n",
+       "HeartRate:logPA    -0.0009      0.002     -0.607      0.544      -0.004       0.002\n",
+       "==============================================================================\n",
+       "Omnibus:                       43.759   Durbin-Watson:                   1.601\n",
+       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               49.451\n",
+       "Skew:                           0.593   Prob(JB):                     1.83e-11\n",
+       "Kurtosis:                       3.217   Cond. No.                     1.28e+03\n",
+       "==============================================================================\n",
+       "\n",
+       "Notes:\n",
+       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
+       "[2] The condition number is large, 1.28e+03. This might indicate that there are\n",
+       "strong multicollinearity or other numerical problems.\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model = smf.ols('Temperature ~ HeartRate * logPA', extended_mi).fit()\n",
+    "model.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "66ddaa3e",
+   "metadata": {},
+   "source": [
+    "### Q\n",
+    "\n",
+    "To get a better intuition about the log-likelihood, plot it (with a dot plot) for different models, with one variable, with two variables, with and without interaction.\n",
+    "\n",
+    "Feel free to introduce one or two extra explanatory variables such as `BMI`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "05844c56",
+   "metadata": {},
+   "source": [
+    "### A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "2588d8d6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>log-likelihood</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>HeartRate</th>\n",
+       "      <td>-186.144939</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>logPA</th>\n",
+       "      <td>-212.101759</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>BMI</th>\n",
+       "      <td>-219.812718</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate + logPA</th>\n",
+       "      <td>-179.888972</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate * logPA</th>\n",
+       "      <td>-179.703757</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate + BMI</th>\n",
+       "      <td>-181.552458</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate * BMI</th>\n",
+       "      <td>-181.532998</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>logPA + BMI</th>\n",
+       "      <td>-208.759586</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>logPA * BMI</th>\n",
+       "      <td>-208.469309</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate + logPA + BMI</th>\n",
+       "      <td>-175.738300</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>HeartRate * logPA * BMI</th>\n",
+       "      <td>-175.402285</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                         log-likelihood\n",
+       "HeartRate                   -186.144939\n",
+       "logPA                       -212.101759\n",
+       "BMI                         -219.812718\n",
+       "HeartRate + logPA           -179.888972\n",
+       "HeartRate * logPA           -179.703757\n",
+       "HeartRate + BMI             -181.552458\n",
+       "HeartRate * BMI             -181.532998\n",
+       "logPA + BMI                 -208.759586\n",
+       "logPA * BMI                 -208.469309\n",
+       "HeartRate + logPA + BMI     -175.738300\n",
+       "HeartRate * logPA * BMI     -175.402285"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "right_hand_sides =(\n",
+    "    'HeartRate',\n",
+    "    'logPA',\n",
+    "    'BMI',\n",
+    "    'HeartRate + logPA',\n",
+    "    'HeartRate * logPA',\n",
+    "    'HeartRate + BMI',\n",
+    "    'HeartRate * BMI',\n",
+    "    'logPA + BMI',\n",
+    "    'logPA * BMI',\n",
+    "    'HeartRate + logPA + BMI',\n",
+    "    'HeartRate * logPA * BMI',\n",
+    ")\n",
+    "\n",
+    "logL = []\n",
+    "for rhs in right_hand_sides:\n",
+    "    model = smf.ols('Temperature ~ ' + rhs, extended_mi).fit()\n",
+    "    logL.append(model.llf)\n",
+    "\n",
+    "\n",
+    "logL_nice = pd.DataFrame(np.array(logL)[:,None], columns=['log-likelihood'], index=right_hand_sides)\n",
+    "logL_for_seaborn = pd.DataFrame(zip(right_hand_sides, logL), columns=['model', 'log-likelihood'])\n",
+    "logL_nice"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7f00836",
+   "metadata": {},
+   "source": [
+    "In `seaborn`, a dot plot can be drawn with the `stripplot` function."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "625111f9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ax = sns.stripplot(y='model', x='log-likelihood', data=logL_for_seaborn, size=10, orient=\"h\", jitter=False, palette=\"flare_r\", linewidth=1, edgecolor=\"w\")\n",
+    "ax.yaxis.grid(True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1ba5537f",
+   "metadata": {},
+   "source": [
+    "Should we add a term, `BMI` brings more information alone than `Heart:logPA` for the same number of model parameters. This would be confirmed by AIC and BIC.\n",
+    "\n",
+    "Note however that we are comparing different models on the data we fitted them to. This is still fine here, because all the models are severely underfitting the data ($R^2\\approx0.1$)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "665a7a5c",
+   "metadata": {},
+   "source": [
+    "# White test for homoscedasticity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d0bdd7b",
+   "metadata": {},
+   "source": [
+    "To keep things simple, let us use the `'Heart + PhysicalActivity'` or `'Heart + logPhysicalActivity'`.\n",
+    "\n",
+    "## Q\n",
+    "\n",
+    "Inspect the residuals plotting them versus each explanatory variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6f37b2e",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "77e350be",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# already done\n",
+    "mi = pd.read_csv('../data/mi.csv', index_col=0)\n",
+    "logPA = np.log(1 + mi['PhysicalActivity'])\n",
+    "extended_mi = mi.copy()\n",
+    "extended_mi['logPA'] = logPA\n",
+    "model = smf.ols('Temperature ~ HeartRate + logPA', extended_mi).fit()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "377783b7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "extended_mi['residuals'] = model.resid\n",
+    "sns.scatterplot(x='HeartRate', y='residuals', data=extended_mi);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "e07bc434",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sns.scatterplot(x='logPA', y='residuals', data=extended_mi);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "789bd3f7",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "We will further inspect the residuals for heteroscedasticity, using the [White test](https://itfeature.com/heteroscedasticity/white-test-for-heteroskedasticity).\n",
+    "\n",
+    "`statsmodels` features an implementation of this test, but the [documentation](https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.het_white.html) is scarce on details.\n",
+    "Try to apply the `het_white` function, but do not feel ashamed if you fail."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a822074",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "85d73982",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(17.463548966032086, 0.0036996120985459207)"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "endog, exog = dmatrices('Temperature ~ HeartRate + I(np.log(1+PhysicalActivity))', mi)\n",
+    "statistic, pvalue, _, _ = diagnostic.het_white(model.resid, exog)\n",
+    "statistic, pvalue"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3ccb464",
+   "metadata": {
+    "heading_collapsed": true
+   },
+   "source": [
+    "## Q\n",
+    "\n",
+    "Instead, we will implement this test, as an application of polynomial regression.\n",
+    "\n",
+    "The algorithm is simple. First part:\n",
+    "\n",
+    "* take the squared residuals as a response variable,\n",
+    "* take the same explanatory variables as in the original model, plus all their possible interaction terms, plus all their values squared,\n",
+    "* fit a linear model to these data."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ce19023",
+   "metadata": {},
+   "source": [
+    "## A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "id": "7dec1d91",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "logPA = np.log(1 + mi['PhysicalActivity'])\n",
+    "white_mi = pd.DataFrame({\n",
+    "    'residuals2': model.resid**2,\n",
+    "    'HR': mi['HeartRate'],\n",
+    "    'HR2': mi['HeartRate']**2,\n",
+    "    'logPA': logPA,\n",
+    "    'logPA2': logPA**2,\n",
+    "})\n",
+    "white_model = smf.ols('residuals2 ~ HR * logPA + HR2 + logPA2', white_mi).fit()\n",
+    "# keep in mind 'logPA' in the formula will be evaluated as the logPA variable\n",
+    "# instead of the 'logPA' column in white_mi; as both logPAs actually contain\n",
+    "# the same data, we do not get errors"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b588b5c1",
+   "metadata": {},
+   "source": [
+    "## Q\n",
+    "\n",
+    "Second part:\n",
+    "* get the coefficient of determination $R^2$,\n",
+    "* get the sample size $n$,\n",
+    "* set the number $k$ of degrees of freedom as the number of predictors (intercept excluded),\n",
+    "\n",
+    "The test is:\n",
+    "$$\n",
+    "H_0: nR^2 \\sim \\chi_{k}^2\n",
+    "$$\n",
+    "$$\n",
+    "H_A: nR^2 > \\tt{Critical Value}(\\chi_{k}^2, 1-\\alpha)\n",
+    "$$\n",
+    "\n",
+    "You do not necessarily need to compute the critical value. Just note the test is one-sided.\n",
+    "\n",
+    "Compute the statistic $nR^2$ and the resulting $p$-value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "db59adce",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(17.463548966032178, 0.003699612098545746)"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "R2 = white_model.rsquared\n",
+    "n = len(white_mi)\n",
+    "dof = 5\n",
+    "statistic = n * R2\n",
+    "pvalue = 1 - stats.chi2.cdf(statistic, dof)\n",
+    "statistic, pvalue"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1bac9cde",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": false,
+   "sideBar": false,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": false,
+   "toc_window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/statsmodels_cours.ipynb b/notebooks/statsmodels_cours.ipynb
index 56915f5..17502d5 100644
--- a/notebooks/statsmodels_cours.ipynb
+++ b/notebooks/statsmodels_cours.ipynb
@@ -15,14 +15,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Requirement already satisfied: statsmodels in /home/flaurent/.local/lib/python3.8/site-packages (0.12.2)\r\n",
-      "Requirement already satisfied: numpy>=1.15 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.21.1)\r\n",
-      "Requirement already satisfied: pandas>=0.21 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.3.1)\r\n",
-      "Requirement already satisfied: patsy>=0.5 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (0.5.1)\r\n",
-      "Requirement already satisfied: scipy>=1.1 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.7.1)\r\n",
-      "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2019.3)\r\n",
-      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2.7.3)\r\n",
-      "Requirement already satisfied: six in /usr/lib/python3/dist-packages (from patsy>=0.5->statsmodels) (1.14.0)\r\n"
+      "Requirement already satisfied: statsmodels in /home/flaurent/.local/lib/python3.8/site-packages (0.12.2)\n",
+      "Requirement already satisfied: scipy>=1.1 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.7.1)\n",
+      "Requirement already satisfied: numpy>=1.15 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.21.1)\n",
+      "Requirement already satisfied: patsy>=0.5 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (0.5.1)\n",
+      "Requirement already satisfied: pandas>=0.21 in /home/flaurent/.local/lib/python3.8/site-packages (from statsmodels) (1.3.1)\n",
+      "Requirement already satisfied: six in /usr/lib/python3/dist-packages (from patsy>=0.5->statsmodels) (1.14.0)\n",
+      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2.7.3)\n",
+      "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas>=0.21->statsmodels) (2019.3)\n"
      ]
     }
    ],
@@ -44,7 +44,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 98,
    "id": "d6590258-e1ac-4f62-8adf-3fa014376a22",
    "metadata": {},
    "outputs": [],
@@ -84,7 +84,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 99,
    "id": "aec2f6b1-c4fc-465e-9434-b32333770e24",
    "metadata": {},
    "outputs": [],
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 100,
    "id": "bd00bd2f-b7eb-47e4-8af4-187ce9473481",
    "metadata": {},
    "outputs": [
@@ -106,7 +106,7 @@
        "F_onewayResult(statistic=2.3575322551335636, pvalue=0.11384795345837218)"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 100,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -126,7 +126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 101,
    "id": "696ff83f-d827-4513-9801-51488e5a1df0",
    "metadata": {},
    "outputs": [
@@ -140,7 +140,7 @@
        "        'C', 'C', 'C', 'C'], dtype='<U1'))"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 101,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 102,
    "id": "c324bd0f-e769-4a0d-8e6b-d4d346e76f68",
    "metadata": {},
    "outputs": [
@@ -371,7 +371,7 @@
        "29  81     C"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 102,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 103,
    "id": "4a2a00ec-43c6-4299-82e3-15b807110828",
    "metadata": {},
    "outputs": [],
@@ -420,7 +420,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 104,
    "id": "21bf5c1d-caa3-4072-bc86-ce860b8f33c8",
    "metadata": {},
    "outputs": [
@@ -433,8 +433,8 @@
       "Dep. Variable:                      Y   R-squared:                       0.149\n",
       "Model:                            OLS   Adj. R-squared:                  0.086\n",
       "Method:                 Least Squares   F-statistic:                     2.358\n",
-      "Date:                Fri, 24 Sep 2021   Prob (F-statistic):              0.114\n",
-      "Time:                        10:19:09   Log-Likelihood:                -96.604\n",
+      "Date:                Tue, 28 Sep 2021   Prob (F-statistic):              0.114\n",
+      "Time:                        11:16:16   Log-Likelihood:                -96.604\n",
       "No. Observations:                  30   AIC:                             199.2\n",
       "Df Residuals:                      27   BIC:                             203.4\n",
       "Df Model:                           2                                         \n",
@@ -473,7 +473,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 105,
    "id": "638bdd6b-6964-4209-b762-2991fd3fb7fc",
    "metadata": {
     "tags": []
@@ -485,7 +485,7 @@
        "F_onewayResult(statistic=2.3575322551335636, pvalue=0.11384795345837218)"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 105,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -502,12 +502,12 @@
    "id": "e64a5b9a-9214-4ecc-ad70-2505c5b9e78c",
    "metadata": {},
    "source": [
-    "To get a more classical table layout:"
+    "To get a more classical table layout, with explicit sums of squares calculation:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 106,
    "id": "0fe841a0-21b1-4c92-a767-c4ab3abd37f8",
    "metadata": {
     "tags": []
@@ -533,12 +533,14 @@
    "id": "e30bf249-4720-488e-a5d4-39497ca1e1c1",
    "metadata": {},
    "source": [
+    "We will come back to `anova_lm` later, as this function is actually mostly useful in multi-way ANOVA.\n",
+    "\n",
     "The residuals are what the model cannot account for:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 107,
    "id": "a5b2750a-8965-4769-b053-cd95e3583320",
    "metadata": {
     "tags": []
@@ -590,7 +592,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 108,
    "id": "fc687c84-7ad2-4055-b00d-efbcb4545ea2",
    "metadata": {
     "tags": []
@@ -624,7 +626,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 109,
    "id": "1ecb4ddd-d9f4-42cb-8611-0f0d69da4972",
    "metadata": {},
    "outputs": [
@@ -634,7 +636,7 @@
        "NormaltestResult(statistic=0.7583012334839461, pvalue=0.6844425164005732)"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 109,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -672,7 +674,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 110,
    "id": "02834d6d-cc6a-4746-9f2e-443c10a65fd3",
    "metadata": {},
    "outputs": [
@@ -714,7 +716,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 111,
    "id": "cdd44a30-6648-495f-98e7-c89739921066",
    "metadata": {},
    "outputs": [
@@ -799,7 +801,7 @@
        "C-B   0.223484      False  "
       ]
      },
-     "execution_count": 16,
+     "execution_count": 111,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -827,7 +829,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 112,
    "id": "86386730-0784-4304-bb82-c8909e7ffb01",
    "metadata": {},
    "outputs": [],
@@ -838,7 +840,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 113,
    "id": "6fd10d16-b7da-4adb-ba6c-2c82b6529ae6",
    "metadata": {
     "jupyter": {
@@ -891,7 +893,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 114,
    "id": "c885739b-16dc-4269-b0cf-1f0379e6c4c8",
    "metadata": {},
    "outputs": [
@@ -979,7 +981,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 115,
    "id": "3511838e-a886-4d0f-8be6-bce37a54aa2c",
    "metadata": {
     "jupyter": {
@@ -993,11 +995,11 @@
      "output_type": "stream",
      "text": [
       "Requirement already satisfied: formulaic in /home/flaurent/.local/lib/python3.8/site-packages (0.2.4)\n",
-      "Requirement already satisfied: astor in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (0.8.1)\n",
-      "Requirement already satisfied: interface-meta>=1.2 in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.2.4)\n",
-      "Requirement already satisfied: pandas in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.3.1)\n",
       "Requirement already satisfied: numpy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.21.1)\n",
+      "Requirement already satisfied: pandas in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.3.1)\n",
       "Requirement already satisfied: wrapt in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.12.1)\n",
+      "Requirement already satisfied: astor in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (0.8.1)\n",
+      "Requirement already satisfied: interface-meta>=1.2 in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.2.4)\n",
       "Requirement already satisfied: scipy in /home/flaurent/.local/lib/python3.8/site-packages (from formulaic) (1.7.1)\n",
       "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2019.3)\n",
       "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas->formulaic) (2.7.3)\n"
@@ -1011,7 +1013,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 116,
    "id": "8960bbfa-ef9f-4530-94eb-2a894140b51b",
    "metadata": {},
    "outputs": [
@@ -1291,7 +1293,7 @@
        "29        1.0        0        0        1"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 116,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1311,7 +1313,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 117,
    "id": "b18356ea-7df2-4596-abe4-b6a320280809",
    "metadata": {},
    "outputs": [
@@ -1330,10 +1332,10 @@
        "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2.358</td>\n",
        "</tr>\n",
        "<tr>\n",
-       "  <th>Date:</th>             <td>Fri, 24 Sep 2021</td> <th>  Prob (F-statistic):</th>  <td> 0.114</td> \n",
+       "  <th>Date:</th>             <td>Tue, 28 Sep 2021</td> <th>  Prob (F-statistic):</th>  <td> 0.114</td> \n",
        "</tr>\n",
        "<tr>\n",
-       "  <th>Time:</th>                 <td>10:19:12</td>     <th>  Log-Likelihood:    </th> <td> -96.604</td>\n",
+       "  <th>Time:</th>                 <td>11:16:26</td>     <th>  Log-Likelihood:    </th> <td> -96.604</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>   199.2</td>\n",
@@ -1388,8 +1390,8 @@
        "Dep. Variable:                      Y   R-squared:                       0.149\n",
        "Model:                            OLS   Adj. R-squared:                  0.086\n",
        "Method:                 Least Squares   F-statistic:                     2.358\n",
-       "Date:                Fri, 24 Sep 2021   Prob (F-statistic):              0.114\n",
-       "Time:                        10:19:12   Log-Likelihood:                -96.604\n",
+       "Date:                Tue, 28 Sep 2021   Prob (F-statistic):              0.114\n",
+       "Time:                        11:16:26   Log-Likelihood:                -96.604\n",
        "No. Observations:                  30   AIC:                             199.2\n",
        "Df Residuals:                      27   BIC:                             203.4\n",
        "Df Model:                           2                                         \n",
@@ -1471,7 +1473,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 118,
    "id": "d3de4753-0da7-4fe9-8412-eff18d66accf",
    "metadata": {
     "tags": []
@@ -1486,8 +1488,8 @@
       "Dep. Variable:                      Y   R-squared:                       0.149\n",
       "Model:                            OLS   Adj. R-squared:                  0.086\n",
       "Method:                 Least Squares   F-statistic:                     2.358\n",
-      "Date:                Fri, 24 Sep 2021   Prob (F-statistic):              0.114\n",
-      "Time:                        10:19:13   Log-Likelihood:                -96.604\n",
+      "Date:                Tue, 28 Sep 2021   Prob (F-statistic):              0.114\n",
+      "Time:                        11:16:26   Log-Likelihood:                -96.604\n",
       "No. Observations:                  30   AIC:                             199.2\n",
       "Df Residuals:                      27   BIC:                             203.4\n",
       "Df Model:                           2                                         \n",
@@ -1535,7 +1537,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 119,
    "id": "44932add-b649-4c6d-a88f-421549bc9481",
    "metadata": {},
    "outputs": [
@@ -1568,7 +1570,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 120,
    "id": "b3fdcfa3-fe7a-48f3-9a2f-b01723a6e440",
    "metadata": {
     "tags": []
@@ -1604,7 +1606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 121,
    "id": "e3e4e71e-27a4-4c96-ab41-050f4f7597d6",
    "metadata": {
     "tags": []
@@ -1626,7 +1628,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 122,
    "id": "552fc5c1-3c95-445b-a91a-41e85d606a41",
    "metadata": {},
    "outputs": [],
@@ -1637,7 +1639,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 123,
    "id": "6768710f-e796-4452-8c52-1ca6f484f170",
    "metadata": {
     "tags": []
@@ -1651,7 +1653,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 124,
    "id": "4be7d27c-bfdf-42c5-8820-62bc0ed65ca8",
    "metadata": {},
    "outputs": [],
@@ -1661,7 +1663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 125,
    "id": "c55b7dd6-a22c-46af-aabb-6128441aa228",
    "metadata": {},
    "outputs": [],
@@ -1734,7 +1736,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 148,
    "id": "cc06b3ed-a066-4de3-884c-a7c82729c359",
    "metadata": {},
    "outputs": [
@@ -1742,15 +1744,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "            df     sum_sq    mean_sq          F    PR(>F)\n",
-      "water      1.0  15.552000  15.552000  16.034261  0.000462\n",
-      "sun        2.0  21.424667  10.712333  11.044518  0.000337\n",
-      "Residual  26.0  25.218000   0.969923        NaN       NaN\n"
+      "             sum_sq    df          F    PR(>F)\n",
+      "water     15.552000   1.0  16.034261  0.000462\n",
+      "sun       21.424667   2.0  11.044518  0.000337\n",
+      "Residual  25.218000  26.0        NaN       NaN\n"
      ]
     }
    ],
    "source": [
-    "anova_table = sm.stats.anova_lm(plant_model)\n",
+    "anova_table = sm.stats.anova_lm(plant_model, typ=2)\n",
     "print(anova_table)"
    ]
   },
@@ -1877,12 +1879,14 @@
     "\n",
     "This inter-factor dependence is called an *interaction*.\n",
     "\n",
+    "### Interaction\n",
+    "\n",
     "To model this interaction, we need an extra term in the model:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 149,
    "id": "60de13e5-b798-4312-8d06-0ef79f480760",
    "metadata": {},
    "outputs": [
@@ -1890,18 +1894,26 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "             df     sum_sq    mean_sq          F    PR(>F)\n",
-      "water       1.0  15.552000  15.552000  19.117394  0.000205\n",
-      "sun         2.0  21.424667  10.712333  13.168203  0.000138\n",
-      "water:sun   2.0   5.694000   2.847000   3.499693  0.046376\n",
-      "Residual   24.0  19.524000   0.813500        NaN       NaN\n"
+      "              sum_sq    df          F    PR(>F)\n",
+      "water      15.552000   1.0  19.117394  0.000205\n",
+      "sun        21.424667   2.0  13.168203  0.000138\n",
+      "water:sun   5.694000   2.0   3.499693  0.046376\n",
+      "Residual   19.524000  24.0        NaN       NaN\n"
      ]
     }
    ],
    "source": [
     "model_with_interaction = ols('height ~ water * sun', data=plant_data).fit()\n",
     "# remember `water * sun` is equivalent to `water + sun + water:sun`\n",
-    "print(sm.stats.anova_lm(model_with_interaction))"
+    "print(sm.stats.anova_lm(model_with_interaction, typ=2))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bec6f02b",
+   "metadata": {},
+   "source": [
+    "Argument `typ` specifies the type of sum of squares. Type 2 is often used for ANOVA because it does not depend on the order of the factors."
    ]
   },
   {
@@ -2022,6 +2034,53 @@
     "ax.legend(colored_points, [ points.get_label() for points in colored_points ], title='sun');"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "846a640e",
+   "metadata": {},
+   "source": [
+    "### Treating interaction"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2a6451f",
+   "metadata": {},
+   "source": [
+    "As we found significant interaction, we should rerun the ANOVA in the shape of one-way ANOVA, with one factor, for each level of the other factor, and possibly vice-versa."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3fe8ac1f",
+   "metadata": {},
+   "source": [
+    "<table><tr><td><img src=\"img/two-way-anova-interaction-significant-flowchart.png\" /></td></tr>\n",
+    "<tr><td><a href=\"https://www.spss-tutorials.com/spss-two-way-anova-interaction-significant/\">SPSS recommendation for two-way ANOVA interaction</a></td></tr></table>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 135,
+   "id": "c380d42c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "daily_water_model  = ols('height ~ sun',   data=plant_data[plant_data['water']=='daily']).fit()\n",
+    "weekly_water_model = ols('height ~ sun',   data=plant_data[plant_data['water']=='weekly']).fit()\n",
+    "low_sun_model      = ols('height ~ water', data=plant_data[plant_data['sun']=='low']).fit()\n",
+    "med_sun_model      = ols('height ~ water', data=plant_data[plant_data['sun']=='med']).fit()\n",
+    "high_sun_model     = ols('height ~ water', data=plant_data[plant_data['sun']=='high']).fit()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a39e6bd5",
+   "metadata": {},
+   "source": [
+    "If main effects are found to be significant, we can proceed to performing post-hoc tests."
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "48953eb2-9d8b-42e4-b086-144f07a54359",
@@ -2031,19 +2090,30 @@
    ]
   },
   {
-   "cell_type": "markdown",
-   "id": "7f5b7972",
+   "cell_type": "code",
+   "execution_count": 136,
+   "id": "93ccdd87",
    "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.03098093333325329"
+      ]
+     },
+     "execution_count": 136,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "If main effects are found to be significant, we can proceed to performing pairwise comparisons between the levels of each factor.\n",
-    "\n",
-    "If the interaction effect were not significant, we could proceed as follows:"
+    "daily_water_model.f_pvalue"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
-   "id": "4d1c85a8-2bd8-450b-8e84-632b25874e4f",
+   "execution_count": 137,
+   "id": "d1392464",
    "metadata": {},
    "outputs": [
     {
@@ -2080,35 +2150,35 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>low-high</th>\n",
-       "      <td>-1.92</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>-4.359308</td>\n",
-       "      <td>0.000182</td>\n",
-       "      <td>-2.825331</td>\n",
-       "      <td>-1.014669</td>\n",
-       "      <td>0.000547</td>\n",
-       "      <td>True</td>\n",
+       "      <td>-1.08</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-1.847481</td>\n",
+       "      <td>0.089466</td>\n",
+       "      <td>-2.35369</td>\n",
+       "      <td>0.19369</td>\n",
+       "      <td>0.170928</td>\n",
+       "      <td>False</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>med-high</th>\n",
-       "      <td>-1.63</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>-3.700871</td>\n",
-       "      <td>0.001015</td>\n",
-       "      <td>-2.535331</td>\n",
-       "      <td>-0.724669</td>\n",
-       "      <td>0.002029</td>\n",
+       "      <td>-1.78</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-3.044923</td>\n",
+       "      <td>0.010180</td>\n",
+       "      <td>-3.05369</td>\n",
+       "      <td>-0.50631</td>\n",
+       "      <td>0.030231</td>\n",
        "      <td>True</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>med-low</th>\n",
-       "      <td>0.29</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>0.658437</td>\n",
-       "      <td>0.516046</td>\n",
-       "      <td>-0.615331</td>\n",
-       "      <td>1.195331</td>\n",
-       "      <td>0.516046</td>\n",
+       "      <td>-0.70</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-1.197442</td>\n",
+       "      <td>0.254253</td>\n",
+       "      <td>-1.97369</td>\n",
+       "      <td>0.57369</td>\n",
+       "      <td>0.254253</td>\n",
        "      <td>False</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
@@ -2116,31 +2186,52 @@
        "</div>"
       ],
       "text/plain": [
-       "          coef   std err         t     P>|t|  Conf. Int. Low  Conf. Int. Upp.  \\\n",
-       "low-high -1.92  0.440437 -4.359308  0.000182       -2.825331        -1.014669   \n",
-       "med-high -1.63  0.440437 -3.700871  0.001015       -2.535331        -0.724669   \n",
-       "med-low   0.29  0.440437  0.658437  0.516046       -0.615331         1.195331   \n",
+       "          coef  std err         t     P>|t|  Conf. Int. Low  Conf. Int. Upp.  \\\n",
+       "low-high -1.08  0.58458 -1.847481  0.089466        -2.35369          0.19369   \n",
+       "med-high -1.78  0.58458 -3.044923  0.010180        -3.05369         -0.50631   \n",
+       "med-low  -0.70  0.58458 -1.197442  0.254253        -1.97369          0.57369   \n",
        "\n",
        "          pvalue-hs  reject-hs  \n",
-       "low-high   0.000547       True  \n",
-       "med-high   0.002029       True  \n",
-       "med-low    0.516046      False  "
+       "low-high   0.170928      False  \n",
+       "med-high   0.030231       True  \n",
+       "med-low    0.254253      False  "
+      ]
+     },
+     "execution_count": 137,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "daily_water_posthoc = daily_water_model.t_test_pairwise('sun')\n",
+    "daily_water_posthoc.result_frame"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 138,
+   "id": "8724bf04",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.001224005685747233"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 138,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "posthoc_tests_sun = plant_model.t_test_pairwise('sun')\n",
-    "posthoc_tests_sun.result_frame"
+    "weekly_water_model.f_pvalue"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
-   "id": "04e77ca6-0d64-4f6a-92d4-de26c0ee3702",
+   "execution_count": 139,
+   "id": "6dc3a0ad",
    "metadata": {},
    "outputs": [
     {
@@ -2176,36 +2267,70 @@
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th>weekly-daily</th>\n",
-       "      <td>-1.44</td>\n",
-       "      <td>0.359615</td>\n",
-       "      <td>-4.00428</td>\n",
-       "      <td>0.000462</td>\n",
-       "      <td>-2.1792</td>\n",
-       "      <td>-0.7008</td>\n",
-       "      <td>0.000462</td>\n",
+       "      <th>low-high</th>\n",
+       "      <td>-1.08</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-1.847481</td>\n",
+       "      <td>0.089466</td>\n",
+       "      <td>-2.35369</td>\n",
+       "      <td>0.19369</td>\n",
+       "      <td>0.170928</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>med-high</th>\n",
+       "      <td>-1.78</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-3.044923</td>\n",
+       "      <td>0.010180</td>\n",
+       "      <td>-3.05369</td>\n",
+       "      <td>-0.50631</td>\n",
+       "      <td>0.030231</td>\n",
        "      <td>True</td>\n",
        "    </tr>\n",
+       "    <tr>\n",
+       "      <th>med-low</th>\n",
+       "      <td>-0.70</td>\n",
+       "      <td>0.58458</td>\n",
+       "      <td>-1.197442</td>\n",
+       "      <td>0.254253</td>\n",
+       "      <td>-1.97369</td>\n",
+       "      <td>0.57369</td>\n",
+       "      <td>0.254253</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "text/plain": [
-       "              coef   std err        t     P>|t|  Conf. Int. Low  \\\n",
-       "weekly-daily -1.44  0.359615 -4.00428  0.000462         -2.1792   \n",
+       "          coef  std err         t     P>|t|  Conf. Int. Low  Conf. Int. Upp.  \\\n",
+       "low-high -1.08  0.58458 -1.847481  0.089466        -2.35369          0.19369   \n",
+       "med-high -1.78  0.58458 -3.044923  0.010180        -3.05369         -0.50631   \n",
+       "med-low  -0.70  0.58458 -1.197442  0.254253        -1.97369          0.57369   \n",
        "\n",
-       "              Conf. Int. Upp.  pvalue-hs  reject-hs  \n",
-       "weekly-daily          -0.7008   0.000462       True  "
+       "          pvalue-hs  reject-hs  \n",
+       "low-high   0.170928      False  \n",
+       "med-high   0.030231       True  \n",
+       "med-low    0.254253      False  "
       ]
      },
-     "execution_count": 42,
+     "execution_count": 139,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "posthoc_tests_water = plant_model.t_test_pairwise('water')\n",
-    "posthoc_tests_water.result_frame"
+    "weekly_water_posthoc = daily_water_model.t_test_pairwise('sun')\n",
+    "weekly_water_posthoc.result_frame"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98126f2f",
+   "metadata": {},
+   "source": [
+    "Problem: with `t_test_pairwise`, the correction operates per factor. We already performed a total of 6 comparisons, therefore we should correct considering this number. We may even perform more comparisons..."
    ]
   },
   {
@@ -2243,7 +2368,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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/iXuYfqZ7WAY4YvJ6OTiU9xfq1P1M93Q0TPcUAOiHunsKLfQAAABAwQj0AAAAQMEI9AAAAEDBCPQAAABAwQj0AAAAQMFaznIDAAAAYLDRQg8AAAAUjEAPAAAAFIxADwAAABSMQA8AAAAUjEAPAAAAFIxADwAAABTsfx7OPsmk2VjmAAAAAElFTkSuQmCC\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 957.6x295.2 with 2 Axes>"
       ]
@@ -2282,18 +2407,10 @@
     "This can be done with a procedure called *correction for multiple comparisons*."
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "48d0f081",
-   "metadata": {},
-   "source": [
-    "### multipletests"
-   ]
-  },
   {
    "cell_type": "code",
-   "execution_count": 45,
-   "id": "d89d9c34",
+   "execution_count": 126,
+   "id": "e6c92946",
    "metadata": {},
    "outputs": [
     {
@@ -2317,121 +2434,73 @@
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
-       "      <th>coef</th>\n",
-       "      <th>std err</th>\n",
-       "      <th>t</th>\n",
-       "      <th>P&gt;|t|</th>\n",
-       "      <th>Conf. Int. Low</th>\n",
-       "      <th>Conf. Int. Upp.</th>\n",
-       "      <th>pvalue-hs</th>\n",
-       "      <th>reject-hs</th>\n",
+       "      <th>df</th>\n",
+       "      <th>sum_sq</th>\n",
+       "      <th>mean_sq</th>\n",
+       "      <th>F</th>\n",
+       "      <th>PR(&gt;F)</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th>low-high</th>\n",
-       "      <td>-1.92</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>-4.359308</td>\n",
-       "      <td>0.000182</td>\n",
-       "      <td>-2.825331</td>\n",
-       "      <td>-1.014669</td>\n",
-       "      <td>0.000547</td>\n",
-       "      <td>True</td>\n",
+       "      <th>water</th>\n",
+       "      <td>1.0</td>\n",
+       "      <td>15.552000</td>\n",
+       "      <td>15.552000</td>\n",
+       "      <td>19.117394</td>\n",
+       "      <td>0.000205</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>med-high</th>\n",
-       "      <td>-1.63</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>-3.700871</td>\n",
-       "      <td>0.001015</td>\n",
-       "      <td>-2.535331</td>\n",
-       "      <td>-0.724669</td>\n",
-       "      <td>0.002029</td>\n",
-       "      <td>True</td>\n",
+       "      <th>sun</th>\n",
+       "      <td>2.0</td>\n",
+       "      <td>21.424667</td>\n",
+       "      <td>10.712333</td>\n",
+       "      <td>13.168203</td>\n",
+       "      <td>0.000138</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>med-low</th>\n",
-       "      <td>0.29</td>\n",
-       "      <td>0.440437</td>\n",
-       "      <td>0.658437</td>\n",
-       "      <td>0.516046</td>\n",
-       "      <td>-0.615331</td>\n",
-       "      <td>1.195331</td>\n",
-       "      <td>0.516046</td>\n",
-       "      <td>False</td>\n",
+       "      <th>water:sun</th>\n",
+       "      <td>2.0</td>\n",
+       "      <td>5.694000</td>\n",
+       "      <td>2.847000</td>\n",
+       "      <td>3.499693</td>\n",
+       "      <td>0.046376</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>weekly-daily</th>\n",
-       "      <td>-1.44</td>\n",
-       "      <td>0.359615</td>\n",
-       "      <td>-4.004280</td>\n",
-       "      <td>0.000462</td>\n",
-       "      <td>-2.179200</td>\n",
-       "      <td>-0.700800</td>\n",
-       "      <td>0.000462</td>\n",
-       "      <td>True</td>\n",
+       "      <th>Residual</th>\n",
+       "      <td>24.0</td>\n",
+       "      <td>19.524000</td>\n",
+       "      <td>0.813500</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "text/plain": [
-       "              coef   std err         t     P>|t|  Conf. Int. Low  \\\n",
-       "low-high     -1.92  0.440437 -4.359308  0.000182       -2.825331   \n",
-       "med-high     -1.63  0.440437 -3.700871  0.001015       -2.535331   \n",
-       "med-low       0.29  0.440437  0.658437  0.516046       -0.615331   \n",
-       "weekly-daily -1.44  0.359615 -4.004280  0.000462       -2.179200   \n",
-       "\n",
-       "              Conf. Int. Upp.  pvalue-hs  reject-hs  \n",
-       "low-high            -1.014669   0.000547       True  \n",
-       "med-high            -0.724669   0.002029       True  \n",
-       "med-low              1.195331   0.516046      False  \n",
-       "weekly-daily        -0.700800   0.000462       True  "
+       "             df     sum_sq    mean_sq          F    PR(>F)\n",
+       "water       1.0  15.552000  15.552000  19.117394  0.000205\n",
+       "sun         2.0  21.424667  10.712333  13.168203  0.000138\n",
+       "water:sun   2.0   5.694000   2.847000   3.499693  0.046376\n",
+       "Residual   24.0  19.524000   0.813500        NaN       NaN"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 126,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "pd.concat((posthoc_tests_sun.result_frame, posthoc_tests_water.result_frame))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c2a6451f",
-   "metadata": {},
-   "source": [
-    "Problem: with `t_test_pairwise`, the correction operates per factor. We performed a total of 4 comparisons, therefore we should correct considering this number.\n",
-    "\n",
-    "Note: there is no need to perform all possible comparisons, but be honest! If you did proceed to compare, then this comparison should count, whatever its outcome is.\n",
-    "\n",
-    "Anyway, as we found significant interaction, we should rerun the ANOVA in the shape of one-way ANOVA, with one factor, for each level of the other factor, and vice-versa."
+    "sm.stats.anova_lm(model_with_interaction)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3fe8ac1f",
-   "metadata": {},
-   "source": [
-    "<table><tr><td><img src=\"img/two-way-anova-interaction-significant-flowchart.png\" /></td></tr>\n",
-    "<tr><td><a href=\"https://www.spss-tutorials.com/spss-two-way-anova-interaction-significant/\">SPSS recommendation for two-way ANOVA interaction</a></td></tr></table>"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "id": "c380d42c",
+   "id": "48d0f081",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "daily_water_model  = ols('height ~ sun',   data=plant_data[plant_data['water']=='daily']).fit()\n",
-    "weekly_water_model = ols('height ~ sun',   data=plant_data[plant_data['water']=='weekly']).fit()\n",
-    "low_sun_model      = ols('height ~ water', data=plant_data[plant_data['sun']=='low']).fit()\n",
-    "med_sun_model      = ols('height ~ water', data=plant_data[plant_data['sun']=='med']).fit()\n",
-    "high_sun_model     = ols('height ~ water', data=plant_data[plant_data['sun']=='high']).fit()"
+    "### multipletests"
    ]
   },
   {
@@ -2439,7 +2508,9 @@
    "id": "b7ea24c3",
    "metadata": {},
    "source": [
-    "This would eventually lead to up to 9 comparisons, but again `t_test_pairwise` would not properly take this into account.\n",
+    "If we consider all 5 factored models, we may proceed to performing up to 9 comparisons, but again `t_test_pairwise` would not properly take this into account.\n",
+    "\n",
+    "Note that you do not need to perform all possible comparisons. Choose what comparisons you are interested in, but do so prior to performing them.\n",
     "\n",
     "We should use [multipletests](https://www.statsmodels.org/stable/generated/statsmodels.stats.multitest.multipletests.html) instead, for the purpose of correcting the $p$-values:"
    ]
@@ -2977,8 +3048,8 @@
       "Dep. Variable:               Response   R-squared:                       0.642\n",
       "Model:                            OLS   Adj. R-squared:                  0.640\n",
       "Method:                 Least Squares   F-statistic:                     354.9\n",
-      "Date:                Fri, 24 Sep 2021   Prob (F-statistic):           4.97e-46\n",
-      "Time:                        10:19:16   Log-Likelihood:                -103.52\n",
+      "Date:                Mon, 27 Sep 2021   Prob (F-statistic):           4.97e-46\n",
+      "Time:                        17:58:02   Log-Likelihood:                -103.52\n",
       "No. Observations:                 200   AIC:                             211.0\n",
       "Df Residuals:                     198   BIC:                             217.6\n",
       "Df Model:                           1                                         \n",
@@ -3017,7 +3088,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 54,
    "id": "50155198",
    "metadata": {},
    "outputs": [
@@ -3079,7 +3150,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 55,
    "id": "bc471543",
    "metadata": {},
    "outputs": [
@@ -3108,7 +3179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "777daba8",
+   "id": "e15946b2",
    "metadata": {},
    "source": [
     "The most distant points may be outliers.\n",
@@ -3116,8 +3187,23 @@
     "We expect the residuals not to exhibit any structure:\n",
     "\n",
     "* systematic (positive-only or negative-only) errors on subdomains of the explanatory variable are indicative of the model not being flexible enough,\n",
-    "* the dispersion of the residuals should not vary as a function of the explanatory variable (homoscedasticity).\n",
-    "\n",
+    "* the dispersion of the residuals should not vary as a function of the explanatory variable (homoscedasticity)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fce469df",
+   "metadata": {},
+   "source": [
+    "<table width=60%><tr><td><img src=\"img/heteroskedasticity.png\" /></td></tr>\n",
+    "<tr><td><a href=\"https://towardsdatascience.com/heteroscedasticity-is-nothing-to-be-afraid-of-730dd3f7ca1f\">\"Heteroscedasticity is nothing to be afraid of\" - Sachin Date</a></td></tr></table>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "777daba8",
+   "metadata": {},
+   "source": [
     "Key criterion: the residuals should be normally distributed."
    ]
   },
@@ -3133,7 +3219,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 56,
    "id": "5492f4e8-2ac8-4ba7-9a6c-241f33994998",
    "metadata": {},
    "outputs": [
@@ -3146,8 +3232,8 @@
       "Dep. Variable:               Response   R-squared:                       0.642\n",
       "Model:                            OLS   Adj. R-squared:                  0.640\n",
       "Method:                 Least Squares   F-statistic:                     354.9\n",
-      "Date:                Fri, 24 Sep 2021   Prob (F-statistic):           4.97e-46\n",
-      "Time:                        10:19:17   Log-Likelihood:                -103.52\n",
+      "Date:                Mon, 27 Sep 2021   Prob (F-statistic):           4.97e-46\n",
+      "Time:                        17:58:02   Log-Likelihood:                -103.52\n",
       "No. Observations:                 200   AIC:                             211.0\n",
       "Df Residuals:                     198   BIC:                             217.6\n",
       "Df Model:                           1                                         \n",
@@ -3183,7 +3269,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 57,
    "id": "0d7780a9",
    "metadata": {},
    "outputs": [
@@ -3235,7 +3321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 58,
    "id": "e79b930e",
    "metadata": {},
    "outputs": [],
@@ -3246,7 +3332,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 59,
    "id": "3cab691b",
    "metadata": {},
    "outputs": [
@@ -3438,7 +3524,7 @@
        "[200 rows x 8 columns]"
       ]
      },
-     "execution_count": 58,
+     "execution_count": 59,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3449,7 +3535,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 60,
    "id": "7f143230",
    "metadata": {},
    "outputs": [
@@ -3494,7 +3580,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 61,
    "id": "bc655fc0",
    "metadata": {},
    "outputs": [],
@@ -3506,7 +3592,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 62,
    "id": "b5b46df6",
    "metadata": {},
    "outputs": [
@@ -3531,7 +3617,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 63,
    "id": "a0b5ffc9",
    "metadata": {},
    "outputs": [],
@@ -3541,7 +3627,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 64,
    "id": "7bb8d264",
    "metadata": {},
    "outputs": [],
@@ -3553,7 +3639,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 65,
    "id": "1ddf4e63",
    "metadata": {},
    "outputs": [
@@ -3581,7 +3667,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 66,
    "id": "7a441682",
    "metadata": {},
    "outputs": [],
@@ -3592,13 +3678,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 67,
    "id": "0d8019bc",
    "metadata": {},
    "outputs": [
     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "<Figure size 957.6x295.2 with 2 Axes>"
       ]
@@ -3661,7 +3747,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 68,
    "id": "b5b96410",
    "metadata": {
     "scrolled": true
@@ -3669,7 +3755,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -3696,7 +3782,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 69,
    "id": "709f2da0",
    "metadata": {},
    "outputs": [
@@ -3754,7 +3840,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 70,
    "id": "02debff3",
    "metadata": {},
    "outputs": [
@@ -3801,13 +3887,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 71,
    "id": "32746edb",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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j9bUWTq6dxMqL3f+k0QKIJQuncwuwZus+DrV2M6uukpWNcwfrLw4dGuwAtWOHS3dasgT+8i/dikVdnSfPV0ZXjIm/OgZJOkHb0VwmJmOtN/2TjTHvAVZYa29Mfv8XwFJr7f8e6TaNjY1269atxRqiiHjkhtWbT0hH6uqLUV9bwd2rluZ0nzmviFjr6h6OH4fu9HUTW3a3jBxApNPWBg884FYqtmxxj7F4sVupuOYamDUrp+c4FnP66dustY0FufMAyvWYUqyJf9PhDq6+47ET8u3vU8cgEfEBY8yIxxQvk3j3AkuNMVW4FKnLAEUPUpL8lu7jdyMVVO8/1pXT/eW0ItLX53bZbmtzhdajWLJw+tgdoXp6YONGF1Rs3AjRKD0nz2Hj29/Ngwveil3Q4AKTWXncH0MKolitQtUxSESCyssajC3GmF8CTwEx4GlgtVfjkYmtkAGAH9N9/G6kguo5U6tyur+RWszeualp6HtgrdtforV1xNWKrMRiboVi/frBDlAzZsANN/Cnc5bx9/vLiJSFXGpVZ29+9sdIp6zMFYlLXhRr4q+OQSIyFr/WaXnahsRa+3Xg616OISh0BrxwCh0AZDy5lQFDCqojYbqjrq7hpmUNOd3fmCsi0agLKlpbx1ytGJO18Oyzrqbi/vvhyBGoqXH1FNdd5+orwmHu+tl2ImW9+dkfI53ycve41dUqDs+zYk381TFIREbj5zot9TkMAJ0BL6xCBwD5TveZCJYvquc23Huz/1gXc8YZVI+0IrKwysBrr0Fn5/gHvXv3YAeovXtdB6hLLnF1FW9/+wmT/HHvjzGcMVBVNRhUqI1twRRr4q+OQSIykkTC8txrx327s7uOQAGgM+CFVegAIN/pPhPF8kX1efv9Tl0RqQ5DqL2NGZ0dfPLtC8YVXDy1ZSf7fvILznz6MRqaX8Uag1m61O2sfcUVMHnyiLfNaX+M4fpTn6qrXXARCuX8XCRzxZz4q2OQiAzXv3Kx82DbmOmaXqVQKcAIAJ0BL6xCBwD5TveR7C1fVM83erq5+6HnOH7wKLMnV7Dy7QtyS0VqbYUHH6Tt57/i7Gef5lwsr5zUwE8ufT+/f+MSPnz9eRndb1b7Y6SqrBwMKsrLsx+/5IUm/iLilf5GEx+/uGHUdE0vU6gUYASAzoAXVqEDgHyn+0gWEgnXBer4cZZV9bHsnW/M7X66u+HRR13606ZNrgPU9JN45ML/xVNnXUjz9JMA6IlmXkMx5v4Y/UIhtzpRXe3Sn8LhtPcnIiITQ3+jiXu27efmS0/jjg270qZrjtTx7s23XEzCUtBVDQUYAaAz4IVVjAAgn+k+koHubrfS0NHhgoxcxGLwxBODHaC6umDmTPjAB+C667jl923UVk7CpPxPzraGYsT2tmVlg7UUVVUMeRDxLb92cxGR0tLfaOJAaw//vflVbryogXAILltUz5mnTBn4v5Ou493Uqkk8tfc4X/31cwVd1VCAEQA6A154CgC8kdfuaPG4W61obXV7WOTCWti+3QUV990HR49CbS1cdZXrAHX++QMrCLN3bB9/DUWq/q5PNTVKfQogP3dzEZHSktpo4kBrD3c93sS333v2kOAC0ne8e0/jnIHgAgpXGK4AIyA0AZZSk7fuaJ2dLqjo7HQBQi5eftm1lV2/Hvbvh0mTXAeo666DZcvSTvhzrqHoFwoN1lPU1KjrU8AVa/M9EZFMG02k63j3xvraouzjoyOaiHhiXN3R+vrcakVbG1tePMSarfs42NrN7JHqGNI5cADuvdcFFS+84Cb8F1wAn/40XH65W7kYRcY1FKnKywfrKSorlfpUQrTrtogUUyaNJtIFItZSlH18FGCIiCey7Y628YVD/NeDf+L4wcOcWhUaWCm4fcMuImFDbUWEo2Pthn38ODzwgAsqnnzSrXi85S3wta+5NKiZM7N6DiPWUPQLhYa2kdUqRcEYY+YC/wXMAiyw2lp7e7EeX7tuS76ppkfyYXggkkjYouzjo6OdSACVws7uGXdH6+vj91tf5vu/eYpyY5lRFuZoZ5TbN+yiKhImEjaj74bd1eU6QK1bB48/7nbtXrDArVRcdx2cemp+n1h5+WBQUZljPYbkIgZ83lr7lDGmFthmjHnIWvt8MR5cu25LPqmmRwqlWPv4KMAQCZg7Hn6J723cTSyRoDwcIp5IBHJn91G7oyUS0N7uait6evjlI3+i3NgTAol9x7o4ddgErrwszJGj7fC737mg4pFHXJBRXw8f+pALKt70pvymJ6XuoB2JjH39FKUQLPqBtfYAcCD5dbsx5gXgFKAoAYZ23ZZ8Uk2PFFIx9vFRgCESIBt3NvO9jbtJWEskHCJuoaUjyvQaTqhd8PvENV13tE+efxLLplpoahrSXvZgaze1FUMn7uVlLtjojcVdwGEtDft38dZnH2fpi3+Erna3k/a117qPxsb87SFhzGBQMY69KfJW6C5DGGPmA+cAW4r5uNp8T/JFNT0SdAowRALkzk1NxBOWspDBYDAGElhau6LsDw3WLgRl4rp8UT3L3zBtoGCbvl5o7T3herPrKtO2hJ0zpZLpB/Zy8YubedsLm5nRepi+sgjtb1tGzco/cx2gJk3Kz2DD4cFViurqvKyAjKvQXdIyxtQA9wB/Za1tS/PzVcAqgHnz5hV5dJJKNQYjU03PxFUqfxcKMEQCZN+xLsrLQsTidmB+awz0xhNDahd8P3G11qVAtbe79rJjGN4StqblEMt3bOb6/U9R/crLJIzhT/MW8+Cl7+GNH3gXjWfmaeI4adJgG9kC1FNkW+guozPGRHDBxU+stb9Kdx1r7WpgNUBjY2OOfY1lvFRjMLpC1/QkEpa9Rzs51NZLZ1+MU6dVs2BGMCeypaSU/i4UYIgEyNypVcTiCVo6+yDhgou4tZSFQkN2dvftxLWry61UZLnD9pKF0/l863GafvorznxqE4tee8n94Oyz4W/+htCKFZw1YwZnDbvdlt0t2bWwTU19qqrKup4iW6mF7m3dUY509NIbS1A1KczGnc3+CAYDwhhjgLuAF6y13/Z6PDI61RiMrpA1PYmEZcOLh9h1qIPbH9kV+Ilsvnm5glBKfxcKMCQv/J7vXyyFfh36C6OnV0+ivSdGbyxBOGT41PKFQx4n4w5NxRCNDqZARaPZ3barCzZsgHXreOvjj/PWWAwWLoRbbnHF2nNH3tRuy+6WzFrYlpUNLdIu4t4U/e/n4fYeFzQCBqguD/sypc3nLgQ+BDxnjNmevOyr1tr7vBuSjEQ1BmMrVE3PnpZOnt3fyupNTSUxkc0nr1cQSunvQgGGjFtQ8v0LrRivQ7rC6HRBzKgdmoohHnerFG1t0N2d3W2jUfj97wc7QHV3w+zZ8JGPuKDi9NMzCgLWbN03cgvbxacMBhRpdukulv738+Y1T5OwloqyMDNry6mtiPgrpS0ArLWP4+IzCQDVGHjnUFsPCUvJTGTzyesVhFL6u1CAIePm+3z/IinW67B8Uf2Y95dpIJJX1rp6irY299mOnd7en8J06HgnS1v38b6D25n1+0fdhnhTpsD117ug4q1vdZvWZSG185TF0Dupgu6aCp6Ol0GRi3tHW9lavqieyZUR5k2rwqQETr5IaRMpEO0b4p1ZkysIm+Ls5hw0Xq8gZPJ3EZQicAUYMm6+zfcvMr+9DpkEInnR0+OCivZ2t3KRoS27W/jVzzZw2YubWfrCZma0HqG3bBJHLlzGjJXvhosuGlcHqNl1VbweBVszmd7yChKhMF19MU6aWtwDaCYrW75KaRMpAu0b4p3506s5c04dt1x22gk1GBM9wPN6BWGsvwuvU7iy4WmAYYyZAvwAOAOwwMestU94OSbJniZHzoR6HaJRF1C0tUFfX3a33b8f7r2XuT/+Bd9q3kfchHh+4Vn8Zvl72dJwNtVT6/jOpWfnNq5weKDr0zvfPZlb179AJGyoNCG6+2LFTRNLymRly/OUNhEPFGvfkKCc8S2WUMhw6emzeMPMGs6dN5Wuvhjz1EUK8MfK2mh/F16ncGXD6xWM24HfWmv/3BgzCSjBmVjp0+TIKfnXIR4fDCp6erK77dGjcP/9rq7i6acBaDv5NDZe+WG2vXkpHdWT3fUsHGrNsmajomJwb4qKwbNMy99cw22hUMHSxDIt6M9kZcuTlDaREtYfVLR09vL68R6+dM+zvj/jW0yhkGH+jBrmzxh9Uhqk4CwfY/X7yprXKVzZ8CzAMMbUAcuAjwBYa/uALE+Fih9ocuSU7OvQ1QWtra5oO4O6igGdnfDww7B+vSvajsfhtNPgs5+Fa6/lzt8fSbt5XmUkzGd/tn3k1rKh0GBAUV096i7ahUoTy6agP9OVraKltImUuNQ0khsvauCux9UtKRdBSsfJ51iLtbKWC69TuLLh5QrGAuAw8B/GmLcA24BbrLVj77olvqPJkVMyr0Nv7+BGeNm0lu3rG9oBqqcHTj4ZbrwRrr3WdYBKWtlYOWTzvN5YnPaeGAaIWTuktezN4TBL33Lq4P4URWwlm042Bf0lv7IlUkC5nJVOTSMxRt2SchWkdJwgjXU8/JDClSkvA4wy4FzgM9baLcaY24EvA3+TeiVjzCpgFcC8Ind+EZlQYrHB/SqyqatIJGDbNhdUPPDAYAeod73LBRXnnpu2A9SShdO5BddO9lBrN7PqKomEQkQTCSoiYeKhMuJVtRwLTeL2PQmWXjErX8903LIp6C/Zla1xMMZcCGy31nYaYz6IOxbcbq191eOhiY/kelZ6eBpJUM74+k2Q0nGCNNbx8HsKVyovA4z9wH5r7Zbk97/EBRhDWGtXA6sBGhsbs8jPEJFUaWsGTpvuUp/a210qVKashRdfdEHFvffCgQNQWQmXXeaCigsvzKgD1JKF04ekP737h9uYVFdHe3kl0YjbnyJsre86kmVb0F8yK1v582/AW5Kr15/HNfv4L+Dtno7KI0HKcy+mXM9Kp6aR3LNtPzdfehp3bFC3pGwFKR0nSGMdLz+ncKXyLMCw1h40xuwzxpxurX0RuAx43qvxiJSy1JqBqeVhOg63cMd/76Xy4nksaZiW+R3t2+cCinXr4OWX3S7YF14In/+8Cy6qcujTUF4OtbVQW8ukhqNu4h7xdycupT2NW8xaa40x7wS+a629yxhzo9eD8kKQ8tyLLdez0qlpJAdae/jZ1r2s/lAjkbApegAX5OAxSOk4QRrrROF1F6nPAD9JdpBqAj7q8XhEPJVpZ6Js3bmpiepEHzOivVT2dmFsgp54nDVP7h07wGhpcR2g1q8f6ABFYyN8/euwYgVMyyJA6dcfVNTUDFnpCMrEXWlP49ZujPkK8EFgmTEmBETGuE1Jmii547nI9ay0X9JIgh48+uV1zESQxjpReBpgWGu3A41ejkHEL7LpTJSxZLF2bPdu5kbMkNro8rLwyC1hOzpcB6h16+CJJ1wHqNNPdysV11wDp5yS/VgqKlxAMSyoSBWkibvSnsblfcD7gRuTq9nzgH/0eEwZyfcZ6YmSO56L8ZyV9kMaSSkEj354HTMVpLFOBF6vYIhIUjadiUbVX6zd3u4CDGBOTSRtS9hZdZWDt+vrg02b3ErFhg3utqecAn/5l66u4rTTsntCxri6jOTGd0QyO0Fd7Il7oVaNZGTW2oPAt1O+34urwfC1QpyRnki549kK+llpBY8ykSnAEPGJbDoTnSCRcKsObW1pi7VXNs49oSVsNG5Zee4p8Mc/DnaAam2FqVM5+I5r+dnst7B58lxmT6liZWgaSzJ5Ev17VNTUuM9pukf5SUFWjWRExph2IF2zDgNYa+3kIg8pK4U4I63c8dEF+ay0gkeZyBRgiPhEtp2JsNYFE21tY26CN6Ql7PEuzu0+xPubn+Xk/34EDh1yxdmXXw7XXssfZy/iXza9QiRsqC0LD+xFcUvyfk4QDg+mPvlgj4ps5G3VSDJira31egzjUYgz0kE/Sy8jU/A4MQW5sD+fFGCI+ETGBc49PYMpUPF42vvasruFNVv3Dd0NO9LJkiO/dylQTU2uA9TFF8MXvwiXXjrQAerun20nEjYD6VTuc5w1W/cNBhhlZS6gqK11aVABNa5VIxk3Y0w9MHA6N5kq5VuFOiMd5LP0MjIvg8dSnuT6+bkFvbA/nxRgiPjEqAXO0ehgUDHGJnhbdrdw+4ZdRMKGU2KdnP27h5n2b0/Agd3uCuedBx/+MFx5JUydesLtD7Z2U1sxdNJdXhbm9fY+t4FegYOKYtZEZL1qJHlhjLke+GfgZKAZOBV4AVjs5bjGojPSkq3RgsdCTZRLeZJbrOeW63tTCoX9+aIAQyTJD8W+QwqcYzEXUOzbB90jdHtK49ePv8jy5//AhTs386ZX/kTIWl6tn8e6d7yf6762Ck46Ke3t+lc9jnb2cayzjxm15VRWlNNdUcVRE6Fu3hSoL+zrUeyaiKC0xS1BfwcsBR621p5jjLkE17LW15TOJPlSyIlyKU9yi/HcxvPeqLB/kAIMEXxU7BuPDxZrZxFUDHSAWruW2x7ZwKRYlMNTZnL/he/kycVv4/UZc+joiXLdKMFF/6pH3ZQaXumGvVQys2YyZeEQ0bjli0WYdBe7JiJIbXFLTNRa22KMCRljQtbaR40x/+L1oDJRaulMfk43KWWFnCiX8iS3GM9tPO/NSGmUsydX0HS4Y0L9nSnAEMHjYl9rXVDR3g6dnaMWaw8Rj7sOUOvXuw5Q7e0wbRpb3nopj562hNdOfeNAwXVvdFhL2mF+/PRBumvr6K6dTKwsQlV3lPb2Hg629XLuvKlFm3R7UROh/Sw8cdwYUwNswm222gx0ejymCSE1oDiproLnD7SXZCqN3xVyolzK3auK8dzG896kS6P87vvPmZB/ZwowRMhsYpvXFKrUDlCdna7NbKa327HDBRX33gvNza44+4or3F4Vb3sbk15tZeeGXURiiaEtaRvnDr2vsjKYPBlqa3k6vJ8pNRFMMiCZXBmhtqKM1u4od69amttzzIFqIiaMdwI9wGeBDwB1wG2ejmgCGJ76cfNlb2D1pqaSTKXxu0JOlEu5VqgYz2087026NEpr4Zp/fWzC/Z0pwBBh7IltXlKorHXBREeH+8g0qADYs8cFFevXwyuvuE3rli1zQcUllwwpuh7Skra1m1n9XaQWTnctZWtrTyjU9svEXjURE4O1NnW14j89G8gEMzz1I2HxPJVmoqZoFXKiXMq1QsV4buN9b4anUT6x+8iof2el+jegAEOEsSe2OadQ9a9UtLdnH1Q0N8N997mg4rnnXLrT+efDxz7mOkDV1Y140yULpw+2lO3f/G7y5BH3qfDLxF41ERPDsA33JgERoNPvG+0FXbrUDy9TaUq529FYCj1RLkStkF8mwoWug8r3ezPaikgp/w0owBBh7IltVrUB1roC7f6gYoS9KtJqb4cHH3RBxebNLiBZvNjtVXHNNTB7dmb3Y4wLKmpr3X4VY2x+56eJ/Ug1EX7o8iX5kbrhnnF5ee/EdZWSAho+0bln235uuew0bn9klyepNKXc7SgTQWoYUMoT4XTy+d6MtiJSyn8DEyLA0MREMjFasW9GKUT9QcUoG+Cl1dsLv/udCyoefdR1hJo7Fz7xCZcCtXBhZvcTDrugon9H7VAo8zHg72Jn33T5kryz1lrgf4wxXwe+7PV4Stnwic6xrj5Om1XDvZ+5mMMdxU+lKXa3o2zOwPvlbL1fBHEi7Jf3cLQVkVLu+FXyAYYmJv4XhABwpBSiTy45GQ4fdkFFLJb5HfZ3gFq71q1YdHTAjBmwciVcdx2ceeaYqw6ACyL6d9QeIf2pFHja5UvyzhjzZynfhoBGXNG3FNBoE52F9cWfzBSz21E2Z+An2tn6TARtIjzSe3jFm2ax91hX0YOOkVZESrnj15gBhjHmM8CPrbXHijCevNPExN+CEgCmphA1Nx9nYaXlY+fOYGllDxzLcF5kraulWL/e1VYcPuxWHK680q1ULFniOjuNJYOailLRH3z+cc9RysOG+skVA7uMF7p9rRTUdSlfx4A9uDQpKTA/peUUs9tRNmfgg3i2vtCCNhFO9x5+67cvEI0n+NI9z/omcCzljl+ZrGDMAp40xjwF/BB4ILmk7Qtjnf32oq++jC71PWvrjlJdHqau0v2T8m0A2NXF8mmw/PJ6iE3L7ravvALr19P9q99Q+fo+ouEyXnjjOVR+/BZOW3kdVGT4D7qqyhV2Z1BTUQpSg8+KshB98QSvH+/h5ClQWxFR+9oAs9Z+1OsxiPeK2e0omzPwQTtbXwxBmwinew+vPeuUgeAC/BE4lnLHrzEDDGvtXxtj/ga4Avgo8F1jzM+Bu6y1uws9wNFkcvbbL+03xRn+nh1s7aG7L055Wdh/Z6ZTuz9lU1MBcOgQ3H+/S4HasQNrDLvnvoktK27k2cVLOF5WQTRqueW1TpYsHCXAmDTJrVRMnpzZ6kYJSV19nFFTzuut3VgszW09hENG7WsDyBjzrwx2jzqBtfbmIg5HfKBYKyrZnIEP2tn6YgjaRDjdexgOed+WOR0/rSrmU0ZVoMkVi4PJjxgwFfilMeb/K+DYxpQ6ATHGfY6EDXduahq4zk3LGojGLV19Max1nzUx8c7w96y8LAQGDrf3DlzH0wCwp8elLjU1wf790NqaeXDR1ga/+AV8+MPw9rfDP/yDu/zLX+ZvP///8483fJk/Nl5KT2U1FZEwkbBhzdZ9J95PKOQCirlzYf58mDZtwgUX4FYfKyNhwG38d3JdJZPCIXrjlvraCm67frG/VrkkE1uBbUAFcC6wK/lxNq5d7bgYY1YYY140xrxsjFHBuAzoPwNfEXHTntHOwGdz3VKWSFiaDnfwxO4jNB3uAKBhZg1LG2bQMLPGt8EFpH8Pzzt12sD3/SZ64FhImdRg3AL8BXAE+AHwBWtt1BgTwh0YvljYIY4sk/QnP7XfDIJCF1wPf8/6z0z3xOJYa73Zf6GnZ3ClIhrN/rYbN7q6io0b3e3nz4dPfcq1lW1wz+Ol1U9QWxYectPysjCHWrsHL6isHNhZO9sOUKVo+Orj5MoIZWFDfW1FUXcXl/yx1v4ngDHmk8BF1tpY8vvvA4+N576NMWHge8A7gP241N611trnxzdqKQXZnIFPd915U6t80ZGoWIJe6D7SexikNK+gy+S06DTgz6y1r6ZeaK1NGGOuHe8AkgeFrcBr1tqs7i/T9Cc/t9/0k2IUXKebNPbG4nT1xWntjhYvAOzuHtxRO9ugIhaDLVtg3TrXAaqzE2bOhPe/33WAOuOME2okZtdVcrSzl4rIYJDRG4szfdpkmD7dBRaRyPBHmtD8svmfFMRUYDJwNPl9TfKy8TgfeNla2wRgjFmDKxxXgCFAdqkoqdcN+mQ7F34tdM+m9Wy697vYaV5+aZXrhTFPk1prvz48uEj52Qt5GMMtQE73k23608adzdywejMXfWsDN6zezMadzeMZd8nJJOVsvNK9Z5PKwtyx8hwe+9Kl3L1qaeGCi+5utzv27t2wbx8cO5Z5cGEtPPMMfOMbLv3pYx+Dhx6CFSvgRz9y+1h89asjtpdd2TiXaNzSE40TNyGOhCt5rbaed//ZhS7AUHBxguWL6rnt+sXU11bQ2h1VWlRp+SbwtDHmR8aY/wSeAv5+nPd5CpCac7g/edkQxphVxpitxpitrxw8ynceegmAS/5pI02HO3hufyvX/qtbTPnG+uf59+T/v/P/z8Mcauvhid0tvO/OJwD4yq+e5adb9gKw+Nbf0tEb4+HnD3Hjj54E4Oa7n+Y3218DYP6X7wXgN9tf4+a7nwbgxh89ycPPH6KjN8biW38LwE+37OUrv3oWgPfd+QRP7G7hUFsP5/+fhwH4901NfGO9i5mu/dfHeG5/K02HO7jknzYC8J2HXtJzyvNzev8PNnPLmqeHTLZvXvM0n0n+PIjPaaz36VM/fSptvcI/P/iiZ8/pMz99ir9b/zxX3/EYN/z7Fq6+4zH+bv3zfOanT2X0nN535xNseeUo1eVl3Hz3dhpm1nDX468U7H1KJCwf+uEWrviXTdzw71u49J9/x/9sf42Hdhwsmb+n0RgvG0IZY+YA/wn8H+BzY61gnH7G2fbcm78/JH0HMkt/Sj07n3o2VBOWQRd9awNTKiOYlAmytZbW7iiPfenSvD1OfxpWUVLW+tOfst2not/u3S79af162LvXFV1fcolLf1q+HMrLM7ufUIg/vN7N6meOsLszwZxp1UrVk6Izxmyz1jZ6PQ4AY8xsYEny2y3W2oPjvL8/B1ZYaz+e/P5DwBJr7adHuk1jY6PdunXreB5WJoAndh/hhn/fcsLla1YtYWnDDA9GVPgz402HO7j6jsdOKHS/z8MVDD+OaTTjGW9QVj5GO6Z4XTn6L7gajtpMrvz68W7mtPcMTd+5fnFG+djaD2Ns2XTcGk+tRsFT1sYbVBw8CPfe64KK55939RBLl7qdta+4wtVIZMIYt19FbS3U1HDBGwwXLMt+OCKlwhizyFq70xhzbvKi/hWHk40xJ1trnxrH3b8GzE35fk7yMpGcJRKWWNz6qqtUMVK2/NiWNmjtg3Mdb6mk5HkWYCTrN5qttduMMctHud4qYBVA+dRZOQcI2g9jbJnmvPtyc7z+mopcg4rWVldPsXYtPPmkS4k680z46ld56s1L+e+mbg62dDP7vt2sbJzLkoXTR76vqioXVKhYW2S4z+H+n/9zmp9ZYDxLpU8CpxljFuACi5XA+8dxfyLsaenkr3/zHDdfehp3bNg1MOH71rvPynmyPd6z08WojxhPW9pCnX0PWvvgXMfr1/qXbHm5gnEhcL0x5mpcy8LJxpgfW2s/mHola+1qYDXAlHmLhuRzZRMgaD+MsWXaccsvq0Gbnt7DTx55nmPNRzmldtLYE//hurvh0UfdSsWmTYMdoD79abez9vz5bNndwu0bdhEJG2orIhzt7OX2Dbu4BYY+1gTer0IkU9baVcnPlxTgvmPGmE8DDwBh4IfW2h35fhyZWA619fBqSzf/vflVbryoAWPc+adTplTkNGnOx9npYp3Jz2V/hkKefffjqspoch1v0FZqRuLZTMha+xXgKwDJFYz/Z3hwMVxiWL1INgFCrh1pCt221W8ySV/ybDXI2oHN7zY/u5fvP7TTraJMCo888R8uFoMnnnBBxYMPuvurr4cPftAFFYsXDynSXrN1n9tJOtn9yX2Os2brPpa8sd6tUkyenPlu3CKCMeY9wG+tte3GmL/G7Ynxd9bap8dzv9ba+4D78jFGERg8C32gtYfvPfoy4M5Cv/vcE/oHZCQfZ6f9fCa/kGffC73ZX75XXnIdr5/f32wE6lSrteTcsjKX/TB8mQrkA0VfDerqcpvYdXRAwv3B/WzLnpEn/sMDDGth+3YXVNx/P7S0uKDgmmtcUHHeeRAeukdFv4Ot3QM7jPczlZXssBVuj4s0HaNEZEx/Y639hTHmIuBy4B+B7zNY9C3iC/k+a56Ps9N+PJPfPzl/6VB7Qc++p1tVyUdgUKiVl1xWgfz4/ubCFwGGtXYjsHGs6508pZL62oqcuw9lW1zsl1QgvynK/gTJlQo6OtLupJ1u4l9eFubVIx189mfbOdjazVt6W/jQ4Wc55fePuF25y8tdB6hrr3WtZieNvXFw//4V5ZMidJdX0VFZQ5tNnklQcCGSq/4/6muA1dbae40x3/ByQCLp5PuseT7OThf6TH62UifnH7+4oahn3/MVGPip7sFv72+ufBFgZKq2oqyoO/iqMDy9guyObi2bnt7DTze8wNEMairSbVx3rKuPqqOHWfLsg1zwwmbmHXqVhDEcP+c8pnzqU64DVE12/yjee+EbuO2x14hWVVNRHgnsZm8TLdVPfO81Y8yduF23v2WMKSeDfZlEvJDLWeiR5OvsdD7HNF6pk/N7tu0/oSC+kGff8xUY+K3uwU/vb64CFWAUmwrDR5aXVrPxuNsFu6ODLc/u5fuPvJRxTcXKxrncvmEXEGdqtJu37NjMW599nLMO7ALglZMXsuaKD/GH084jPGsW3/mzszMflzGutmLKFN72xgq+dPKc4u3bUQBK9RMfei+wAvgna+1xY8xJwBc8HlPgBKVXfrH5+XUplbPTqVIn5wdaewYK4s86ZTKnzaot6PPLV2BQKnUPfqIAYxRFSQWaaGKxwdSn7u6Bi9c8uTfzmgpgyclV/L/hPfT+z1oW7dpOWSLO3imz+Y/G63ns9CX0nTyH6vIyrIWO1u4Tbp9WWRnU1cGUKUNqMgq+b0eBKdVP/MZa22WMaQYuAnYBseTnCS/TyXGp9MrPtyC8LqVwdjrV8Mn5gdYe7nq8qSgb4OUrMCiVugc/UYAxioKkAk1EPT1upaKz032dxkg1FYdSg4NoFP7wB1es/fDDnNbVBbNm8fq73se/Vi3i6epZJKxxbQTbeqmfDOGQYVZd5ejjq6x0QUVNTUnWVSjVT/zGGPN1oBE4HfgPIAL8GNe+fMLKZnLsp5xxP9HrUnxeTs7zmXJWaitLXlOAMYagn732hLVudaK93QUVGWx8l66mojcWZ9bkCnjqKVi3znWAOnbMdYC69lr30djIP/7yOY529jI9bmlu78Ukuxkfae9lWk05KxvnnviA4bBLg6qrc8XfJUypfuJD7wLOAZ4CsNa+boyp9XZI3stmcuy3nHG/8Mvr4uc0rXzzcnKez8cutZUlrynAkPxIJFznp44OF1Sk6fw0mtSaivKyMDMOvMqSHX/gyj3b4NABFwRceqkLKpYtG9IBqn/1o38B5FhXH9G4xQK3XHra0BSrykoXVNTWgjETovhZqX7iQ33WWmuMOx1gjFEeAtlNjpUznp7Xr0siYdl7tJOn9h7nq79+zrdpWvnm5eRcgYE/KcCQ3MViA0XadHW5lYscLVk4nS8cOsD+n97DW57exLwj+7GhMObCC+BzfwWXXz5iB6jU1Y+aijJqKsroicaZVl3ugotw2K161NUNBCYbdzbzzftfYNfhDiKhELMml5ds8bNS/cRPjDEGWJ/sIjXFGPOXwMeAf/d2ZN7LZnKsnPH08v26ZLMS0Z/itvNgG6s3NSlNSyY0BRiSnb4+F1B0dIxYT5GVo0fhgQdg3TrO2baNcwDOPhs++VHMVVfB9FF25U4avvrRG4sTTcB7lp0OJ58M1dVDaiv6uyo1t/cQNgYLHGjt5eQpFUTCZqD4uZRWN5TqJ36RXLl4D/A5oA1Xh3GrtfYhb0fmvWwmx8oZTy+fr0u2BeP9KW4fv7jBF2laIl4KVIDR3hPjhtWbS2LC52fDJ9afWHoKb59T7WoqenvH/wBdXfDII65Y+/HH3UrIwoXwV3/lUqDmpqmZGMWShdO5BVizdR/7O2LUzZ7FR684kwsWn5T2+v1dleIJS9gYjDEksBxu72XBjGr2H+tSa1eRwnoKOG6tVWvaFNlOjpUakl6+XpdsC8ZTU9yUviYTXaACjNePdzOnvUcTvgLauLOZr//Pc9Qk+pif6IM9B7lz10tUDK9lyFY0Cr//vSvWfuQRVwR+0knwkY/AddfB6afn3sEpFGLJuQ0sueQcqBj7H3h/V6VJ4RCxuMUYSCQSdMVg58F2qiaF+dZvdwamtetYKy2ltBIjJWMJ8AFjzKtAZ/+F1tqzvBuSPyho8I9sC8b7U9yKvdmciB8FKsAwhkBM+AIpGoWODn7xm82ceryNykhyU90w9CTMiPtRjCqRGOwA9dvfwvHjrh3s9de7j3PPhdA4Nu8dVrCdqf6uSjNqynm9tZt4LEEsWT5igOryMC81dzBnytBgpdCtXXMJBMZaadFKjPjUlV4PQGQs2RaMp6a4/ffmV/nc5aex6KTJxOKWU5PBxUTqLiUTW6ACjNCwSaR6+Y9Tb+9gPUUy9eno4WNj70cxlhdfdEHFvffC66+7VYXLLnPpTxddNKQDVNbSFGxnq7+rUiRsOLmugn3H3HOrKAsxu66C2ooIx7qiHGrrZXLl4GMUsrVrroHAWJvoaZM98SNr7atej6GYNKkMpmwLxlNT3I529vLa8R5W/fe2gdt+9/3n0Bezvt4EUCRfAhVgJIZ1KVIv/xx0dw8GFdHoCT8ecT+KsTar27/fBRTr18NLL7lA4KKLXF3F5Ze7QutcGeNuP3nyCQXbkP2Z/+FdlSLhELMnlw8JJmbVlrP/eHfRWrvmGgiMtYmeNtkT8VYQdpb2G78EZLkUjPenuAF88K4/DqnfeHZ/q7pLFYBffl8KIcjPLVABhrWknfApx3wUWe5PkbYjU9ym36zu6FG3+d26dfD00+6yc86BW2+Fq66CadPGN/ZJk9xKxeTJLmBJI9cz/6ldlW5YvZnm9qEdscrCIU6bWcPU6vKitHbNNRAYaxM9bbIn4q1i7ywd5AkJ+C8gy7UmJl39RsKi7lJ55rffl3wK+nMLVIBx8pRK6msrhkz4AOWYD5esp6Cz061YZLE/RWpHpkOt3cyqq2Rl49zB+ovOTlekvW6dK9qOx+GNb4TPfx6uvhrmzBnf2EOhwR22MyjYzkcK0Egb0f3NNW8u2u9QroHAWJvoaZM9EW8Vc2fpoE9IoPgBWaGkq98IG3WXyrdS+X1JJ+jPLVABRm1FGXevWjrkshtWb1aOOQymPnV2ur0qxmHJwulDC7r7+mDDBpf+9Mgjbv+Lk0+GG290dRWnnz7OweOCif6C7SwKv/ORAuSHjehyDQTGGrsfnpvIRFbMnaWDPiGB4gZkhZSufuPMOXXaHDHPSuX3JZ2gP7dABRjpTNgc80TCBRP9H2OkPuV0/9u2uZWKBx4Y7AD1rne5oCLHDlBbdrewZus+DrZ2M7uuivcsfxMXnPeGjFYr0slXClAmG9EVMhVvPIHAWGPXJnsi3inmjttBn5BAcQOyQhqpfgPQ5oh5VCq/L+kE/bkFPsCYUDnm8fhggXZXV1apTxmxdmgHqAMHXCvYyy5ze1VceCFEImPfzwi27G7h9g27CEXKYPp0/lRWybYnDnPbzHqWL8rtD6ZYKUDFaPeqQECk9BRzx+2gT0iguAFZoY1Uv6F9TvLH778v46mJSn1uU6sm8Z7GObyxvhZr3f36PTA1Nt+T1AJqbGy0W7duHXJZ6sQvdYJ52/WLS2Oy1tvrVig6OlxqUiHs2+fSn9avh5dfhrIy1wHq2mtdcFGVn2DtU7/eyZ54hFBNzUAnqK6+GPW1FSekvmWjf2WhkClA/YXgqYFsPsYuUkzGmG3W2kavx+EX6Y4pQVYKNRgwOCnTWX7JhF9/X7L5exwpEEkkLHuPdvLU3uN89dfP+e7verRjimcrGMaYucB/AbMAC6y21t6e7f2USo75QPrN0U4W1oRZdc5MLjy5Km0r2bxoaXEdoNavH+wA9da3wt/+LVx55fg7QPUzxnWBmjKFZ9jPlJrIkDaz+UhnK8aZ/wmbiicigVHM1ZJC0m7mkg2//r5kWhM1ViCSsAwEF6Pdj994mSIVAz5vrX3KGFMLbDPGPGStfT7bOwp6asnv/vQ637pnG7XxXt5ko/Qdj/G9V/dSdulp2e+ePZqODnj4YZcC9cQTQztAXXutK9zOl0jE1WzU1Q3UagQ5nS3IYxeRicOvky2RIMsl1SnTmqixApGg1lZ5FmBYaw8AB5JftxtjXgBOAbIOMIJm485m7npkJy2HWmioMvS0dVKfSAxsbuc+x1mzdd/4A4y+PnjsMRdUbNjgUq5OOQX+8i/hmmtcgJFP1dUusEizsV6QW6YGeewiUhqCvseFSBDlmnqYaU3UWAFEUGurfFHkbYyZD5wDbEnzs1XAKoB58+YVd2D5ZC10dvL77Xv4t3XPUGESzCkL0348zv5jPcyePAlSds8uLwtzqLU7t8dKJODJJ1360wMPQGsrTJ0Kf/7nbqXinHNO2A17XEKhgTQoJk0a8WpBTmcL8thLmTbZlInCr/UVCnqk1OXa/jnTAvSxAgi/F7KPxPMAwxhTA9wD/JW1tm34z621q4HV4Ary8v34BZ2gxOODBdqdnWAtv3z0eSrM0NWKSBhaOvqoqRjM8e+NxZlVV5n5Y1kLL7ww2AHq0CFXnH355S6ouOCCcXWASqu83AUVWexdEZR0tpF+L4Iw9omiGJ29RPzCj3tc+DXoCQoFZ8GQa4pSpjVRYwUQQa2t8jTAMMZEcMHFT6y1vyr24xdkgtLf9al/F+1hDrZ2U1sxdKI/vXoSB9t66YnGKS8L0xtz6TcrG+eO/Xh79w52gNq92wURF18MX/oSXHqpazObT8a4gGLKlJz3rvA7TVyDIR+7uIsEhR/zsP0Y9ARF0IKziRwMjSdFKZOaqEwCiCDWVnnZRcoAdwEvWGu/7cUY8jJBsdbtSdG/UhGLjXr12XWVHO3sHVjBACgLh5g/rYrJVZM41NrNrLpKVjbOHbn+4vDhwQ5QzzzjLjvvPPjwh+GKK1w6VL6Vl7uC7cmTc9pgL0g0cQ0GdfaSfsaYfwSuA/qA3cBHrbXHPR1UnhUrDzubiaQfg57xKtZEOkjBWdCCoX75ei+LkaIUxABiLF6uYFwIfAh4zhizPXnZV6219xVrADlPUGKxwVWKri5X85ChlY1zuX3DLmDoasX/vvQNoxd0d3TAQw8NdoBKJGDRIvjCF1yx9kknZTyGjE2A1Yp0NHENBnX2khQPAV+x1saMMd8CvgJ8yeMx5VUxJjnpJpLfff85LJheQ3P7iZO0oBafjqSYE+lCBmf5DpKCFgztaemkpbOX14/38KV7nh33exnUFCWvedlF6nHA03cnqwlKd/dgUNHbm/NjLlk4nVuANVv3jb1a0dcHmzbB2rWwcaN73DlzYNUqt7P2G96Q8zhGNYFWK9LRxDUY1NlL+llrH0z5djPw516NpVCKMckZPpGcWjWJXYc6+PRPn047SQtq8elIijmRLlRwVoggKSgrVanP/caLGrjr8aa8vZeluMJQaJ4XeXtp1AlKIjEYUHR2uoLtPFmycPrIqxXxOPzxj4MdoNrbYfp0eO973UrF2WfntwNUvwCtVhS6c5AmrsGgzl4ygo8BP/N6EIVQ6EnO8Inkn507h9sf2TXiJK3UzuwWcyJdqOCsEEFSUFaqUp+7MQQiKCplEzrAGD5BmTd5Ep986ywuqulzBdM2702r0rMWduxwQcW990Jzs+sAdcUVLqi44AIoK9BbFbDVimIUYGviGhzq7DVxGGMeBman+dHXrLW/SV7na7hNXH8yyv2URuvzAhg+kcxkklZKZ3aLOZEuVHBWiCApKCtVw597EIKiUjahAwysZfmptSz/szekpD4li7aLYc8eF1SsW+e+jkRg2TLXVvaSS/LfAapfKORWK+rqslqt8MOeA8UqwNbEVcRfrLWXj/ZzY8xHgGuBy6wd+exQoVufB9nwiWTYTKxJWqEn0ulqI/IdnBUiSArKSlXqc79n235uvvQ07tiwy9dBUSmbeAFGNDpYnJ1lgXZeNDe7DlDr1sFzz7lTROedBx//uFuxqKsr3GNHIq7DVA6rFX5p3aoCbBEZzhizAvgi8HZrrf4Z5Gj4RHL25ApOnz3Z92eu86WQE+liFZDnGiSNVRgehJWq1Od+oLWHn23dy+oPNRIJmwnXWtcPzCgnenynsbHRbt26NbsbpbaR7epyhdPF1t4ODz7oVis2b3ZBzZvf7Aq1r74aZqdb9c+jykoXWNTk/o/hhtWbTyh87uqLUV9bwd2rluZjlIEah0gQGWO2WWsbvR5HvhljXgbKgZbkRZuttZ8Y63Y5HVMmmP6Jp5/PXI/FD3s4NB3u4Oo7HjthZeG+AhSQZ/ueBbUNbTql8PsaJKMdUwK1grHzYDs3rN48dmpOLDa4e3ZXV/FqKVL19sLvfudWKjZudIHNvHnwiU+4FKiFCwv7+Ma4gGLq1LwUbftl5UAF2CIynLW2QC31JAhnrkcTiyW4908H8tKudDyKWUCe7XsWpDa0Ywn672spCVSAURYyI6fm9PQMBhXjaCM7LvE4bNnigooHH3TjmTEDVq50QcVZZxWmA1SqUMilWU2dmtfCcL+0blUBtoiIZCKRsPyhqWUguADvJs9+7sQUlDa0EiyBCjAgpaj3d7tZPqdqcAftPLaRzYq1rpZi/Xq47z63y3Z1NVx5pesAtXRp4TpApYpEXIvZurqCdIPy08pBoQqw/VDELiIi+bGnpZOtrx71xeTZz52Y/Bz8SHAFK8Cwluqudqb1dtN3sANeH2Xn60JranItZdevH+wAtXy5W6lYvrx4e0lUV7vAorqw/6RKfeXAL0XsIiKSH4faekhYf3TC8nMnprGCHz/UsEjwBCrAiMSj1HUcoycaZ/ZkDyLrQ4fcKsW6dW7fCmPg/PNdB6grr3TdmYqhrMw9Vl2dC2yKpJRbtxar/a2IiBTHrMkVrHvmtRPalX7r3Wcxf3p10SfOfq0PGC34KaUCcCmuQAUYWOhJpuasbJxbnMdsa3M7aq9f7+orrIXFi+ErX4GrroJZs4ozDnCb7/WvVhS6lqOI/JCa5JcidhERyY/506v50oo38a3fvsCNFzUQDkHjqdO4oMFlP2jiPGik4KeUCsCluAIVYCSsZVp1OSsb57JkYQHTo3p6XOen9evd52gUTj0VPvUplwK1YEHhHnu4UMitVkyZApMmFe9xi+SOh1/iext3E0skKA+HiCcSA6lJQNECD78UsYuIjEUpK5kZODM/u/aEM/NNhzs0cc6ACsAlV4EKMBbMqOY77zu7MHcei7k9Ktavdx2gOjth5kz4wAdcsfaZZxZ31aDARdt+sHFnM9/buJuEtUTCIeIWWjqiTK+Bb97/Al3RRNFqIvxUxC4iMhKlrGRnpDPzmjhnRgXgkqtABRh5Zy08+6yrqbj/fjhyxO0dsWKF2wTv/PMhHC7umKqqXIvZAhdt+8Gdm5qIJyxlIYPBYAwksLR2RTnaGWXO1Mqi1USUehG7iJQGpazkhybOmfFz9yvxt4kZYOze7VYq1q+HvXtd6tEll7iViuXLoby8uOMp8TSokew71kV5WYhY3A4sDhkDvfEEZaEQlZGhwV2hayJKuYhdREqDzrznhybOmfFz9yvxt4kTYBw8ONgB6vnn3aR+6VL45CfhHe+A2tqs73LL7hbWbN3HwdZuZtdVZl8bMgHSoEYzd2oVsXiCls4+SLjgIm4tZaEQDTOq6Y7GVRMhIpJCZ97zQxPnzPm1+5X4W2kHGMePu3qKdevgySddStQZZ7gOUFdfDfW5n63esruF2zfsIhI21FZEONrZy+0bdnELjB1kFGnvCr/rr3uYXj2J9p4YvbEE4ZDhU8sXctacKaqJEBEZRmfe80cTZ5HCKb0Ao6cHNmxw6U+bNrkOUAsWwKc/7TpAzZ+fl4dZs3UfkbChIpnG4z7HWbN1X/oAIxweTIMq4t4VfjZW3YNqIkREhtKZ92BRxy+ZqEojwIjF4IknBjtAdXW51YkPftAFFYsX570D1MHWbmorhgYK5WVhDrV2D71iZaVLgaqtLXgXKj/sJ5Gt0eoeVBMhInIinXkPBnX8konM0wDDGLMCuB0IAz+w1n4z4xtbC88849Kf7rsPjh51k/irr3ZBRYE7QM2uq+RoZ+/ACgZAbyzOrLrKwaLturqiFYxv3NnMrWt3FK2tq4iIiIxMHb9kIvMswDDGhIHvAe8A9gNPGmPWWmufH/WGL7/sgop774V9+9wE/pJLXFDx9rePqwtTNkXbKxvncvuGXUCc8rIwvbE4XaaMj684Fxoail60feemJiJhU7S2riIiIjIydfySiczLFYzzgZettU0Axpg1wDuBkQOM3btdK9lQCN72Nrez9jve4fauGKdsi7aXLJzOLcCarftp6jXUzZ3Jpy57Exd7NJnfd6yLKZVDU7YK3dZVRERE0lPHL5nIvAwwTgH2pXy/H1gy/ErGmFXAKoCzIhH467+Gq66CGTPyOpisi7YjEZYsXcSSK05MxfKiFmLu1Cqa23vU1lVERMQH1PFLJjLfF3lba1cDqwEazzjD8qEPFeRxMi7arq52O21XpZ+4e1UL0d/yVW1dRUREvKeOXzKReRlgvAbMTfl+TvIyT4xZtF1Xl1GL2ULWQoy2MjJWy1cREREpLnX8konKywDjSeA0Y8wCXGCxEni/V4PJV9F2vmohhgcTb2uYxi+fem3UlRG1dRURERERr3kWYFhrY8aYTwMP4NrU/tBau8Or8aQWbb/SA5PnnMynLn9z1kXb+aiFSJdm9b2Nu5lWHaGu0hWHqUtUMPf9EBERESl1ntZgWGvvA+7zcgwDwmGWnHcaS95xHpTl/rLkoxYiXZpVPGFp7Yoyo2aw+8RE7hKlfT9ERLKX687S2pFaRLLh+yLvgisvd0XbedppOx+1EOnSrMrLQvTE4kMum8hdorTvh4hIdnLdWVo7UotItiZmgGGM2ztjyhSorMz73Y+3FiJdmlVtRRmxLjvhukSNlAalfT9ERLKT687S2pFaRLJV3O2mvRYOw7RpsGABnHRSQYKLfLhpWQPRuAsmrHWfJ5WF+dTyhdTXVtDaHaW+toLbrl9c0mfr+9Ogmtt7hqRBbdzZzNypVXRHtaIjIpKp0XaWLsTtRGTiKukVjC27W1izdR97u+LUza7nL644g+V53qCvEEZLs7rZ68EV0WhpUNr3Q0QkO7nuLK0dqUUkWyUbYGx55Rh//4fX6a2eQtlJlbwajXPruue5zZiczvoXu2ORWs6O3vJX+36IiGQn152lS3VH6tEK11XULjI+pRdgJIu2b99whI4p0/NSBKyORd4Yq+WvgjARkczlurN0Ke5IPVrhOqCidpFxKp0ajOpqmDMHTj0VJk9mb2sPlSm7ckPuRcCpqTrGuM+RsOHOTU35Gr2kka4WRWlQIjISY8znjTHWGOP/XFiP9O8svbRhBg0zazKeMOd6O78aqXB9T0vnqD8TkcwEO8AwxnWCmj8fTjkFqgYLfPNZBLzvWFfeghXJ3PJF9dx2/eIJVdguIrkxxswFrgD2ej0W8b/RCtdV1C4yfsFMkYpEoK7OfYTDaa+SzyLgfOzOLblRGpSIZOg7wBeB33g9EPG/sQrXVdQuMj7BWsEIh91KxYIFrt3sCMEF5Pfst1J1RET8yxjzTuA1a+0zGVx3lTFmqzFm6+HDh4swOvGj/sL1ioibBqUWro/2MxHJjLHWej2GjDU2NtqtW7d68tj9XaTUsUhEgsoYs81a2+j1OHJhjHkYmJ3mR18DvgpcYa1tNcbsARqttUfGuk8vjynivf5OUekK10f7mYg4ox1Tgpki5QGl6oiIeMdae3m6y40xZwILgGeMMQBzgKeMMedbaw8WcYgSMP2F6+l2Ix/tZyIyNgUYIiISWNba54CBsz/ZrGCIiEhhBKsGQ0REREREfE0rGCIiUjKstfO9HoOIyESnFQwREREREckbrWDkoL+j1L5jXcxVRykRERERkQFawcjSxp3N3Lp2B83tPUypjNDc3sOta3ewcWez10MTEREREfGcVjCydOemJiJhM7Crd9WkMrr6Yty5qaloqxhaQRERERERv/JkBcMY84/GmJ3GmGeNMb82xkzxYhy52Hesi8rI0B3EKyNh9h/rKsrjawVFRERERPzMqxSph4AzrLVnAS8BX/FoHFmbO7WK7mh8yGXd0ThzplYV5fFTV1CMcZ8jYcOdm5qK8vgiIiIiIqPxJMCw1j5orY0lv92M23k1EG5a1kA0bunqi2Gt+xyNW25a1lCUx/d6BUVEREQkaBIJS9PhDp7YfYSmwx0kEtbrIZU0P9RgfAz42Ug/NMasAlYBzJs3r1hjGtHyRfXchltJ2H+sizlFroGYO7WK5vaegRoQKO4KioiIiEiQJBKW3+44yOd+vp2eaIKKSIhvv/dsViyeTShkvB5eSSpYgGGMeRiYneZHX7PW/iZ5na8BMeAnI92PtXY1sBqgsbHRF+Hm8kX14wooxlOkfdOyBm5du4OuvhiVkTDd0XhRV1BEREREgmRPS+dAcAHQE03wuZ9vZ9HNF9Mws8bj0ZWmggUY1trLR/u5MeYjwLXAZdZaXwQOxdBfpB0JmyFF2rdBRkGG1ysoIiIiIkFyqK1nILjo1xNN0NzeowCjQDxJkTLGrAC+CLzdWjuhigfy0eZ2vCsoIiIiIhPFrMkVVERCQ4KMikiI+toKD0dV2rzqIvVdoBZ4yBiz3RjzfY/GUXQq0hYREREpnvnTq/n2e8+mIuKmvf01GPOnV3s8stLlyQqGtfYNXjyuH6hIW0RERKR4QiHDisWzWXTzxTS391BfW8H86dUq8C4gr1YwJiyv29yKiIiITDShkKFhZg1LG2bQMLNGwUWBKcAosuWL6rnt+sXU11bQ2h2lvraC265frJoKERERESkJftgHY8IJepH2eNrsioiIZCKRsOxp6eRQWw+zJiulRSRIFGBIVsbbZldERGQs2hhNJNiUIiVZSW2za4z7HAkb7tzU5PXQRESkRIy0Mdqelk6PRyYimVCAIVlRm10RESm00TZGExH/U4AhWZk7tYruaHzIZWqzKyIi+dS/MVoqbYwmEhwKMCQrarMrIiKFpo3RRIJNRd6SleWL6rkNV4ux/1gXc9RFSkRE8kwbo4kEmwIMyVrQ2+yKiIj/9W+M1jCzxuuhiEiWlCIlIiIiIiJ5owBDRERERETyRgGGiIiIiIjkjQIMERERERHJGwUYIiIiIiKSN8Za6/UYMmaMOQy86vU40pgBHPF6EBnSWAtDYy0MjTW/TrXWzvR6EH6RxTHFz++tn8cG/h6fxpYbjS03pTi2EY8pgQow/MoYs9Va2+j1ODKhsRaGxloYGqv4gZ/fWz+PDfw9Po0tNxpbbiba2JQiJSIiIiIieaMAQ0RERERE8kYBRn6s9noAWdBYC0NjLQyNVfzAz++tn8cG/h6fxpYbjS03E2psqsEQEREREZG80QqGiIiIiIjkjQKMURhjVhhjXjTGvGyM+XKan3/OGPO8MeZZY8wjxphTU34WN8ZsT36s9cFYP2KMOZwypo+n/OzDxphdyY8P+2Cs30kZ50vGmOMpPyv26/pDY0yzMeZPI/zcGGPuSD6XZ40x56b8rNiv61hj/UByjM8ZY/5gjHlLys/2JC/fbozZ6oOxLjfGtKa817em/GzU3x8PxvqFlHH+Kfk7Oi35s6K+rpK9DP4flRtjfpb8+RZjzPyUn30lefmLxpgrPRibZ8cgPx9z/HyM8fMxxc/HED8fM/x8jDDGzDXGPJr8P7HDGHNLmusU5nfOWquPNB9AGNgNNACTgGeANw+7ziVAVfLrTwI/S/lZh8/G+hHgu2luOw1oSn6emvx6qpdjHXb9zwA/9OJ1TT7eMuBc4E8j/Pxq4H7AAEuBLV68rhmO9YL+MQBX9Y81+f0eYIaPXtflwPrx/v4UY6zDrnsdsMGr11UfWb+3mfzv/N/A95Nfr+z/Pw+8OXn9cmBB8n7CRR6bJ8cgPx9z/H6M8fMxxc/HED8fM/x8jABOAs5Nfl0LvJTmb7Ugv3NawRjZ+cDL1toma20fsAZ4Z+oVrLWPWmu7kt9uBuYUeYz9xhzrKK4EHrLWHrXWHgMeAlYUaJyQ/VhvAO4u4HhGZa3dBBwd5SrvBP7LOpuBKcaYkyj+6zrmWK21f0iOBbz9fc3kdR3JeH7Xc5LlWD39fZWsZfL79E7gP5Nf/xK4zBhjkpevsdb2WmtfAV5O3l/RxubhMcjPxxxfH2P8fEzx8zHEz8cMPx8jrLUHrLVPJb9uB14AThl2tYL8zinAGNkpwL6U7/dz4puS6kZcBNivwhiz1Riz2RjzvwowvlSZjvXdyeWvXxpj5mZ523zJ+PGSy/0LgA0pFxfzdc3ESM+n2K9rtob/vlrgQWPMNmPMKo/GNNzbjDHPGGPuN8YsTl7m29fVGFOF++d7T8rFfnxdZVAmv08D17HWxoBWYHqGty302FIV8xjk52NO0I8xQTmm+PEY4utjhtfHCOPSO88Btgz7UUF+58pyGqUMYYz5INAIvD3l4lOtta8ZYxqADcaY56y1u70ZIQDrgLuttb3GmJtwZ+Qu9XA8mVgJ/NJaG0+5zG+va+AYYy7BHRwuSrn4ouTrWg88ZIzZmTwr45WncO91hzHmauB/gNM8HE8mrgN+b61NPZPlt9dVSpBPj0FBOOboGJMDnx5DgnDM8OwYYYypwQU2f2Wtbcv3/aejFYyRvQbMTfl+TvKyIYwxlwNfA6631vb2X26tfS35uQnYiIsaPRurtbYlZXw/AN6a6W3zLJvHW8mwpcQiv66ZGOn5FPt1zYgx5izc+/9Oa21L/+Upr2sz8Gvym+qRNWttm7W2I/n1fUDEGDMDn76uSaP9vvridZUTZPL7NHAdY0wZUAe0ZHjbQo/Nq2OQn485QT/G+PqY4tdjSECOGZ4cI4wxEVxw8RNr7a/SXKUwv3O2QIUlQf/Are404ZZP+wuDFg+7zjm44qHThl0+FShPfj0D2EUBC1EzHOtJKV+/C9hsB4t4XkmOeWry62lejjV5vUW44ifj1eua8rjzGbmw7BqGFkf90YvXNcOxzsPliV8w7PJqoDbl6z8AKzwe6+z+9x73D3dv8jXO6PenmGNN/rwOl4Nb7fXrqo+s3tdM/nd+iqFF3j9Pfr2YoUXeTeS3yNu3x6AMx+bJMSfT/xF4eIwZ43+fp8eUMcbm6TFkjLF5eswYbWzJn3tyjEi+Bv8F/Mso1ynI71xeX+BS+8BV1r+E+wf+teRlt+HOFAE8DBwCtic/1iYvvwB4LvmL/Bxwow/G+g/AjuSYHgUWpdz2Y8l/Gi8DH/V6rMnv/xb45rDbefG63g0cAKK4/MMbgU8An0j+3ADfSz6X54BGD1/Xscb6A+BYyu/r1uTlDcnX9Jnk78jXfDDWT6f8vm4m5YCW7vfHy7Emr/MRXMFv6u2K/rrqI6f3d6z/nRXAL5J/x38EGlJu+7Xk7V4ErvJgbJ4dgzIYm2fHnLHGlvz+b/HgGJPB/z7PjikZjM2zY0gGY/PsmDHW2JLX+QgeHCNwaWwWeDblfbu6GL9z2slbRERERETyRjUYIiIiIiKSNwowREREREQkbxRgiIiIiIhI3ijAEBERERGRvFGAISIiIiIieaMAQ0RERERE8kYBhoiIiIiI5I0CDJFxMsacZ4x51hhTYYypNsbsMMac4fW4REQkeHRMkVKgjfZE8sAY8w3cjr+VwH5r7T94PCQREQkoHVMk6BRgiOSBMWYS8CTQA1xgrY17PCQREQkoHVMk6JQiJZIf04EaoBZ31klERCRXOqZIoGkFQyQPjDFrgTXAAuAka+2nPR6SiIgElI4pEnRlXg9AJOiMMX8BRK21PzXGhIE/GGMutdZu8HpsIiISLDqmSCnQCoaIiIiIiOSNajBERERERCRvFGCIiIiIiEjeKMAQEREREZG8UYAhIiIiIiJ5owBDRERERETyRgGGiIiIiIjkjQIMERERERHJGwUYIiIiIiKSN/8XRhekovBfCmsAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<Figure size 957.6x295.2 with 2 Axes>"
       ]
@@ -3845,7 +3931,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 72,
    "id": "9a3edfab",
    "metadata": {},
    "outputs": [
@@ -3919,7 +4005,7 @@
        "4  2.486747  0.075106  0.005641"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 72,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3931,7 +4017,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 73,
    "id": "24c100a8",
    "metadata": {},
    "outputs": [],
@@ -3951,7 +4037,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 74,
    "id": "d6ac4ac8",
    "metadata": {},
    "outputs": [],
@@ -3962,7 +4048,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 75,
    "id": "078047e2",
    "metadata": {},
    "outputs": [
@@ -4019,7 +4105,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 76,
    "id": "fba76906",
    "metadata": {},
    "outputs": [],
@@ -4030,7 +4116,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 77,
    "id": "424e6080",
    "metadata": {},
    "outputs": [
@@ -4067,7 +4153,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
+   "execution_count": 78,
    "id": "74c19b10",
    "metadata": {},
    "outputs": [
@@ -4148,7 +4234,7 @@
        "6  445.311406  "
       ]
      },
-     "execution_count": 77,
+     "execution_count": 78,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4164,7 +4250,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 79,
    "id": "572d19c8",
    "metadata": {},
    "outputs": [],
@@ -4206,7 +4292,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 80,
    "id": "42c8cdf3",
    "metadata": {},
    "outputs": [],
@@ -4216,7 +4302,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 81,
    "id": "3131de8c",
    "metadata": {},
    "outputs": [
@@ -4299,7 +4385,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 82,
    "id": "43ac886e",
    "metadata": {},
    "outputs": [
@@ -4380,7 +4466,7 @@
        "6  445.311406  "
       ]
      },
-     "execution_count": 81,
+     "execution_count": 82,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4415,7 +4501,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 83,
    "id": "60322cd4",
    "metadata": {},
    "outputs": [
@@ -4563,23 +4649,266 @@
    "id": "7c272448",
    "metadata": {},
    "source": [
-    "## Families"
+    "### Families"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 84,
    "id": "01e6b10d-fc3a-4fe8-9f94-b3ff3a1278ea",
    "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>PassengerId</th>\n",
+       "      <th>Survived</th>\n",
+       "      <th>Pclass</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Sex</th>\n",
+       "      <th>Age</th>\n",
+       "      <th>SibSp</th>\n",
+       "      <th>Parch</th>\n",
+       "      <th>Ticket</th>\n",
+       "      <th>Fare</th>\n",
+       "      <th>Cabin</th>\n",
+       "      <th>Embarked</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Braund, Mr. Owen Harris</td>\n",
+       "      <td>male</td>\n",
+       "      <td>22.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>A/5 21171</td>\n",
+       "      <td>7.2500</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
+       "      <td>female</td>\n",
+       "      <td>38.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>PC 17599</td>\n",
+       "      <td>71.2833</td>\n",
+       "      <td>C85</td>\n",
+       "      <td>C</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3</td>\n",
+       "      <td>1</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Heikkinen, Miss. Laina</td>\n",
+       "      <td>female</td>\n",
+       "      <td>26.0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>STON/O2. 3101282</td>\n",
+       "      <td>7.9250</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
+       "      <td>female</td>\n",
+       "      <td>35.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>113803</td>\n",
+       "      <td>53.1000</td>\n",
+       "      <td>C123</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>Allen, Mr. William Henry</td>\n",
+       "      <td>male</td>\n",
+       "      <td>35.0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>373450</td>\n",
+       "      <td>8.0500</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>S</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   PassengerId  Survived  Pclass  \\\n",
+       "0            1         0       3   \n",
+       "1            2         1       1   \n",
+       "2            3         1       3   \n",
+       "3            4         1       1   \n",
+       "4            5         0       3   \n",
+       "\n",
+       "                                                Name     Sex   Age  SibSp  \\\n",
+       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
+       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
+       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
+       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
+       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
+       "\n",
+       "   Parch            Ticket     Fare Cabin Embarked  \n",
+       "0      0         A/5 21171   7.2500   NaN        S  \n",
+       "1      0          PC 17599  71.2833   C85        C  \n",
+       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
+       "3      0            113803  53.1000  C123        S  \n",
+       "4      0            373450   8.0500   NaN        S  "
+      ]
+     },
+     "execution_count": 84,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv('data/titanic.csv')\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "id": "e959c8a9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table class=\"simpletable\">\n",
+       "<caption>Generalized Linear Model Regression Results</caption>\n",
+       "<tr>\n",
+       "  <th>Dep. Variable:</th>       <td>Survived</td>     <th>  No. Observations:  </th>  <td>   714</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>   709</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Model Family:</th>        <td>Binomial</td>     <th>  Df Model:          </th>  <td>     4</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Link Function:</th>         <td>logit</td>      <th>  Scale:             </th> <td>  1.0000</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -323.64</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Date:</th>            <td>Tue, 28 Sep 2021</td> <th>  Deviance:          </th> <td>  647.28</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Time:</th>                <td>10:39:11</td>     <th>  Pearson chi2:      </th>  <td>  767.</td> \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>No. Iterations:</th>          <td>5</td>        <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
+       "</tr>\n",
+       "</table>\n",
+       "<table class=\"simpletable\">\n",
+       "<tr>\n",
+       "         <td></td>           <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Intercept</th>      <td>    3.7770</td> <td>    0.401</td> <td>    9.416</td> <td> 0.000</td> <td>    2.991</td> <td>    4.563</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.2]</th> <td>   -1.3098</td> <td>    0.278</td> <td>   -4.710</td> <td> 0.000</td> <td>   -1.855</td> <td>   -0.765</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Pclass)[T.3]</th> <td>   -2.5806</td> <td>    0.281</td> <td>   -9.169</td> <td> 0.000</td> <td>   -3.132</td> <td>   -2.029</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>C(Sex)[T.male]</th> <td>   -2.5228</td> <td>    0.207</td> <td>  -12.164</td> <td> 0.000</td> <td>   -2.929</td> <td>   -2.116</td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "  <th>Age</th>            <td>   -0.0370</td> <td>    0.008</td> <td>   -4.831</td> <td> 0.000</td> <td>   -0.052</td> <td>   -0.022</td>\n",
+       "</tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "<class 'statsmodels.iolib.summary.Summary'>\n",
+       "\"\"\"\n",
+       "                 Generalized Linear Model Regression Results                  \n",
+       "==============================================================================\n",
+       "Dep. Variable:               Survived   No. Observations:                  714\n",
+       "Model:                            GLM   Df Residuals:                      709\n",
+       "Model Family:                Binomial   Df Model:                            4\n",
+       "Link Function:                  logit   Scale:                          1.0000\n",
+       "Method:                          IRLS   Log-Likelihood:                -323.64\n",
+       "Date:                Tue, 28 Sep 2021   Deviance:                       647.28\n",
+       "Time:                        10:39:11   Pearson chi2:                     767.\n",
+       "No. Iterations:                     5                                         \n",
+       "Covariance Type:            nonrobust                                         \n",
+       "==================================================================================\n",
+       "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
+       "----------------------------------------------------------------------------------\n",
+       "Intercept          3.7770      0.401      9.416      0.000       2.991       4.563\n",
+       "C(Pclass)[T.2]    -1.3098      0.278     -4.710      0.000      -1.855      -0.765\n",
+       "C(Pclass)[T.3]    -2.5806      0.281     -9.169      0.000      -3.132      -2.029\n",
+       "C(Sex)[T.male]    -2.5228      0.207    -12.164      0.000      -2.929      -2.116\n",
+       "Age               -0.0370      0.008     -4.831      0.000      -0.052      -0.022\n",
+       "==================================================================================\n",
+       "\"\"\""
+      ]
+     },
+     "execution_count": 97,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model = smf.glm('Survived ~ Age + C(Pclass) + C(Sex)', df, family=sm.families.Binomial())\n",
+    "model = model.fit()\n",
+    "model.summary()"
+   ]
+  },
+  {
    "cell_type": "markdown",
    "id": "4d16690d-a3b2-4903-b746-04ce95030288",
    "metadata": {},
    "source": [
-    "### Hierarchical models"
+    "## Hierarchical models"
    ]
   },
   {
@@ -4594,8 +4923,405 @@
     "* crossed designs;\n",
     "* etc.\n",
     "\n",
-    "We cannot cover all cases and variations; just be careful whether your observations are independent and were sampled randomly ([good read](https://online.stat.psu.edu/onlinecourses/sites/stat503/files/lesson14/recognize_split_plot_experiment.pdf))."
+    "We cannot cover all cases and variations. Especially, the field of mixed-effects models is too vast to even give an introduction.\n",
+    "\n",
+    "A key point is to be careful whether your observations are independent and were sampled randomly ([good read](https://online.stat.psu.edu/onlinecourses/sites/stat503/files/lesson14/recognize_split_plot_experiment.pdf))."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec030ec2",
+   "metadata": {},
+   "source": [
+    "### Repeated measures ANOVA and sphericity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "647f42e4",
+   "metadata": {},
+   "source": [
+    "Example (one-way): each animal observed multiple times, *e.g.* at different ages; and we are not interested in the putative differences between animals.\n",
+    "\n",
+    "$$\n",
+    "SS_{\\textrm{total}} = SS_{\\textrm{treatment}} + (SS_{\\textrm{subject}} + SS_{\\textrm{error}})\n",
+    "$$\n",
+    "\n",
+    "$$\n",
+    "F^* = \\frac{\\frac{SS_{\\textrm{treatment}}}{k - 1}}{\\frac{SS_{\\textrm{error}}}{(k-1)(n-1)}}\n",
+    "$$\n",
+    "\n",
+    "Designs are balanced.\n",
+    "\n",
+    "Let us borrow an example from `pingouin` documentation:"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 142,
+   "id": "bea2319c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Subject</th>\n",
+       "      <th>Time</th>\n",
+       "      <th>Metric</th>\n",
+       "      <th>Performance</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Product</td>\n",
+       "      <td>13</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Product</td>\n",
+       "      <td>12</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Client</td>\n",
+       "      <td>12</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Client</td>\n",
+       "      <td>19</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>20</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Action</td>\n",
+       "      <td>17</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>21</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Pre</td>\n",
+       "      <td>Action</td>\n",
+       "      <td>18</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>30</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Post</td>\n",
+       "      <td>Product</td>\n",
+       "      <td>18</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>31</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Post</td>\n",
+       "      <td>Product</td>\n",
+       "      <td>6</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "    Subject  Time   Metric  Performance\n",
+       "0         1   Pre  Product           13\n",
+       "1         2   Pre  Product           12\n",
+       "10        1   Pre   Client           12\n",
+       "11        2   Pre   Client           19\n",
+       "20        1   Pre   Action           17\n",
+       "21        2   Pre   Action           18\n",
+       "30        1  Post  Product           18\n",
+       "31        2  Post  Product            6"
+      ]
+     },
+     "execution_count": 142,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import pingouin as pg\n",
+    "\n",
+    "data = pg.read_dataset('rm_anova2')\n",
+    "data.loc[[0,1,10,11,20,21,30,31]]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7cdbf3b2",
+   "metadata": {},
+   "source": [
+    "In this example, each subject (`Subject`) has undergone all possible measurements, for all levels of the `Time` and `Metric` factors.\n",
+    "As a consequence, the observations for each subject are not independent, and this must be accounted for by the model.\n",
+    "\n",
+    "In a standard repeated measures ANOVA, the covariance structure is just assumed to exhibit a property called sphericity.\n",
+    "\n",
+    "`Time` and `Metric` are called *within-subject* factors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "831d8c07",
+   "metadata": {},
+   "source": [
+    "`statsmodels` features [AnovaRM](https://www.statsmodels.org/stable/generated/statsmodels.stats.anova.AnovaRM.html) but corrections for departure from sphericity are not implemented and we should first perform a Mauchly's test for sphericity, for example with [pingouin.sphericity](https://pingouin-stats.org/generated/pingouin.sphericity.html):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 143,
+   "id": "a7df0d24",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SpherResults(spher=True, W=0.6247989838343564, chi2=3.762602454747652, dof=2, pval=0.15239168046050933)"
+      ]
+     },
+     "execution_count": 143,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pg.sphericity(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 144,
+   "id": "6a8362eb",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>F Value</th>\n",
+       "      <th>Num DF</th>\n",
+       "      <th>Den DF</th>\n",
+       "      <th>Pr &gt; F</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>Time</th>\n",
+       "      <td>33.85228</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>9.0</td>\n",
+       "      <td>0.000254</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Metric</th>\n",
+       "      <td>26.95919</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>18.0</td>\n",
+       "      <td>0.000004</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Time:Metric</th>\n",
+       "      <td>12.63227</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>18.0</td>\n",
+       "      <td>0.000373</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              F Value  Num DF  Den DF    Pr > F\n",
+       "Time         33.85228     1.0     9.0  0.000254\n",
+       "Metric       26.95919     2.0    18.0  0.000004\n",
+       "Time:Metric  12.63227     2.0    18.0  0.000373"
+      ]
+     },
+     "execution_count": 144,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from statsmodels.stats import anova\n",
+    "result = anova.AnovaRM(data, depvar='Performance', subject='Subject', within=['Time', 'Metric']).fit()\n",
+    "result.anova_table"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bb44cf31",
+   "metadata": {},
+   "source": [
+    "In contrast, [rm_anova](https://pingouin-stats.org/generated/pingouin.rm_anova.html) from `pingouin` does implement Greenhouse-Geiser correction."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 145,
+   "id": "a66cb913",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Source</th>\n",
+       "      <th>SS</th>\n",
+       "      <th>ddof1</th>\n",
+       "      <th>ddof2</th>\n",
+       "      <th>MS</th>\n",
+       "      <th>F</th>\n",
+       "      <th>p-unc</th>\n",
+       "      <th>p-GG-corr</th>\n",
+       "      <th>np2</th>\n",
+       "      <th>eps</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>Time</td>\n",
+       "      <td>828.816667</td>\n",
+       "      <td>1</td>\n",
+       "      <td>9</td>\n",
+       "      <td>828.816667</td>\n",
+       "      <td>33.85228</td>\n",
+       "      <td>0.000254</td>\n",
+       "      <td>0.000254</td>\n",
+       "      <td>0.789976</td>\n",
+       "      <td>1.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>Metric</td>\n",
+       "      <td>1365.233333</td>\n",
+       "      <td>2</td>\n",
+       "      <td>18</td>\n",
+       "      <td>682.616667</td>\n",
+       "      <td>26.95919</td>\n",
+       "      <td>0.000004</td>\n",
+       "      <td>0.000005</td>\n",
+       "      <td>0.749716</td>\n",
+       "      <td>0.969103</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>Time * Metric</td>\n",
+       "      <td>224.433333</td>\n",
+       "      <td>2</td>\n",
+       "      <td>18</td>\n",
+       "      <td>112.216667</td>\n",
+       "      <td>12.63227</td>\n",
+       "      <td>0.000373</td>\n",
+       "      <td>0.001708</td>\n",
+       "      <td>0.583955</td>\n",
+       "      <td>0.727166</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "          Source           SS  ddof1  ddof2          MS         F     p-unc  \\\n",
+       "0           Time   828.816667      1      9  828.816667  33.85228  0.000254   \n",
+       "1         Metric  1365.233333      2     18  682.616667  26.95919  0.000004   \n",
+       "2  Time * Metric   224.433333      2     18  112.216667  12.63227  0.000373   \n",
+       "\n",
+       "   p-GG-corr       np2       eps  \n",
+       "0   0.000254  0.789976  1.000000  \n",
+       "1   0.000005  0.749716  0.969103  \n",
+       "2   0.001708  0.583955  0.727166  "
+      ]
+     },
+     "execution_count": 145,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pg.rm_anova(data, dv='Performance', subject='Subject', within=['Time', 'Metric'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccd20d1c",
+   "metadata": {},
+   "source": [
+    "Note that neither `AnovaRM` nor `rm_anova` give access to the model's coefficients.\n",
+    "\n",
+    "Mixed effects models are increasingly popular and preferred over the standard repeated measures ANOVA, especially because sphericity simply cannot be expected from the data in most cases."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4de57a31",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
-- 
GitLab