diff --git a/notebooks/statsmodels_TP_solutions.ipynb b/notebooks/statsmodels_TP_solutions.ipynb
deleted file mode 100644
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-{
- "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": {},
- "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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\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 for different types of sum of squares.."
- ]
- },
- {
- "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(Sex) * C(Pclass)', df).fit()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "f09c5fea",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
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- "<table border=\"1\" class=\"dataframe\">\n",
- " <thead>\n",
- " <tr style=\"text-align: right;\">\n",
- " <th></th>\n",
- " <th>df</th>\n",
- " <th>sum_sq</th>\n",
- " <th>mean_sq</th>\n",
- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>46.721986</td>\n",
- " <td>46.721986</td>\n",
- " <td>126.001800</td>\n",
- " <td>5.241061e-27</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>318.408489</td>\n",
- " <td>159.204245</td>\n",
- " <td>429.348645</td>\n",
- " <td>1.619836e-122</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>5.990345</td>\n",
- " <td>2.995172</td>\n",
- " <td>8.077506</td>\n",
- " <td>3.402042e-04</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>12.274132</td>\n",
- " <td>12.274132</td>\n",
- " <td>33.101391</td>\n",
- " <td>1.306440e-08</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>1.486269</td>\n",
- " <td>1.486269</td>\n",
- " <td>4.008232</td>\n",
- " <td>4.566288e-02</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>0.296834</td>\n",
- " <td>0.148417</td>\n",
- " <td>0.400257</td>\n",
- " <td>6.703004e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Sex):C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>1.335653</td>\n",
- " <td>0.667827</td>\n",
- " <td>1.801023</td>\n",
- " <td>1.658921e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>702.0</td>\n",
- " <td>260.304489</td>\n",
- " <td>0.370804</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Sex) 1.0 46.721986 46.721986 126.001800 5.241061e-27\n",
- "C(Pclass) 2.0 318.408489 159.204245 429.348645 1.619836e-122\n",
- "C(Sex):C(Pclass) 2.0 5.990345 2.995172 8.077506 3.402042e-04\n",
- "Age 1.0 12.274132 12.274132 33.101391 1.306440e-08\n",
- "Age:C(Sex) 1.0 1.486269 1.486269 4.008232 4.566288e-02\n",
- "Age:C(Pclass) 2.0 0.296834 0.148417 0.400257 6.703004e-01\n",
- "Age:C(Sex):C(Pclass) 2.0 1.335653 0.667827 1.801023 1.658921e-01\n",
- "Residual 702.0 260.304489 0.370804 NaN NaN"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(model, typ=1)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "cf4e3edc",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<div>\n",
- "<style scoped>\n",
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- "<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(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\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)</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):C(Pclass)</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(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)</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):C(Pclass)</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(Sex) 12.597516 1.0 33.973508 8.516312e-09\n",
- "C(Pclass) 318.183365 2.0 429.045083 1.856872e-122\n",
- "C(Sex):C(Pclass) 3.489752 2.0 4.705654 9.331214e-03\n",
- "Age 12.274132 1.0 33.101391 1.306440e-08\n",
- "Age:C(Sex) 1.421046 1.0 3.832335 5.066866e-02\n",
- "Age:C(Pclass) 0.296834 2.0 0.400257 6.703004e-01\n",
- "Age:C(Sex):C(Pclass) 1.335653 2.0 1.801023 1.658921e-01\n",
- "Residual 260.304489 702.0 NaN NaN"
- ]
- },
- "execution_count": 9,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(model, typ=2)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "bc136eb5",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<div>\n",
- "<style scoped>\n",
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- " }\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(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>Intercept</th>\n",
- " <td>252.996076</td>\n",
- " <td>1.0</td>\n",
- " <td>682.290368</td>\n",
- " <td>1.334116e-105</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>0.819888</td>\n",
- " <td>1.0</td>\n",
- " <td>2.211108</td>\n",
- " <td>1.374692e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass)</th>\n",
- " <td>31.940629</td>\n",
- " <td>2.0</td>\n",
- " <td>43.069411</td>\n",
- " <td>2.273902e-18</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):C(Pclass)</th>\n",
- " <td>1.012273</td>\n",
- " <td>2.0</td>\n",
- " <td>1.364970</td>\n",
- " <td>2.560654e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>0.776183</td>\n",
- " <td>1.0</td>\n",
- " <td>2.093243</td>\n",
- " <td>1.483980e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Sex)</th>\n",
- " <td>0.179743</td>\n",
- " <td>1.0</td>\n",
- " <td>0.484739</td>\n",
- " <td>4.865140e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Pclass)</th>\n",
- " <td>0.437814</td>\n",
- " <td>2.0</td>\n",
- " <td>0.590357</td>\n",
- " <td>5.544041e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age:C(Sex):C(Pclass)</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",
- "Intercept 252.996076 1.0 682.290368 1.334116e-105\n",
- "C(Sex) 0.819888 1.0 2.211108 1.374692e-01\n",
- "C(Pclass) 31.940629 2.0 43.069411 2.273902e-18\n",
- "C(Sex):C(Pclass) 1.012273 2.0 1.364970 2.560654e-01\n",
- "Age 0.776183 1.0 2.093243 1.483980e-01\n",
- "Age:C(Sex) 0.179743 1.0 0.484739 4.865140e-01\n",
- "Age:C(Pclass) 0.437814 2.0 0.590357 5.544041e-01\n",
- "Age:C(Sex):C(Pclass) 1.335653 2.0 1.801023 1.658921e-01\n",
- "Residual 260.304489 702.0 NaN NaN"
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(model, typ=3)"
- ]
- },
- {
- "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": 11,
- "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>Mon, 04 Oct 2021</td> <th> Prob (F-statistic):</th> <td>9.94e-131</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time:</th> <td>16:44:52</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(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]</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]:C(Pclass)[T.2]</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(Sex)[T.male]:C(Pclass)[T.3]</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(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]</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]:C(Pclass)[T.2]</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(Sex)[T.male]:C(Pclass)[T.3]</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: Mon, 04 Oct 2021 Prob (F-statistic): 9.94e-131\n",
- "Time: 16:44:52 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(Sex)[T.male] -0.3766 0.253 -1.487 0.137 -0.874 0.121\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]:C(Pclass)[T.2] 0.2608 0.338 0.771 0.441 -0.404 0.925\n",
- "C(Sex)[T.male]:C(Pclass)[T.3] 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(Sex)[T.male] -0.0044 0.006 -0.696 0.487 -0.017 0.008\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]:C(Pclass)[T.2] 0.0058 0.009 0.617 0.537 -0.013 0.024\n",
- "Age:C(Sex)[T.male]:C(Pclass)[T.3] -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": 11,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "model.summary()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ecf3bcd9",
- "metadata": {},
- "source": [
- "## Q\n",
- "\n",
- "Because we have a large sample, we will ignore the not-normal residuals and play with post-hoc tests instead.\n",
- "\n",
- "First proceed considering type-3 sums of squares."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "06c5bc0c",
- "metadata": {},
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "f203eea0",
- "metadata": {},
- "source": [
- "We found a single main effect and no interaction. Therefore a single call to `t_test_pairwise` is enough."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "id": "248c081c",
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
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- "<div>\n",
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- "<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>|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>2-1</th>\n",
- " <td>-1.460550</td>\n",
- " <td>0.251403</td>\n",
- " <td>-5.809591</td>\n",
- " <td>9.496387e-09</td>\n",
- " <td>-1.954142</td>\n",
- " <td>-0.966958</td>\n",
- " <td>1.899277e-08</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-1</th>\n",
- " <td>-2.016639</td>\n",
- " <td>0.217384</td>\n",
- " <td>-9.276845</td>\n",
- " <td>2.121528e-19</td>\n",
- " <td>-2.443439</td>\n",
- " <td>-1.589838</td>\n",
- " <td>0.000000e+00</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-2</th>\n",
- " <td>-0.556089</td>\n",
- " <td>0.211313</td>\n",
- " <td>-2.631590</td>\n",
- " <td>8.685267e-03</td>\n",
- " <td>-0.970969</td>\n",
- " <td>-0.141208</td>\n",
- " <td>8.685267e-03</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " coef std err t P>|t| Conf. Int. Low \\\n",
- "2-1 -1.460550 0.251403 -5.809591 9.496387e-09 -1.954142 \n",
- "3-1 -2.016639 0.217384 -9.276845 2.121528e-19 -2.443439 \n",
- "3-2 -0.556089 0.211313 -2.631590 8.685267e-03 -0.970969 \n",
- "\n",
- " Conf. Int. Upp. pvalue-hs reject-hs \n",
- "2-1 -0.966958 1.899277e-08 True \n",
- "3-1 -1.589838 0.000000e+00 True \n",
- "3-2 -0.141208 8.685267e-03 True "
- ]
- },
- "execution_count": 12,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "model.t_test_pairwise('C(Pclass)').result_frame"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "dc0a30ce",
- "metadata": {},
- "source": [
- "## Q\n",
- "\n",
- "Let us suppose we want to use type-1 sums of squares instead.\n",
- "\n",
- "Proceed again to performing with `Sex` first, `Pclass` second, and `Age` last.\n",
- "\n",
- "In the post-hoc comparisons, we will disregard the effect of the slope of `Age`."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "7a417d76",
- "metadata": {},
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "id": "9466f266",
- "metadata": {},
- "outputs": [
- {
- "data": {
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- "<table border=\"1\" class=\"dataframe\">\n",
- " <thead>\n",
- " <tr style=\"text-align: right;\">\n",
- " <th></th>\n",
- " <th>df</th>\n",
- " <th>sum_sq</th>\n",
- " <th>mean_sq</th>\n",
- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>46.721986</td>\n",
- " <td>46.721986</td>\n",
- " <td>126.001800</td>\n",
- " <td>5.241061e-27</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>318.408489</td>\n",
- " <td>159.204245</td>\n",
- " <td>429.348645</td>\n",
- " <td>1.619836e-122</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>5.990345</td>\n",
- " <td>2.995172</td>\n",
- " <td>8.077506</td>\n",
- " <td>3.402042e-04</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>12.274132</td>\n",
- " <td>12.274132</td>\n",
- " <td>33.101391</td>\n",
- " <td>1.306440e-08</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):Age</th>\n",
- " <td>1.0</td>\n",
- " <td>1.486269</td>\n",
- " <td>1.486269</td>\n",
- " <td>4.008232</td>\n",
- " <td>4.566288e-02</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass):Age</th>\n",
- " <td>2.0</td>\n",
- " <td>0.296834</td>\n",
- " <td>0.148417</td>\n",
- " <td>0.400257</td>\n",
- " <td>6.703004e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):C(Pclass):Age</th>\n",
- " <td>2.0</td>\n",
- " <td>1.335653</td>\n",
- " <td>0.667827</td>\n",
- " <td>1.801023</td>\n",
- " <td>1.658921e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>702.0</td>\n",
- " <td>260.304489</td>\n",
- " <td>0.370804</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Sex) 1.0 46.721986 46.721986 126.001800 5.241061e-27\n",
- "C(Pclass) 2.0 318.408489 159.204245 429.348645 1.619836e-122\n",
- "C(Sex):C(Pclass) 2.0 5.990345 2.995172 8.077506 3.402042e-04\n",
- "Age 1.0 12.274132 12.274132 33.101391 1.306440e-08\n",
- "C(Sex):Age 1.0 1.486269 1.486269 4.008232 4.566288e-02\n",
- "C(Pclass):Age 2.0 0.296834 0.148417 0.400257 6.703004e-01\n",
- "C(Sex):C(Pclass):Age 2.0 1.335653 0.667827 1.801023 1.658921e-01\n",
- "Residual 702.0 260.304489 0.370804 NaN NaN"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sstype = 1\n",
- "model = smf.ols('LogFare ~ C(Sex) * C(Pclass) * Age', df).fit()\n",
- "sm.stats.anova_lm(model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "b81407bd",
- "metadata": {},
- "outputs": [],
- "source": [
- "class1_model = smf.ols(data=df[df['Pclass']==1], formula='LogFare ~ C(Sex) * Age').fit()\n",
- "class2_model = smf.ols(data=df, formula='LogFare ~ C(Sex) * Age', subset=df['Pclass']==2).fit()\n",
- "class3_model = smf.ols(data=df, formula='LogFare ~ C(Sex) * Age', subset=df['Pclass']==3).fit()\n",
- "female_model = smf.ols(data=df, formula='LogFare ~ C(Pclass) * Age', subset=df['Sex']=='female').fit()\n",
- "male_model = smf.ols(data=df, formula='LogFare ~ C(Pclass) * Age', subset=df['Sex']=='male').fit()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 48,
- "id": "7a8fb3ff",
- "metadata": {},
- "outputs": [
- {
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- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
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- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>16.921191</td>\n",
- " <td>16.921191</td>\n",
- " <td>24.642531</td>\n",
- " <td>0.000002</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>3.609442</td>\n",
- " <td>3.609442</td>\n",
- " <td>5.256474</td>\n",
- " <td>0.023009</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):Age</th>\n",
- " <td>1.0</td>\n",
- " <td>0.179743</td>\n",
- " <td>0.179743</td>\n",
- " <td>0.261762</td>\n",
- " <td>0.609532</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>182.0</td>\n",
- " <td>124.973231</td>\n",
- " <td>0.686666</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Sex) 1.0 16.921191 16.921191 24.642531 0.000002\n",
- "Age 1.0 3.609442 3.609442 5.256474 0.023009\n",
- "C(Sex):Age 1.0 0.179743 0.179743 0.261762 0.609532\n",
- "Residual 182.0 124.973231 0.686666 NaN NaN"
- ]
- },
- "execution_count": 48,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(class1_model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 49,
- "id": "c5285b28",
- "metadata": {},
- "outputs": [
- {
- "data": {
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- " <th>sum_sq</th>\n",
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- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
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- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>0.342733</td>\n",
- " <td>0.342733</td>\n",
- " <td>1.606820</td>\n",
- " <td>0.206683</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>1.837992</td>\n",
- " <td>1.837992</td>\n",
- " <td>8.616976</td>\n",
- " <td>0.003794</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):Age</th>\n",
- " <td>1.0</td>\n",
- " <td>0.014816</td>\n",
- " <td>0.014816</td>\n",
- " <td>0.069461</td>\n",
- " <td>0.792444</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>169.0</td>\n",
- " <td>36.047528</td>\n",
- " <td>0.213299</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Sex) 1.0 0.342733 0.342733 1.606820 0.206683\n",
- "Age 1.0 1.837992 1.837992 8.616976 0.003794\n",
- "C(Sex):Age 1.0 0.014816 0.014816 0.069461 0.792444\n",
- "Residual 169.0 36.047528 0.213299 NaN NaN"
- ]
- },
- "execution_count": 49,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(class2_model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 50,
- "id": "ed33eab1",
- "metadata": {},
- "outputs": [
- {
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- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
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- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Sex)</th>\n",
- " <td>1.0</td>\n",
- " <td>6.706018</td>\n",
- " <td>6.706018</td>\n",
- " <td>23.707935</td>\n",
- " <td>1.698447e-06</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>7.188755</td>\n",
- " <td>7.188755</td>\n",
- " <td>25.414566</td>\n",
- " <td>7.423701e-07</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Sex):Age</th>\n",
- " <td>1.0</td>\n",
- " <td>2.562140</td>\n",
- " <td>2.562140</td>\n",
- " <td>9.057990</td>\n",
- " <td>2.804656e-03</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>351.0</td>\n",
- " <td>99.283729</td>\n",
- " <td>0.282860</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Sex) 1.0 6.706018 6.706018 23.707935 1.698447e-06\n",
- "Age 1.0 7.188755 7.188755 25.414566 7.423701e-07\n",
- "C(Sex):Age 1.0 2.562140 2.562140 9.057990 2.804656e-03\n",
- "Residual 351.0 99.283729 0.282860 NaN NaN"
- ]
- },
- "execution_count": 50,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(class3_model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "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='LogFare ~ Age', subset=(df['Pclass']==3)&(df['Sex']=='female')).fit()\n",
- "class3_male_model = smf.ols(data=df, formula='LogFare ~ Age', subset=(df['Pclass']==3)&(df['Sex']=='male')).fit()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 51,
- "id": "ecfbec15",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<div>\n",
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- " <thead>\n",
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- " <th></th>\n",
- " <th>df</th>\n",
- " <th>sum_sq</th>\n",
- " <th>mean_sq</th>\n",
- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>161.657909</td>\n",
- " <td>80.828955</td>\n",
- " <td>298.564938</td>\n",
- " <td>1.564532e-67</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>1.190732</td>\n",
- " <td>1.190732</td>\n",
- " <td>4.398312</td>\n",
- " <td>3.695942e-02</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass):Age</th>\n",
- " <td>2.0</td>\n",
- " <td>0.437814</td>\n",
- " <td>0.218907</td>\n",
- " <td>0.808596</td>\n",
- " <td>4.466221e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>255.0</td>\n",
- " <td>69.034842</td>\n",
- " <td>0.270725</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Pclass) 2.0 161.657909 80.828955 298.564938 1.564532e-67\n",
- "Age 1.0 1.190732 1.190732 4.398312 3.695942e-02\n",
- "C(Pclass):Age 2.0 0.437814 0.218907 0.808596 4.466221e-01\n",
- "Residual 255.0 69.034842 0.270725 NaN NaN"
- ]
- },
- "execution_count": 51,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(female_model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "id": "27783db9",
- "metadata": {},
- "outputs": [
- {
- "data": {
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- "<div>\n",
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- " <thead>\n",
- " <tr style=\"text-align: right;\">\n",
- " <th></th>\n",
- " <th>df</th>\n",
- " <th>sum_sq</th>\n",
- " <th>mean_sq</th>\n",
- " <th>F</th>\n",
- " <th>PR(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>C(Pclass)</th>\n",
- " <td>2.0</td>\n",
- " <td>162.740925</td>\n",
- " <td>81.370462</td>\n",
- " <td>190.163977</td>\n",
- " <td>1.748903e-60</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Age</th>\n",
- " <td>1.0</td>\n",
- " <td>12.569668</td>\n",
- " <td>12.569668</td>\n",
- " <td>29.375501</td>\n",
- " <td>9.770492e-08</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>C(Pclass):Age</th>\n",
- " <td>2.0</td>\n",
- " <td>1.194674</td>\n",
- " <td>0.597337</td>\n",
- " <td>1.395985</td>\n",
- " <td>2.486663e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>447.0</td>\n",
- " <td>191.269647</td>\n",
- " <td>0.427896</td>\n",
- " <td>NaN</td>\n",
- " <td>NaN</td>\n",
- " </tr>\n",
- " </tbody>\n",
- "</table>\n",
- "</div>"
- ],
- "text/plain": [
- " df sum_sq mean_sq F PR(>F)\n",
- "C(Pclass) 2.0 162.740925 81.370462 190.163977 1.748903e-60\n",
- "Age 1.0 12.569668 12.569668 29.375501 9.770492e-08\n",
- "C(Pclass):Age 2.0 1.194674 0.597337 1.395985 2.486663e-01\n",
- "Residual 447.0 191.269647 0.427896 NaN NaN"
- ]
- },
- "execution_count": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(male_model, typ=sstype)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 52,
- "id": "d27e6f05",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<div>\n",
- "<style scoped>\n",
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- " .dataframe thead th {\n",
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- " }\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>|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>-0.376602</td>\n",
- " <td>0.344650</td>\n",
- " <td>-1.092709</td>\n",
- " <td>2.759659e-01</td>\n",
- " <td>-1.056625</td>\n",
- " <td>0.303421</td>\n",
- " <td>2.759659e-01</td>\n",
- " <td>False</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>2-1 [female]</th>\n",
- " <td>-1.460550</td>\n",
- " <td>0.214814</td>\n",
- " <td>-6.799136</td>\n",
- " <td>7.430834e-11</td>\n",
- " <td>-1.883585</td>\n",
- " <td>-1.037514</td>\n",
- " <td>1.486167e-10</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-1 [female]</th>\n",
- " <td>-2.016639</td>\n",
- " <td>0.185746</td>\n",
- " <td>-10.856966</td>\n",
- " <td>8.025683e-23</td>\n",
- " <td>-2.382430</td>\n",
- " <td>-1.650847</td>\n",
- " <td>0.000000e+00</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-2 [female]</th>\n",
- " <td>-0.556089</td>\n",
- " <td>0.180558</td>\n",
- " <td>-3.079828</td>\n",
- " <td>2.297810e-03</td>\n",
- " <td>-0.911664</td>\n",
- " <td>-0.200513</td>\n",
- " <td>2.297810e-03</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>2-1 [male]</th>\n",
- " <td>-1.199737</td>\n",
- " <td>0.243363</td>\n",
- " <td>-4.929821</td>\n",
- " <td>1.162003e-06</td>\n",
- " <td>-1.678016</td>\n",
- " <td>-0.721459</td>\n",
- " <td>2.324005e-06</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-1 [male]</th>\n",
- " <td>-1.540414</td>\n",
- " <td>0.214036</td>\n",
- " <td>-7.196980</td>\n",
- " <td>2.619517e-12</td>\n",
- " <td>-1.961057</td>\n",
- " <td>-1.119772</td>\n",
- " <td>7.858714e-12</td>\n",
- " <td>True</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>3-2 [male]</th>\n",
- " <td>-0.340677</td>\n",
- " <td>0.181482</td>\n",
- " <td>-1.877194</td>\n",
- " <td>6.114252e-02</td>\n",
- " <td>-0.697341</td>\n",
- " <td>0.015987</td>\n",
- " <td>6.114252e-02</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] -0.376602 0.344650 -1.092709 2.759659e-01 \n",
- "2-1 [female] -1.460550 0.214814 -6.799136 7.430834e-11 \n",
- "3-1 [female] -2.016639 0.185746 -10.856966 8.025683e-23 \n",
- "3-2 [female] -0.556089 0.180558 -3.079828 2.297810e-03 \n",
- "2-1 [male] -1.199737 0.243363 -4.929821 1.162003e-06 \n",
- "3-1 [male] -1.540414 0.214036 -7.196980 2.619517e-12 \n",
- "3-2 [male] -0.340677 0.181482 -1.877194 6.114252e-02 \n",
- "\n",
- " Conf. Int. Low Conf. Int. Upp. pvalue-hs \\\n",
- "male-female [1st class] -1.056625 0.303421 2.759659e-01 \n",
- "2-1 [female] -1.883585 -1.037514 1.486167e-10 \n",
- "3-1 [female] -2.382430 -1.650847 0.000000e+00 \n",
- "3-2 [female] -0.911664 -0.200513 2.297810e-03 \n",
- "2-1 [male] -1.678016 -0.721459 2.324005e-06 \n",
- "3-1 [male] -1.961057 -1.119772 7.858714e-12 \n",
- "3-2 [male] -0.697341 0.015987 6.114252e-02 \n",
- "\n",
- " reject-hs \n",
- "male-female [1st class] False \n",
- "2-1 [female] True \n",
- "3-1 [female] True \n",
- "3-2 [female] True \n",
- "2-1 [male] True \n",
- "3-1 [male] True \n",
- "3-2 [male] False "
- ]
- },
- "execution_count": 52,
- "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(female_model.t_test_pairwise('C(Pclass)').result_frame, ' [female]'),\n",
- " suffix_label(male_model.t_test_pairwise('C(Pclass)').result_frame, ' [male]'),\n",
- "])\n",
- "comparisons"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 53,
- "id": "80024bdf",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(array([False, True, True, True, True, True, False]),\n",
- " array([2.75965894e-01, 3.71541686e-10, 0.00000000e+00, 6.87760334e-03,\n",
- " 4.64800385e-06, 1.57174274e-11, 1.18546626e-01]))"
- ]
- },
- "execution_count": 53,
- "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": "5e3fa114",
- "metadata": {},
- "source": [
- "Compared with type-3 sums of squares, we lost one effect whose test-wise $p$-value was very close to the significance threshold.\n",
- "Of note, this difference comes from the type of sum of squares and not the correction for multiple comparisons."
- ]
- },
- {
- "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": 23,
- "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": 54,
- "id": "7a8dacd7",
- "metadata": {},
- "outputs": [],
- "source": [
- "mi = pd.read_csv('../data/mi.csv', index_col=0)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "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": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "mi.head()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "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": 55,
- "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": 56,
- "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": 57,
- "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": 58,
- "id": "87455d20",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(4.715752340548497, 0.2806838326518803)"
- ]
- },
- "execution_count": 58,
- "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": 59,
- "id": "645ef445",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "SkewtestResult(statistic=23.771971688844314, pvalue=6.512720346814304e-125)"
- ]
- },
- "execution_count": 59,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "stats.skewtest(mi['PhysicalActivity'])"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 60,
- "id": "f5984bf0",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "SkewtestResult(statistic=3.242519136674468, pvalue=0.0011847799127530753)"
- ]
- },
- "execution_count": 60,
- "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": 61,
- "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": 62,
- "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": 63,
- "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": 36,
- "id": "93e6b4ee",
- "metadata": {},
- "outputs": [],
- "source": [
- "import statsmodels.api as sm"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 64,
- "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",
- "X = np.stack((np.ones_like(logPA), logPA), axis=1)\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": {},
- "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": 65,
- "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>Mon, 04 Oct 2021</td> <th> Prob (F-statistic):</th> <td>1.17e-19</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time:</th> <td>16:58:36</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: Mon, 04 Oct 2021 Prob (F-statistic): 1.17e-19\n",
- "Time: 16:58:36 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": 65,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "model = smf.ols('Temperature ~ HeartRate + logPA', extended_mi).fit()\n",
- "model.summary()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 66,
- "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>Mon, 04 Oct 2021</td> <th> Prob (F-statistic):</th> <td>7.55e-19</td>\n",
- "</tr>\n",
- "<tr>\n",
- " <th>Time:</th> <td>16:58:39</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: Mon, 04 Oct 2021 Prob (F-statistic): 7.55e-19\n",
- "Time: 16:58:39 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": 66,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "model = smf.ols('Temperature ~ HeartRate * logPA', extended_mi).fit()\n",
- "model.summary()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 68,
- "id": "a33e1981",
- "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(>F)</th>\n",
- " </tr>\n",
- " </thead>\n",
- " <tbody>\n",
- " <tr>\n",
- " <th>HeartRate</th>\n",
- " <td>6.099911</td>\n",
- " <td>1.0</td>\n",
- " <td>66.738819</td>\n",
- " <td>1.183498e-15</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>logPA</th>\n",
- " <td>1.147271</td>\n",
- " <td>1.0</td>\n",
- " <td>12.552240</td>\n",
- " <td>4.183161e-04</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>HeartRate:logPA</th>\n",
- " <td>0.033699</td>\n",
- " <td>1.0</td>\n",
- " <td>0.368699</td>\n",
- " <td>5.438840e-01</td>\n",
- " </tr>\n",
- " <tr>\n",
- " <th>Residual</th>\n",
- " <td>74.216587</td>\n",
- " <td>812.0</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",
- "HeartRate 6.099911 1.0 66.738819 1.183498e-15\n",
- "logPA 1.147271 1.0 12.552240 4.183161e-04\n",
- "HeartRate:logPA 0.033699 1.0 0.368699 5.438840e-01\n",
- "Residual 74.216587 812.0 NaN NaN"
- ]
- },
- "execution_count": 68,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sm.stats.anova_lm(model, typ=2)"
- ]
- },
- {
- "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": 69,
- "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": 69,
- "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": 70,
- "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": {
- "heading_collapsed": true
- },
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 42,
- "id": "77e350be",
- "metadata": {
- "hidden": true
- },
- "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": 43,
- "id": "377783b7",
- "metadata": {
- "hidden": true
- },
- "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": 44,
- "id": "e07bc434",
- "metadata": {
- "hidden": true
- },
- "outputs": [
- {
- "data": {
- "image/png": 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RLQLwXwDuBvAAgI9memEisgL4CYDTABwA8CIRbZa0pt0khLg86dhaAOsBdAEQAF6KHTuY6XhkBMIRlNutqgZF5XYrAhHz4a7ZzGjNmFMyefj3HJH3OZnTWJlSRiMf+IMR/PTpXarr//TpXfjRuYuyOm8uFGMkIvD0zsOJUiZv9Qyjb9SPFXMaJ6VQLfZkgpnYmFUgISGEIKI1iK4C7iGiy7K89lIAu4QQuwGAiDYCWAPATG/zTwB4UggxEDv2SQCrAPw6yzGpqC134t7n9iRyAsIR4N7n9uDezy81fY5sHLtGyifTh//9Ia+0z0nPkLcgCmRwLCi9/uBYdiuQXJj89g94sLN3VNXs6sqVHZjdUIG2+snnRC92SDkzsTEbxjtCRN8E8DkAfyQiCwB7lteeAeBfitcHYtuSOYeIXiei3xHRzDSPBRGtJaJuIuru6+tLa4BWC3DhSS2qcNcLT2pBuu1A4vb7Ze31aG+oMD2zU5pT7vzcidi09oM4fd74TDjT3hVOq1Xa58RhLUwmek2ZXXr9mrLsflK5qBnVO+yXVsntHTYfODGR4DpbTDaYXYFcAOAiAJcJIQ4RUQuivol88xiAXwsh/ET0fwDcD2BFOicQQmwAsAEAurq60qqK1zPkw5/e6MFN5y7CmD+EcqcNd217D0taphRkNhqJCPz5rV7NFYbWw7/PwKTlCYSkx3kCobTHl4ntPJPrm7lWLiKotMbmVYxtMvkMOOqMyQZTCkQIcQjArYrX+xH1gWTDQQAzFa+bMe4sj1+nX/HybgA3KY79WNKxT2c5nhSaql345IImfP13r5lq+pNrjMwLWg//K/86ituf2qVp0mqpdUuPa6k1H2mUje1csxaXXf5zjEQEtr7Tm1JiPdkvkYsIqlaDe5Pu5y51ZcNRZ0w26BpjiGiEiIYl/0aIaDjLa78IoIOIZhGRA8CFADYnXb9J8XI1gLdifz8B4HQiqiGiGgCnx7blFK2mPwUqGWVoXpBlXl+5sgO/7T6Q2Fdm0ppVL8/YnlVvXmhk0/o1IiJYf2an6vrrz+yEgPzGKv0S8RLrO3tHsX9Afa1Uk98ylcnPDEb3Jp3PHVc2Z9z+LD5z1z9xxu3P4vEdhzIqMZ8v4j66LeuWY+Pak7Fl3XJ2oDOm0V2BCCEq83VhIUSIiC5HVPBbAdwrhNhBRNcB6BZCbAawjohWAwgBGADwhdixA0T0fUSVEABcF3eo55J0mv7kAyPzQrKDnkD4z02vomdo3H4tC/vNRahqNiXhy2w23LltlyoT/c5tu3D7BfJMdC2/xIktNSpTYiQi8Nd3D+ONg+MRVIdH/Fg517wSMQp6SCe0eqI4qAuVY1PqqzEmfdJKJCSiqQAS9puYKStjhBBbAGxJ2naN4u9vAvimxrH3Arg3m+sbUWz7sBnzgvLh3903ikGvup6UbLxGvhUzZFMS3hsMS1v1eoPyGmNm/BIAsPfIKHYdTo2gOq7ejfap5udCegJ1aqX8N9FQkV4jqFJSIIWAw4UnJ6biiYhoNRHtBLAHwDMA9gL4Ux7HVRLkqyOgWdI1L5gdbzbmpzjxkvDJBRHNlITXKo6o1Ws+7pdI3j/ZZ/P+kE+6Unl/KHcRRVYLcOXKjhSzodWSWjQzrmySx30sOqhz8ZtjSg+zK5DvA1gG4C9CiCVE9HFEQ3onNcUuOhgfg1nzgtnx9g77UFPuwKdPbE4k8j380oG0ZsZ1bie2vn1IFaF2/3O7TZWET9dxO6vejVvOW4z/+u34/recl+qzGfHJVyoj/vSiy/ToGfLhgef3qcxvDzy/Dye11eDNnhHVZ7rjoiXsoI7Bq7HJiVkFEhRC9BORhYgsQoi/EtH/5nNgpUIkIjDiC+KoN4gyuw2RiCjpJbcZhdNU7cJXPn4cDo/4E1FNX/n4cSnRZXo265aacly4tFUVoZZO3wyHjVQZ/g6b/j112tX7O+2p+0+rdsrLxlQ6TY3JDI1VLgx6AyrzW7yXSfIM+/KHXsHjVy43rHl2LFBsczCTH8wqkKNEVAFgG4BfEdFhAJN+7RkKRfDIawdTmgudvWgGbLaJ20olqhRDKb4CZXSQkc1aq2/GiS3aBRHj7O334PKHXkkRJls0nMtm969y2qW1y6pd6SUo6ilOrdWTNxCWzrAPDfsSCaTHMhwuPDkxq0DWAPAB+CqAzwKoBnBdvgZVKuzoGcKPt+5U1Wz68dad6JhagUUza4o7uCzoGZb7ChY2VyeczUYRRNmYJNI91uz+u/s9UvPS7KkVOK7RnBPdSHFqmQn39nt4hq1DIc3BHO1VOMwmEipXGzmveluq9Hv8uPRDs9DvDSRMPZd+aBYGPBO7rIWmr8A37iswEtrpRCMlk+6xZs0fbqdVal4yExkWx0zorcxMmMkMO9eCrtQFZyHChTnaq7CYLec+gmjVWwBwIFoHyyOEkHcAmiTUljtxYGBMtY0IqCnPnU3diHwIhfoKh1Qg17kdiddGQttqAb71ybk44hlXrnVuh6k6YfFIpmRTk9axZoWz2y4vv+92ZN+/xWhlle4MO9eCjgVnlImSezNZMLsCSaz/iYgQNWkty9egSoVQRMATCKf4CsIFyiTOl1CwWYDrVnfims07Eue9bnUnlBN1I6HdN+rHWDCiujdfPfV4HBn1G9YJ04pkWjxTXmPMbOLjEY9fet7jG80LjsYqF1rryhIVmAHgsdcOmjJFpTPD3nNELujmXLE8oyRVFpxRONqrsKTdkVAIIQA8QkTrAXwj90MqHfyhsNRXcM/nuwpy/VwLmTihCOEnT6szwX/y9C7cct7ixD5GM2qH1YL/+cu7qrH9z1/exaa1xvOKcodNFXVFsSgsLVOT2cTHcqdNw4Rl/mfeUlOOK1Z0pAROmI0uM8v+AY9U0O0f8GT03bLgjMLRXoXFrAnr04qXFkQbOU36es/+YET6UPqTtuWLXAuZOIdHfNJM8OQS3nozaq2oI29Ank2uJCIi+PePzMa1fxhfAa0/sxPRuUkqZmfXIhKtsZV6XvPfVzbRZengdsoz+dMxtylhwRmFo70Ki9lf61mKv0OIZqKvyfloSoz6SnleQX2FQ+eo3JFrIRNnqsbnaqgw79vRMvVoZZMrsRAlhDwQFdLX/mGH5urF7Oy63GHHndu2p9TYuk2jxlY218oWfyiayZ/cVCsQNlbAMlhwRimF5N9jCbM+kC/meyCliD8UxldPPT5hqonb+f0FKsebayETR0DuxEYaz1g2ph691YssaMDs7HrQG5CurI4m1QfTo7HKha7WalzyoXZVhn2uZ/LTq8vxnUfUym5T9358otN8t0slLDjHKVRxSMZAgRDRjzEefZWCEGJdzkdUQjisVjz5ZqyhVCCEckdUmCybVZv1uc1EV+VayMQ56g1Knc0daZjF9g3ITT1LZtYYmte0w3id0qCB0+c1movCctqkq6J0fCDN1WU4/yR1hv11a+ajubrM9Dni6H3Hs+rd+O6ZJyR6nNgswHfPPCGtkvrJlLrgLPUwYyZ9jJ6s7tj/HwZwAoBNsdfnwVzv8gnNWDCIc05sUQmT9Wd2whfKrraS2eiqWfVuXL1qXsp+ekLGzENaXWaXOpur02gpuy8L/4xWCLAvFJb6OuJFJI1m15q+FY0+IzLe6h3GNY+qFeM1j27HnMbx5FEz99jMdxwICVUU263nLzY9ThmlLKA5zHhyYtQP5H4AIKL/AHCKECIUe30ngGfzP7ziYiGLqm8FELWp33zuoqzOa9YpbMYsoRQaTdWulIJ+soe0scqJG89ZgPf6PAkB3t7gxtQq8z4Qt2Y5d+PZvlYIsFb/lbj/wWh2XWazyX0rXzYfcd4zJC80eWjIh0Uz9QUhgMR3Ue6w4cbH39L8jnMddlvqAprDjCcnZtf2NQCqEG3qBAAVsW2TGl8whAu6WlJ8EL5gdiuQdBy1emaJZKGxbuXshFCOn1P2kIbCAr3DfpUAv+q04xEKm89vaaxySv0ojSaUkMMiDwH+5WUnZxVJ5NHyrWj0GZHRXFOGSz7YmvK5ZtRETVhagnDOFcuxp39U1Xb30g/Nwp3bdicafCm/42wacskodQHNYcaTE7MVAW8A8AoR/YKI7gfwMoAfZntxIlpFRO8Q0S4iSskpIaKriOhNInqdiJ4iolbFe2EiejX2b3PysbmgzG5LKA8g+oO/fetOuDR6d5tFqx9Guo7aZKEREdB8SJX0DPlw65NqAX7rk++qOhka0VLrRkdjBdZ+pB2Xr5iNtR9pR0djham+6gPegHSco75gop9JU7UL61bOxo/OXQQhYKoNbDxqTUm6pUxcNqs098dli55DSxDK2u56g2Fc8sHW8XMrvuN4Qy6zY03uNZJ8P4zaHxebXP3mmdLCbBTWfUT0JwAnxzZdLYQ4lM2FicgK4CcATgNwAMCLRLRZCKH0rbwCoEsI4Y2Z0W4CcEHsvTEhxOJsxmDEoIagO+oNZnXeXIVcyoSGmRn8qEaHP4/f/EzdYiGsmNOI9vqKtKN+tLoZljls+MjxtTjhyuV4ef9RfOv3b6RljomICL53Vie+99i4D+R7Z2nnl8joG/VL780Rjx+zUakZEeZ22KSK50cxc2fydxwIh/HNVXNVddZqyx3ShlxmzFOlngfCYcaTE6MorLlCiLeJ6MTYpn/F/p9ORNOFEC9nce2lAHYJIXbHrrUR0dyShAIRQvxVsf8/UOAmVlVldulDWVWW3QokVyGXyULj4ZcOpJiVZA9pTbm8FtaU8vTKnmca9dNY5cRVpx2fWAXFTWiNVU5YLISIQEJ5AObNMXarBRYS+NG5i+AJhOB22OANBGEzU6ArMTZ9QawlCP1hufnMabdg49qTU77jercT/nAkxYxY5041AZoxT5W6gOYw48mJkSS8CsBaALdI3hMAVmRx7RkYV0hAdBVyssa+AHAZ1G10XUTUjWhi4w1CiEdkBxHRWkQ/A1paWtIa4FgwJM3D8KVhU9ciFyGXyUJj0BtAR2MF/njFcvSNaj+k4XAY68/qxLWKmfr6szoRjmT/uczQPKUcrXXlKkFvtxGap0RzSDK1l/uDEfR7grhm85sq/0U6lQOMBLGWINxzRF7Ovb2+QhqVNuILSs2IshBxM/cj3YCLYkRplXqYcToU+16WCkZRWGtj/3+8MMORQ0SfQ7R8ykcVm1uFEAeJqB3AViJ6QwjxXvKxQogNADYAQFdXV1pVEK1kwabu/Sl5GN9fMz+LT5M79ISGXiit22HHnc8kZWw/k17GNmD8EGm9f+CoF71DvpQw3gNHvWirr8jYHOMLhfHUW6ltdhc2V5v+TGYLNwLR+xZnVr1c8WiFXL8/JFcKPUM+LJyp3jfd+yGz2JV6lNZEgu/lOGZrYZ0H4HEhxAgRfQfAiQC+L4R4JYtrHwSgfFSaY9uSr30qgG8D+KgQItGIQwhxMPb/biJ6GsASACkKJBuqXDZceFJLSkROlTM7E1Y6GAnpTGZ1nkBYmrE9lsbKyugh0nu/fzQAXyjVfNM/GkBbvXwVcMdFSyAE8Px7RzRnfASBcz+gztv53lmdIO1cWOnn0ivcGIkIbH2nVxVttaC5GivmNKZlommqLpMqhWnVqUpBa1XUUlOO3X2jpkK4Sz1KayLB93Ics5Lwu0KI3xLRKQBOBXAzgDuhb3Iy4kUAHUQ0C1HFcSGAi5Q7ENESAD8HsEoIcVixvQaAVwjhJ6J6RBMdb8piLFIcNgtm1JSpenHPqCmDw16Ydrb5mulo1dhKJ1rJqFKw3kMWCEfwq3/uU+XX/Oqf+7BgRnSlkLyymlYVFY7/9uNnde+Dw2pNONDj1/zeYzvw4KXmM/eNhMP+AQ/29XtVyu9rn5iD/QMetNUb56rE6WyqwvVnz08pBdPZlLpakq00W2rKVYrOKIS7FMJoJ4vZpxTuZalgVoHEp6b/BmCDEOKPRHR9NhcWQoSI6HIATwCwArhXCLGDiK4D0C2E2IyooqoA8NtoGxLsF0KsBjAPwM+JKIJoKPINSdFbOWFoLIjhMXXE1fBYEENj2UVhmSVfM51AOIxvnzEPfaP+xCy6vsIpjQDSYl+/fia63kMWCIVx0dLWlBpjgdD4Cki5strdN2rqPvSNyqPmjoyar4XVOyxPJIwLhyOjftz8xDuqsdz8xDtY1Fxt2AdFic1mwdmLZqBjagUODfkwLWYqs9nkk5PklWbyPdEL4W5vMGcWzKeAn0xmn1KPeCskZhXIQSL6OaIhtzcSkRPmc0g0EUJsAbAlads1ir9P1TjuOQALsr2+EeEIcP0f30r5odx9SWH6gZiZ6WTy0E+tdGJ3n0c1i752dScaKs1norscFulD5IgJQL2H7MioX5pI+IDGSsHsjK/SJV9ZVbrMmxybql3SRMJpsSrDA56gdCwDnvQnFTabBYtm1mDRTON9k0k3hNsoOEDPNJcLAT+ZzD6lHvFWSMw+WecDWAXgR0KIo0TUBOBr+RtWaRAIyfuBpDNTzwajmU6ms7pBTxDrN6tNPes378DGLy9Da525sTmtVmkmejzhTu8h23V4RHpftfJrzM74at126Zhq3ObDk8MRYOOL+1XmtY0v7sfpJ0RLlZQ5rBo5LObNf7kgkxBuh41U5lhlUy9lIqTy3s1uqEhrZaXFZDL7cEjyOGYTCb1EdBjAKQB2Iho6uzOfAysF6ivkfTNq3YXpB2I008l0Vvf+0Jj0YX5/aAyLTVaoqatwoNJlUwmkSpcNdbFeKXoPmWYdLadcCJud8XkCYdSW21Vjqi23Y8xEk6s4A16/tHzNoNcPoAL1FXZpCHR9RXo5NEB2JqN0Q7j39ntw+UOvpNzzLQkfiV+aCHliS01OFMhkM/tMppDkbDAbhbUe0TDaOQDuA2AH8EtEndeTlkA4Iq0aG0yjZlQ2GIWUZjqr01KM9Wk0lGqeUo7qMjsOjyQC41BdZk/kcsTHL3vIKl02qRDWim4zO+Orcztx40tvRXt5KMrv33TuYtOfy2GxSMvXxAsy2i1W3PnMrpQQ6HsuOcn0NYDsfQLphnAb1d7y+OXVCbwB/bpvZpUgm30mJ2ZNWJ9CNEz2ZQAQQrxPRJV5G1WJMOoPSKvGjvqzd6KbLQmuF1Ka6ayuusyKa1d3JsxYcR9IdZl5M8z+QS++9rvXU67dOb3acFY25AtJhfD1Z2u7tczM+HLRy0OrTtdgrClV36hfGgIdL3Villz0u09nFqxVPiYeeafVfbNOZ7WdjhJMnQyVobOp6pg0+0wmzCqQgBBCEJEAACI6JqYNLptN6uy97wvpzzaVyiI5BFPrwdvb78GNj7+lssff+PhbmDutEu0NFWipKZeGghp1BRz0hvHTp9UC/KdP78JN55gvU5+NTXvUF5IK4VF/dlWOzfTyMEI7xDn6qKSjtPUmCdn0U8mEQFje3TLuz9PqvhnQ8felY0I1mgwxExNDBULR+Nk/xKKwphDRlwFcCuCufA+u2GS6rFcim6XdeM5C3PrkO4YPXr9Hbo8f8PijOQmDXvx4606VIvjx1qjdWk+Ij/qCUgE+4jO/ssrGpt1YJZ/tTk3DhCajRyO7O97LwwyhcFhakDEUK/Ni1hRjNDvPpp9KJtS5ndKqCqvmT0u8/9AL6i6VD72wD6ed0Kh5znQmEZMpCosZx/DXGlt5nIdoXaxhRP0g1wghnsz34IpNpUYxxUqXeYep7MG5+uHXcdkp7SoBLnvwHFYNe/zaqD2+d9gnVQRGq4Bqjc+VTkfCbGzawUhEWkwxJLKLbjOb3S1bEe4f9KJ32AeHzYpyB0XrdPlDcLts8PqDiJfwN2uKMRKY2fRTyYS2Onl3y/j3ZfS+jHQmEZMpCosZx+x052UAR4UQkz50V8lRb1BacvtoGomEWg9OcoFY2YPnDYSlSW3eWFRRpquAYDiM9Wd2prR+DYbTK+eeqU17eCyE+/6+VzXbve/ve3Hdmk7T15fR2VSFm89diJ2HRxPf1+ypFars7uSVQWtdGa5Y0ZEwA7bWleHfPzob1z72mkqwt0UiieO1TDHAeEdCCxFqyh2qHitKgdlS68YJ0ytViqrSZTXVTyUTjAIRMglNTWcSMdmisJgoZhXIyQA+S0T7AHjiG4UQC/MyqhKhvsKBvf2elJpN9WmE8TZWudBaV4YzF85IKIHHXjuIrtbaxAOl9eA1VbvwHx9tV0WB/cdH29FUrZ8cZiH9mlE2ixUPv7w/pejg1z8xT/NzyGbtT7zZi//67fi1bzlvMT4539im3VjlkvZkb0wjkVGGxUJw2dWBAC67NcWvpFwZnLlwRkJ5xF9fm1QO5bandiaSR7Wc38dffgrePTyq+i6uXNmBB57fl1AiyQIzGBZ49/CIKnEvn5h1upttn5KO0uEorMmJWQXyibyOokQJRSLSktsPXGreid5SU66a4cYd3cvaarHF4METIprbkJzcFX/Akx/ghgoX9vSPYtVt+jWjAuEwVsydpopWWreiAwGNFYjMnn/vF7oSyiN+b/7rt69iTuMpmN2oH40kIkIaxptG3ycp+/o92HVYngw3KyY0k0uVzJxSppoVO23qWXL8s8VzSbSc33skJqvbntqJtR9px+1P7UoRmPlI3Mu0OnL8vUzCis0qJU6+Kw75rj9mNpFwX86uOIE46pU70Y96zTvR9w96VTNcXzCC7zyyPeHo1nvwDo9oJ3fFBWJyzShlspiWo7LSaZf6VjbGch2Skdnz+0flJT329HsMFchoIISHX4qtgBT5Gi2nzdE9zoj3h8ak92thc3XifiWXKrly5WyVaWVWvVtqaqmK+Ye0nN8uu1V6P5bMnCJtKJVu4p4Z5ZBpdeRCVevl5LvCUoj6Y4WrSz4BqSrLvrZSNs5Dj0brWWUUmFKwjAXlXfGSrzXgDUh9K4PegFRQyQoMVmnUnUo2IcmIRATWLG7GLoX5Zs3i5rRaz8rw+OWfX9mqNxyBSnD/pltdAuTIiE8j3DXud5I7v2vK5YEJrXVu6fecToSfGUFgFPJtpCDYyT35KMSkgBWIDj6NjoT+kHlnczbOw9aacumxM2N5HsmCJXk2rXWt6jK7tGBgrdshFVSd0ytT9j++cWFKJFVckBpRU+7A9veHU8w3U8qyKxFT55a36lUmwx0eUQvKniEfHnh+H+7/4lIICNgsFvzXb19NCXf90HHRZlvNU8rRnFTiv7mmDMc3VKZl408ncc+MIOj3+KUVjuMh30YKgp3ck49CTAoK09higuKwWROx85evmI3LTmnHpu79cOj02I5EBHb3jeL5945gd98oWmrKcev5i+GyR49Jx3lotRKuOu141bFXnXY8bNbxWadSsMRn00bXikSE1HwSCEWkguqoJ5iy/9d/9zrmz6jCj85dhBvPWYAfnbsI7Q1uzG2sMvxcR8eCiYKFl6+YjS8tb8fGF/enFd0mIwKBdSvUn3/dig5EFA2lpla6Eu/HGfQGUF/hxLL2eviCIVzQ1YJ7/rYbd2zdhXv+thsXdLUkqg/sH/TiR39+B/H8unAE+NGf38GBoTGs6pyGLeuWY+Pak7Fl3XKcPq8Re/s9id9CJDI+jnjinnKsWol7eoIgjtNqkSa9xn+rcQWhRKkg4k7uTH6nTGli9J3nAl6B6FDlsuPLy9txeCTaN8NmAb68vD1hD09Gy9Rw+rxGQ4e5jJ4hnzTcdWGs90SyYOkZ8uFPb/TggS8uxYA3oBla2zvil5qwDg37pYKqR0OAHRkJ4OsPv574rD/4lLkK+/5QWJogGQiHEYmIjO2ztWUObH07taXt6YpkOKsFUhNUfE7gVEwalCuQk9qiWfpGuTfxf0Zmp9pyeeLeqfNSE/fMrA6OaPRC6fdES7Bk2uudndwTl0JEvhVVgRDRKgC3IdpQ6m4hxA1J7zsBPADgAwD6AVwghNgbe++bAC5DtNnVOiHEE7ke33G1brx9aERlarn+7Pk4TiNWX8vUEK94mu6ysbHKpSq5TbES3HHBkSxYmqpd+OSCJlxy3wu6TjOtnhczpsgFVVO1fPuuvlHVZ/3279/A7Aa3YdmQKpfcif+LL56Ex3ccMnTyaTmUA5EwzutSt7S9dnUngpFxk2PcZKUU3A88vw9LWqagrb4CEQhpG2MRW8WYNfUYmZ2sFuCyD89KhGjbYq+PegPY3TeqEt5mStYYlWAxoyDYyT25KMSkoGgKhIisAH6CaJOqAwBeJKLNSZ0FLwMwKISYTUQXArgRwAVEdAKiLXA7AUwH8BciOl4IYd45YYK3D49II6iOq3djSWttyv65tjlqhQDHBUdbnRt3XLQk0QRobmMl/jsmPOPXljnNQmG5CevBS5dKZyydTdUp268/ez5u+fO7KZ+1d9gPIwY1CxYGDZ18ejP7AY0+J/d8frwBmFYOSlwBDHlDUgVzXGw8Zmd1Rr+FvlG/tFDni/sG8L9/2alS/GZK1pjJbJ8sCmKytMYtBPn+zou5AlkKYJcQYjcAENFGAGsAKBXIGgDfi/39OwB3xGpzrQGwUQjhB7CHiHbFzvd8LgfYOyI36RwekbdIzVWhvThGIcAAEAiJhBBat3K2KQV2dExbgGvNWJK3j4wFExVqlZ9Vr3prHK3KsBUOm6HC1ZvZm4nCMlIA1eV2qYKJl3kxO6sz+i04NHwWN527SBohJTObDXiiyrp3ONo3XubcV5bXnwxMpta4k4FiOtFnAPiX4vWB2DbpPkKIEIAhAHUmjwUAENFaIuomou6+vr60Blge6z6nxGW3oMwhv21mHZHxh+CM25/FZ+76J864/Vk8vuOQyskKAIc0igP2Dkedp8nCNCJgymkWb/2avF+ly5qYsSxrr0d7Q4Wq1IVy+7AvKHVYjwWNc2RsFkiDAywWbYUbCkXw2r8G8WbPMG4+dxEWzhh31seVjvbnGp8nKUuw3Pm5E7Fp7Qdx+rzxtq1jgZDUuS37XHpRx0a/BY9Pruz6Yt+t0kkuc4a21pXh4FFf4jf0ydufxdBYEPOmVWFmTRk6plbi/uf2YP+gV3uQExCtCcTefo/BkUw+mPROdCHEBgAbAKCrqyutRIPqMnn3Oa2ig2Znp2bjs502ed9xe8zjm2wmefilAylhxzIFZrdapMUMbTrRZck4NJzNH2g1Lglf5rChuaZMVQcq3mJVVoolEhF45LWDKlPe+jM7gRf24fWDwwmlc9QTkDYAcyo+l1FZ8QqnTercvuW8RYnjzcyAjZqBOe3y73Z2Y0Xib71+5t9fswBrH+xW/Yau/+Nbqsx3ZeXmyQLnq5QWxVQgBwEoi2w3x7bJ9jlARDYA1Yg6080cmzWBUETa+OhH52oLSTM2R7MPQTASkjZ+Ckeis+FkM0nPkA+buvdj09plGAuGNRWYNxDCFJdNXXHWF8RYGmXqG6ucsaKDauVqppqszULY1++VOPHL4LCFUkqxzKh2pZjyrv3DDtx07iJ8/XevJZTkswMeqV9hRNEAzEh511c48cUPzcINj7+dOMc3Vs1NdGs0q/yNFNWQLyDNMTrqDZiKkNL6DcUXsfHAhHjl5skC56uUFsVUIC8C6CCiWYgK/wsBXJS0z2YAn0fUt3EugK2x8vKbATxERLci6kTvAPBCrgeo1X2ub1TbUWzGt2H2IbCSVdr4Ka7AZDPTq1fNw4IZU3TtwW6HHf3eEVzz2JsqAX7cVPMd9YbHglLl2tm0xPDYo2OpeSXxkiOyUiy3nr9IKiwtBGxZtzxxj8sd6tUDEF09KBW+kfJunlKOpimuqHINhOB22GC3UcKXYFb5GymaOrcLm7rfTFnB3XzOItVniiObmMh+Q8c3VuLyFbMBqCs3Txa4KGNpUTQFIoQIEdHlAJ5ANIz3XiHEDiK6DkC3EGIzgHsAPBhzkg8gqmQQ2+83iDrcQwC+kusILCDaZEeeLSyfZZs1bzRXl+G6NfMT3fNcdnnr1b4RYwXmsJHKcaoM+9XCEwhJBfiGiz9gfFNivD/kQyA0bhEkijr0e4Z8WGjQvEnP2S3brtXDfVqVSyVQvYGQNL9EWR7ESHkfOOrFvn5vinnvwFEv2urNZ2wbKZrOpipphN2JLTWw2YxNiTJBuv6sTtzy57exr38sMSloqp5YM3OjCRjnq5QWRfWBCCG2ANiStO0axd8+AOdpHPsDAD/I5/g8gaC0zac3IM+YNmveeKt3GD/5qzos8yd/3ZnSelWr3EW9e9ycopyxx9/fYlDrxqdRMyt5mx7NNWXyXJIa4/7jWnWjpmhsj4iItH9Jspwtd9ik+SUPXro0sY/RDPbwiF9agXnJzGieiNkZsFYZ/7iisdksWL1gOtrq3Dg07ENTlQsLplebUh5AqiAts1mxbtMr2Nc/lhj3bU/txOknTDN1PqD44bHp+JcmQzjyZGDSO9Gzoc7txAH7mGqGX2a3oFZjBSIrOvjwSwdSzBs9Q/KwzOTWq41VTqkTv7HambheJg7Ftjp5xdm2OvMhny6bVbqKOU2SSZ3M0JhcMQ/7glLh3FBRhh898U6iem+Zw4YHntuNm85drDrvoFdeIfiod1zhG81gh8Y0zhErs2K2kZZRDk8kIvDk24cz6qei/CxxQfr8e0cSykM57r5Rn6ke66UQHsttbycerEB0CIYFfvint1ME7S8vO1m6v1YDqGlVrqT9NFqvJu03o7octe6RFHv8jOqoEMrUoei0W/D9NZ347qPjiun7azrhtJuPwuoblefIHPH4MRv6vpQatwMP/fFNSaTTYpzYUpMi3CMRgXUr56B73wAiIjqTv3rVvJRZv0sjsin5c+nNYI3a/UYiAk/vPJxI3nyrZxh9oz6smNOoErRGOTzv9Y1K+6kc33gKOiTl8I1WB0YrHqNzlILwnugRVsVewRUDViA69GnUjOobkTvRtRpAAcDuvtHED6vGbZOuLKa41eHB+wa8uGvbe7jkQ+3R8wO4a9t7mN1QieOmmjenJHNkJICxQFi1shoLhHFkJIDWOvkxyQ9HvCihGeWVfKzNQtJyIVYC/rmnH41VLixtq0v0sUiOZrrxnIWq3I04U8rs+N5Znfie4r5+76xOTEkKu9Z70MsdVmlGd7kjWqZerxFUS63bdGn9PUc0GlMd8aQoEDOrAzMrHr1zlILwnsgRVqWwgisGrEB0qHVrlT2X54HIGkBtfHE/Gqtc+Nbv30ic44efWoA/b+9RmWTu3vYeZtWXo7Vu/GF9f8gr7RzYM+TFcVMrMnYo+kJh3PP3PYnZakQA9/x9D/5/jWKIsofjjouW4JbzFqtMMHpJk+ochvn40xs9KeVCpk8pw5UbX1U9fLKZ8dUPv44FM6pTBJvLbsHPkiLDfvbMLtylCA4wetCHx+SlTBbPnAJAvxHUrr7R8bIy0yp1hWGZxmopOWEQ0F4dzLliOYiiM/dyh1V3xaPVinfOFctx3NTSKOc+kSOsSmEFVwxYgehgt1qkwuKhL8lNWLIGUGcunJFQHvFzfOv3b2DtR9qx7tevJPaTPaxOq1XqFH7gi+NO4UwcioGwVjVcuRNd9nBc/tAruO8LJxlGgMmO/e6j2xMJb8rPPyXWS0T58KUzM943MCb1Le0bGMPx06o1x6N80N1Om7SUSXwFotXka8QXxPtHx30Q7w96U3J4lMKw0mWXrnSqXKmTE6178NahYfz3b6OTC6MyNlqtePcPeLJazeaSiRxhVQoruGLACkSHfq0S2aPyWlittanOaasF0nMc3zg+Q9V6WLWElSeNhD8ZLps8Wum+L8h7vWs9HM/v7k9RAo9fuRwRgYR5SOvY4xoqVJ//2tWd+MXf9qj2OTziS2tm7LJbNWb1410SjR70QDis0ZEweozsO46GdjuwM6kf+7c+ORcPXroUYSFShKE/HMaMKU5suPgDGPQEUeO246jXL+1Lr3UP3u0dSWyLl7HRuk9arXiV1XrNBAfkGzMTolL0NZTCCq4YsALRoVojrLRao+verPrUWdxJrbXSc8ybVmXYI6RFQ1i1aJSTN8uIT2sWLVdMWg9H8oKlptyBl/cfVZnr7rq4S3rsqC+In1/8ARz1BtFQ6cQv/v4e/vrukcQ+rXVlKLNb0e/x48ZzFuLWJ9/BmQtnwGoBTmqtVZUyj1PltEln9ZXO8Z+50YNe53ZKS7Ssmh8Nh22tlZdW94UiiSZZcX/ZPX/fgx9+agE+PLshZazBcBhjQYGvP/iSSokGJatA2ergh59agJufeCexz7Z3DqeEOit9II1VTmmZl3jlALPBAcWmVH0NpbCCKwasQHTwxgrrpeaByAWtrP7RvMYq6Q9rVr07MdvSQqaQ4sdmQ1O1PGJnWrU8PFn2cMSFupLzuppTzHXfefQN3HjOQlytaDx1y3mLUV1uQSQSFdCRiMBZi5qxbecAfMEIWuvKcMWKDlyw4R/wBSPoaq1OcRDLhIYvHIbbYVWZ1dwOK/xh89V42+rcuG5NJ0bGwokyL0tndSbe3z/oxcYX9iX8V+WOaNOqK1Z0SM2CWn3enVYb1m9+WXWv1m/eocpZiSMz7VgIqmrIy4+fiju37dIs+d48pRzlThs2/OltlYKJZ9jrBQe01ZeOCaZUfQ0T2fyWDaxAdHDZrCizW1LyQFw2q3R/rfpHmXYkNPOjzGQ5P7vOja98rAPXbFZkwq+ej4469QOoPPecxko8fuVyHBqOjqOlphxTym0qQeu0WaRRazOmuFSff3qlC5vf6FFd//tr5mPLFafg8KgfZXZrQnkAwMntDSkOYpnQGB4L4WfP7E5cPxwBfvbMbly3utP0PY1EBPpGAikrjHinxH6PH2sWN2PX4ZHETH7N4mbNJMZNX5bXotJuFSCP8Es27UQiQqUIrRbodko0CivWCw4oJQVSyr6GYzHBkRWIDhYiaR6I0omtJNcdCQH9H2Wmy/k3e0cSwjs+zms2b8dxDW58oK3W1LlDoQiGx0LYeXg0IUg7Z1Tjix9uU5UBuXJlB+ornGirH/8M3XsHUq7/3Ue345eXnYxl7fV4/r0jqntOJPcjJQuNaRrNohqTVlZ693RHz5BU0HZMjVYJcFgtGPWHUmbqWgmI3qC8wk6d2yE1pdWa6KcS/wyqTHS7LTEm5fnipjkjwevV8LdprbaLxbHqayhVitkPpOQZ8smFwtCYvJSJ3kOaDzLtjaDV4/zQ8Pg4jc79Tu8wDgyOYcO23bhj6y78fNtuhMMipQzIbU/tTPGVHDK4vqz/hex1Q4VaaAgI3HTOAqxbORuXr5iNK1fOxk3nLEA6RoQejR4sh4aiYxv2yeuIVWj0IolHbyVT6YzmAsWPiecCVTjTn9MJAVQ4bbjjoiWq8ylNc1r3NC54a2N135Lfry03p9AKhdmeO0xh4BWIDvEGRcmzncoy+W0r9OzIaFapZd6aqlFjq6HSafrcA97UirpvHRqWHpNcTqOxyin1wTTGrp/sp3jstYMpiZdXnXY8ktuXiAhwaNivWh1cddrxaQUdaFYJiBUl9Pg1IuP8Id3orWSqym2oKbepqgzYrEB1ublHUmuFqDQzKk1zRr4freizQMR8fbRCcKz6GkoVViA6eANyoaDVdS8fkRh6Pg49haVngnLa5A2llI2XjJShTJAahZLGqXJZpT6YqjJr4vM2VDqwae0yeANhWC2Et2OdCL3+EPpG/bjv73uxsLk6YZ+PRASO+oLSQoh3XdIFs3Q2VeHmcxeqTHOzp1agsymaRzJdQ8FMKXfoRm8lc3DQhz9vP4RzT2pBZFSgrsKB3764H9VlDrTUGps69cyly9rrU/Y3ErwOqxVb3z6UEhzw4dkapQmKyLHoayhVWIHoUOm0S4WCVkMprYcUUJcyMTtjikQEtr7TmwittBKwoLk6EVqpp7D0olUGvVFHtTo4wIrBsfGoHiNlWF+RasN/7LWD+OGnFqjCeGUKdGgsLPXBPHjpUqnSO6GpEpfcm+qLUiqmvf0ezfBkv4YfQgsLkebrE5qqpGG8C5qqcfWqeaYnD5UuGzqmVeHSX7yo8qUo2+8qJw9N1S6EI0jkxmTiTNb1p4kIzjmxRVX1YP2ZnZpRZAwDsALRZSQQxKUfmoV+bzR23mYBLv3QLIxqlHMH5NEymcatG4VW6s0q9QRMpcuBH2xJLQP/K0WGvdGM1eNPDXG+aGkrplU5DCPO+j3yBM0BT0Cq9P54xXLDlV3vsA8VTnki4dRK4y6Jcd7pHcb+AW/KPX+ndxidM6bAZrPgzM4mtNaW49CwH9OqnFjQVA2Hw5qWacUbCEt9KV2t0XL+oVAEz+3uR/e+AThtFlQ6bYmADr38mjK7VdUO2HRlX6JEDkl8PNf+YYdhR8NSTOpjCgcrEB2qnHaEhFqYfO0Tc1DhlCcSyjBTx0jrwTMTWqk1q9QzQe3VKOQ35FUrRr0Zq8su7x1+0zmLDM0L1WVy31KZw6rpQzESzo1VLhweHpMWqQymYceX+XZue2on5s+ImrBCoQj+sKMnZQVy9qIZsNkspk0ro/6QNOR51B9CJCLwx+09qtyZK1d2oKbckXDyy/Jrrj97PtZtfCXRUCqdBDtvQF78Ua+jYakm9TGFoyhRWERUS0RPEtHO2P81kn0WE9HzRLSDiF4nogsU7/2CiPYQ0auxf4vzMc5QRODmJ95RCZObn3gH4Yj5Zb1eHaMzbn8Wn7nrnzjj9mfx+I5DiCSdV6uUiTK0MhIR2N03iuffO4LdfaOJc+hFq7id8oghdxoRQI1VTlx4Ugvu+Vs0Cuuev+3GhSe1mOqJ7rBGBaJybFeu7NAc19RKV0KZLWuvR3tDRYqAaqtzIxhGos3u5Stm47JT2nHnM7vgDZhXIHpOckA7zHdHz5DpawDArNpyXPLB1sT9u/vZ3bjkg61orS3H3n5PQjHEr3HbUzvx6RObE8fv6x/D9CkubFq7DHd+7kT88rKT8eOtO1UNpZIj8rR+K4B2lFZjlXYASLpRgHrXZyYmxVqBfAPAU0KIG4joG7HXVyft4wVwiRBiJxFNB/ASET0hhDgae/9rQojf5XOQWrH9w2PmY+PN1DFS+ieUs1etukvxqCKjGaDWrL2xyikt+WFG+MdpqXWjo7FC5UfpaKwwFfF01BuUVrw9oaky4yAEi4XgC4WlyXTp+ECmTymTRohNr9bPp+gdlicAajHil4cDf/i4Ong0VgNK14zLbsFYIIKLH3wBvmC0mKKsoZQyIk/vt5JJAEg6fhherUxOiqVA1gD4WOzv+wE8jSQFIoR4V/H3+0R0GEADgKMFGSGAcrtVKkySZ2p6tNSk1k66bs18/PL5var9ZA+eUSkTo7IOWiao5inlaK4pUwn/5pqyRFkLM1gshI91TEVDhTPt4nutdW5pwt/0KeU4rqFCqvTM2Npba8s1FK75z1XlsuHfPzo7xQxWFespUueWh0DXuh1p+QPe18g36RnyoaNRXgo+fqp4KZnvPjpeNsYoAs7MbyW5DE9nU7Xu95lO2HqpliBhsqNYCqRRCNET+/sQAN0+qES0FIADwHuKzT8gomsAPAXgG0II6RSQiNYCWAsALS0taQ2yQkOYKCNljNg/6MWPt6b2P1+zeAZePzic2E/24BlVSNWaAe4zEGL7B724/7k9uORD7aqQzc7pqT02tNAq22JmRmmzkHQFZLOQVOmZnb2OBcLS847p2PGT6R32J75vIOZMfmwH7v/iUrTVVyAshLQ+mtWCtGbYevkmstXATecsxIIZ1fjQcXWYWulCv8evWnE8/NKBlJBz5QrCTM5Qut9nOquWUi5BwmRO3hQIEf0FgCwI/tvKF0IIQUSaxlAiagLwIIDPCyHiv8BvIqp4HAA2ILp6uU52vBBiQ2wfdHV1pWV0FQJSYaLVD0RG77C8/7mZcu6RiMATb/Zq9s3WmgG+8q+juP2pXZpCoN/jlzaqGvD4TT/Me454cOPjb6mqz974+FuY01hp2IN7b79HasKaO60SsyTXNzt7fX/Ihz+9EWvU5Q+h3GnDXdveQ1udG/LA61S0fCBxv1O5Q14fjUBpzbA7NcKB47N+LfOj8v4ov/ueIR82de/HprXLMBYMpwQaGK0W9vbLv8+50yp1w4LNRp4VMsmWI8MKR94UiBDiVK33iKiXiJqEED0xBXFYY78qAH8E8G0hxD8U546vXvxEdB+A/87h0BPohZuaRevBMVPOfbdG3+w5jadgdmOldAZ45coOPPD8vsT+MiHmsFjSKvwn4/0hr7T6bLxboh7lDq2mTfKfo9nZa63bjk8uaFIpRlkHST0BU1+hbaICotFKsvpod1/SldYM22azYPWC6Wirc+PQsA/TqlxYOL0aNlvUPGqULNdW58YdFy1JyRGqLrNLI6dkplRlufd+j1/6fRpNKswm9WmNN9clSNjXUliKZcLaDODzAG6I/f9o8g5E5ADwewAPJDvLFcqHAJwNYHs+BumyyfMKnHZ5fSMZWst8M+Xc9/Rr9M3u92B2Y2XKDJBA+M9Nr6JnyKfaP1mIDXgD0hDSAa95xWimW6IWY8EgvrlqbiK/xkpAbblDM8Pf7OzVTAdJIwEz5Avg22fMQ9+oPzG2+gonRnzREOdRjRXKWDCc1gw7EhH4yzuHsxJ0gZBQhZhff/Z8fP6+F6RhvDJTqrLcu8OqMakwyANJh+Tx3nr+4pydOw77WgpLsYop3gDgNCLaCeDU2GsQURcR3R3b53wAHwHwBUm47q+I6A0AbwCoB3B9PgZZ6bLi2tXqgnfXru5EpdO8AokL+S3rlmPj2pOxZd1y00Ii3mFPvU3dYU8Z3tpQ6VT1iIjvnyzEqsvs+OqpszFvWiVmTinD3GmV+Oqps1FdZj6/JZtuiWV2G/zhiKoQoz8cQZmGYo7PnpXfg3L2HOeo17j4pVHoabndhrFgWDW2sWAYZfboXCseGafEZbdgVppF/jIthKl3/Hce2Y4zF86Qnk9pSr1j6y785K+7sK9/LFHoUysPpGfIl5OQ22w/r1kKXdD0WKcoKxAhRD+AlZLt3QC+FPv7lwB+qXH8irwOMEYgLPDb7v0p9YG+vmpeWufJtHZPfYVdmhhXXyEX9GadmlYLISwI/60sW3FWJ6xpLPGz6ZZoIZLWrJI1UwLkgQjK2XPi+g6LdEwO27jANzKH2a3ysf0mNhPX6kjYVudGu0YEmYxsncpaxytDfZXnM1rFab3/xsFh/OemV7M2AxXKic7l3gsLZ6LrMDQWlDqbh33apUxyic1iTSTGxQXnnc/swt2XjPcuD4Ui2NEzlIjSOnXOVEPfijcQlgYHaPVEl2GmW6KWr0HLDBRP1ktGKxAhWfi47TZcu7oT6zePK9xrV3eiQuFbMSwSqTET98T8CkbKzOxEobHKhdNPqMdnl83CoCeIWrcdv/zHHtOCrlyjx7mydJXyc5npxJj8/roVHXjwH/tyYgYqlGA/VlvLFgtWIDpUl9kztvPngn8NeqWC88CgFx2NlQiFInjktYPSshp6D/pADoIDjEKM9XwNtRq5FDUavSfMCh+blUAQqhLp3kAQNuu4AjVy5k6t1L9W77APgdC4lCaK2vbTnUlPr3Th1HnT8X8UPdGvWz0f000KVFn59fVnduLObbsSY1YKTqOIKeX77/aO4I2Dw3jwH/sS/rRsVwuFEuxc7r2wsALR4ciovO1ovye9rONMcWvMMuPRSkbd87SYWiUX4OkUHTTKG9BzZmr1ntCqWWVW+IwFI+j3BHHN5jdVUVjJ36GeM9dqgTSXJF7pvqnahUs+2Jry/rQqV1rho9sPDUsrErc3uNEV6wqpR53bmVIp+uGX9+P2C5dIw3gBY1OqMqjjPze9aqiw06GQgp3LvRcOViA6NGrMRht0HqRcxqAblRzR6563aKb2ea1EWH9mZ6L6anz2qpypG2EU7aJn855a6Uqrd4ZZ4eMLyivc3q3oB2I07h5lLknM73XXtvewpGVKNJEwAuk1VnVOSyt89PBIds7etjp3Svn4Oy5aggqnPIzXDMrf7l0Xd+E7j76hiujKdrXAgn3ywQpEB6tOxrSMXMegG9WbMuqep4XNasHDL48HB5Q5bHjgud245sxO02MzcorqmZ1kws9IQJkRPlqRRMpMdKNxN1W7pLkk02JFBbUFv1+z6rIsL8bIVGZEslKdVuXCmz0j+LcfP5vRb0/2273xnIWYMcWFWreTzUCMFO6JrsP7Q2OJjOl4ddcHnt+H94fGpPtrzW73D3gyqkIarze1cu5UzJ9ehZVzG/GxjqmJBzmezZwc3hrvnqdFMBTB+V0zo19+TDGd3zUTwbD5UE2jHtt61YCV/pM7P3ciNq39IE6f16groMxUcq0pt0vHNKV8PGrNaNyhsJCuMEKxexMX/MnHD/vkIcT7B7TDVGUVidMR0coQ7ohAzsOCr374ddS6ndLqxwwD8ApEl+Yp5XDYxh8cIsBhI8yYUibdXza7rSl34OX9R1O69JmZGRr5GZKzmZuqXFigyGbWIhgJS8N4QxHzpg+jzGY9s5NRiRbZfTCzshvyBaW+lSFF1JyRP2X/oFeqCP416MXsxkpNH8mUMruuvyqZYZ+8IvHcaZWmvwMl+QoL5lpVjB6sQHSodFnllVk1iinKzDbndTUnlAeQXmaskb0+02xmm8UqDeP95WXma3ztH/Ri4wv7UnJklLkZWmYnoxIt6d6HOBVOm9S3csOnFyb2MfKnVDjlgQsVsV4pPUM+qeBfMKMKX/vEnET/GJc92nxMq0R+a628IrGZPBoZ2YbJcv4EkwlswtLh4FGfVNAePCp3dMrMNh1TKzUjuYxMMkZZtZlm9x4ZkUeXHRk1H12mLMh49cNv4Gu/ew0r5k7DgIkINb0SLTLMZheX2aMKX9nk6t8/OhtuhzrDXa85VaXLivVnqasPrD+rExWu6Dkaq1wJwR/P6B70BtBcU46GSifWfiRq7lz7kXY0VDoxvUq+Wo3n0SSb+JR5NOmgZzIsxPHMsQmvQHTQSngb1Uh4AwC306LKQ5CFzLbWleHAwBguvucF3ZVDY5VL2o9EmZMgG1/vsL7Zoa7CIZ1t1rnleRgysqmdFC/Rknx9l0YpE7Oz4+oyOyqcFmy4+AMYiCXnDY0FEr08zDDiC0uTN28+N1rPV8sENuQN4uu/ez1ljK1ry6Uh1bkOa832fJw/wWQCKxAdGtPMl9g/4MGb74+o7OM/+NT8lP4RyggkQNsk01JTjitWdGj6GbSykcsd+rW6wiKMG89ZgPf6PIlkuvYGNyLCvA8kkx7acaqcNnzrk3NxxDNeTLHO7UClRktds3kgzVPK0b1vEGsVyXnXnz0/rUZZQ96gNHkz3i9eS9D++c1DaYdU5zqsNdvzcZgtky6sQHSwEElrUWnVjOod9qdE8Hz799tx1akdqhntgQG5ozZ55bB/0CtNFIz7GTQT8sLyhLw4LpsdR0ZHVcl0X/vEHLSmYX/XWhXo9dCOExIROO1W1fWvXd2JsJCP2+zs2Oh+maGyTMMHovB7yQRtpiHVDDORYR+IDsNjoYQ5Ix7Ge+czuzDsk5uwtCrUNk0pU9nlFzRXS0NBk1cOeiYqQJ2NHB/fpu79qHXrZ5R7AqGEszd+zpufeCfRNMkM2djM/cFIol5V/PrrN++AP6it+PT8FnGM7pcZfMGoUlZ+rnUrOuAP6a+sMg2pZpiJDK9AdPAEQlJzhlbRv1aNCrXJzaP6PX5TKwcjE1UmCXkAMOKTK7oRn3kTVjY2c49fo2ChP7MM6jiZmvSSzyGL5Ir7QLSw2Sw4e9EMdEytwKEhH6bFeoobhVQzzESGFYgODRrd6eor5DN8rQq18Rmz0uRhppSHkYlKJsRbasoNS6nMmCI3tzRNMV8LK379TGzmVRo5E+k4u2VkatJTMrXSic+e3Joo6e6yW3DVacebqhNms1mwaGaNbhkZJdx6lZnoFEWBEFEtgE0A2gDsBXC+EGJQsl8Y0aZRALBfCLE6tn0WgI0A6gC8BOBiIYT5UrImGfIFUhzgXz31eIz65JcyOys3u3KQFcxLVjRKIW424Y4gT4azpJUHnTlTK+U1vtIp5ijDzP0yoqXWjfYGt6p8THuDO+P8DC249SozGSjWCuQbAJ4SQtxARN+Ivb5ast+YEGKxZPuNAP5HCLGRiO4EcBmAn+V6kA6rFQ+9oE4ae+iFffjB2Qs0jzEzK8+1ooljNuFOWaJFmQx3XEMF5jenc4cygwhwO6wqIe12WFXNkDIhU5NeMeDWq8xkoFgKZA2Aj8X+vh/A05ArkBRifdBXALhIcfz3kA8FYidceFJLykxZWd4kU8yafxw2UglavWubLUdRU+6QZkHXlGdnQjJLz5APP3tmd6InezgC/OyZ3Th+WiXa6jMXnrnIZdjb78HlD72SYl7bkmPBzqVDmMlAsRRIoxCiJ/b3IQCNGvu5iKgbQAjADUKIRxA1Wx0VQsQ92QcAzNC6EBGtBbAWAFpaWtIaZLndJp0pl9sLc9vSFWZmE+48AXnNKDP9zHOBMptbb5yZkG0uA7deZRjz5C1EhIj+QkTbJf/WKPcTQggAWmVgW4UQXYiuNv6XiI5LdxxCiA1CiC4hRFdDQ0Nax44Fw6oWodHzAWMGIZ25wmwJjzhmQ2tryl3Y+vYh3HTuItx4zgLcfO4ibH37kGZHwFxTymUzjKr15opSvgcMY5a8TaWFEKdqvUdEvUTUJIToIaImAIc1znEw9v9uInoawBIADwOYQkS22CqkGcDBnH8ARH0g9z63J1FKJBwB7n1uD26/cEk+LpdCurNUsyaceY2VOP+kVlXPi+vWzMe8xqq8fp50x1kMuPUqw5iHRPIUuxAXJboZQL/CiV4rhPh60j41ALxCCD8R1QN4HsAaIcSbRPRbAA8rnOivCyF+anTdrq4u0d3dbXqcL+7tx4t7BlNMPUtn1aCrrS6dj5wR+YrU2d03ijNufzbvdv6JSigUwY6eIVWvd87nYI5liOilmDVIRbF8IDcA+A0RXQZgH4DzAYCIugD8uxDiSwDmAfg5EUUQNbXdIIR4M3b81QA2EtH1AF4BcE8+BpmLsNBsyNcsdTI7cLPNrTDqwcIwzDhFUSBCiH4AKyXbuwF8Kfb3cwCk8bJCiN0AluZzjEBphIXmo8DdZHXg5mLFxuG1DGMeXpfrEF8BbFm3HBvXnowt65ZPipnoZHXgZtofRUm6gQsMcyzDpUwMyMUKoNRKVkxWB24uTHOTdXXGMPmAFUieKdWSFZOx90MuhH+horAYZjJQlCisYpFuFFYu4IinwpErZR1fMU6m1RnDZEOpRWEdM0zmiKdSI1emucm4OmOYfMAKJM+wTb2wsPBnmMLBUVh5ZrJGPDEMw/AKJM9M1ognhmEYViAFgM0qqZRaaDPDMOnDCoQpOJGIwNZ3evH6gSFEBGAlYEFzNVbMaWQlwjATCFYgTMHZP+DBzt5RbNi2W9Woa3ZDRVYNpRiGKSzsRGcKTu+wP9HlEYiGNd/21E70DvuLPDKGYdKBFQhTcDyBkDQ3xlugjogMw+QGViBMwWmtdUu7/rXUcmgzw0wkWIEwBWdWvTw3ZlY9KxCGmUiwE50pOJwbwzCTg6KsQIioloieJKKdsf9rJPt8nIheVfzzEdHZsfd+QUR7FO8tLvRnYLIjnhuzrL0e7Q0VrDwYZgJSLBPWNwA8JYToAPBU7LUKIcRfhRCLhRCLAawA4AXwZ8UuX4u/L4R4tQBjZhiGYRQUS4GsAXB/7O/7AZxtsP+5AP4khPDmc1AMwzCMeYqlQBqFED2xvw8BaDTY/0IAv07a9gMiep2I/oeInFoHEtFaIuomou6+vr4shswwDMMoyZsCIaK/ENF2yb81yv1EtKOVZlcrImoCsADAE4rN3wQwF8BJAGoBXK11vBBigxCiSwjR1dDQkM1HYhiGYRTkLQpLCHGq1ntE1EtETUKInpiCOKxzqvMB/F4IEVScO7568RPRfQD+OyeDZhiGYUxTrDDezQA+D+CG2P+P6uz7GURXHAkUyocQ9Z9sN3PRl1566QgR7ctoxEA9gCMZHptveGyZwWPLjFIdW6mOC5j4Y2uVbSxKT3QiqgPwGwAtAPYBOF8IMUBEXQD+XQjxpdh+bQD+DmCmECKiOH4rgAYABODV2DGjeR5zt6wncCnAY8sMHltmlOrYSnVcwOQdW1FWIEKIfgArJdu7AXxJ8XovgBmS/Vbkc3wMwzCMMVzKhGEYhskIViDm2VDsAejAY8sMHltmlOrYSnVcwCQdW1F8IAzDMMzEh1cgDMMwTEawAmEYhmEyghVIEkS0iojeIaJdRJRS5JGInES0Kfb+P2OhxqUyti8QUZ+iSvGXZOfJw7juJaLDRCTNx6Eot8fG/ToRnViIcZkc28eIaEhxz64p0LhmEtFfiehNItpBRFdK9inKfTM5tmLdNxcRvUBEr8XGdq1kn6I8oybHVpRnVHF9KxG9QkR/kLyX/n0TQvC/2D8AVgDvAWgH4ADwGoATkvb5/wDcGfv7QgCbSmhsXwBwRxHu20cAnAhgu8b7ZwD4E6J5O8sA/LOExvYxAH8owj1rAnBi7O9KAO9Kvs+i3DeTYyvWfSMAFbG/7QD+CWBZ0j7FekbNjK0oz6ji+lcBeEj23WVy33gFomYpgF1CiN1CiACAjYhWDlairCT8OwArYxnxpTC2oiCE2AZgQGeXNQAeEFH+AWBKrIRNKYytKAgheoQQL8f+HgHwFlJznopy30yOrSjE7kU8adge+5ccCVSUZ9Tk2IoGETUD+DcAd2vskvZ9YwWiZgaAfyleH0Dqg5PYRwgRAjAEoK5ExgYA58TMHb8jopkFGJcZzI69WHwwZnb4ExF1FvriMVPBEkRnrEqKft90xgYU6b7FzDCvIlpD70khhOZ9K/AzamZsQPGe0f8F8HUAEY33075vrEAmF48BaBNCLATwJMZnE4w2LwNoFUIsAvBjAI8U8uJEVAHgYQD/KYQYLuS1jTAYW9HumxAiLKKN5poBLCWi+YW6thEmxlaUZ5SIzgRwWAjxUi7PywpEzUEAyhlBc2ybdB8isgGoBtBfCmMTQvQLIfyxl3cD+EABxmUGM/e1KAghhuNmByHEFgB2IqovxLWJyI6ogP6VEOL/SnYp2n0zGlsx75tiDEcB/BXAqqS3ivWMGo6tiM/ohwGsJqK9iJq/VxDRL5P2Sfu+sQJR8yKADiKaRUQORB1Jm5P2iVcSBqKdEreKmNep2GNLso+vRtR2XQpsBnBJLKpoGYAhMV6Sv6gQ0bS4nZeIliL6TORd2MSueQ+At4QQt2rsVpT7ZmZsRbxvDUQ0JfZ3GYDTALydtFtRnlEzYyvWMyqE+KYQolkI0Yao7NgqhPhc0m5p37dilXMvSYQQISK6HNHmVVYA9wohdhDRdQC6hRCbEX2wHiSiXYg6Zy8sobGtI6LVAEKxsX2hEGMjol8jGpVTT0QHAKxH1IEIIcSdALYgGlG0C9He9l8sxLhMju1cAP9BRCEAYwAuLNCE4MMALgbwRsxmDgDfQrRCdbHvm5mxFeu+NQG4n4isiCqt3wgh/lAKz6jJsRXlGdUi2/vGpUwYhmGYjGATFsMwDJMRrEAYhmGYjGAFwjAMw2QEKxCGYRgmI1iBMAzDMBnBCoRhcgwRjRrvpXns0xStuPwaEf2diOYo3nuEiP6Rm1EyTPawAmGY0uOzsRIh9wO4GQBiCWofAFBNRO1FHBvDJGAFwjB5IpZBfjMRbSeiN4jogth2CxH9lIjeJqIniWgLEZ0rOcU2ALNjf38a0TpKG1G4xDiG0YUVCMPkj08DWAxgEYBTAdwcK2XxaQBtAE5ANOP7gxrHnwXgjdjfnwHw69i/z+RtxAyTBlzKhGHyxykAfi2ECAPoJaJnAJwU2/5bIUQEwCEi+mvScb8iojEAewFcQUSNADoA/E0IIYgoSETzhRDSLosMUyhYgTBM6fFZIUR3/AURXQGgBsCeWP3CKkRXId8uzvAYJgqbsBgmfzwL4IJYk6EGRNvrvgDg74g2FbLEVhcfMzjPZwCsEkK0xaqpfgDsB2FKAF6BMEz++D2i/o3XEG1t+nUhxCEiehjASgBvItoB7mVEu7+lEOsI2AogEb4rhNhDRENEdLJGxzuGKQhcjZdhigARVQghRomoDtFVyYeFEIeKPS6GSQdegTBMcfhDLLfDAeD7rDyYiQivQBiGYZiMYCc6wzAMkxGsQBiGYZiMYAXCMAzDZAQrEIZhGCYjWIEwDMMwGfH/AMMJ7NrgPGqfAAAAAElFTkSuQmCC\n",
- "text/plain": [
- "<Figure size 432x288 with 1 Axes>"
- ]
- },
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- }
- ],
- "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": {
- "heading_collapsed": true
- },
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 45,
- "id": "85d73982",
- "metadata": {
- "hidden": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(17.463548966032086, 0.0036996120985459207)"
- ]
- },
- "execution_count": 45,
- "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": {
- "heading_collapsed": true
- },
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 46,
- "id": "7dec1d91",
- "metadata": {
- "hidden": true
- },
- "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": {
- "heading_collapsed": true
- },
- "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": "e4207c4c",
- "metadata": {},
- "source": [
- "## A"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 47,
- "id": "db59adce",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(17.463548966032178, 0.003699612098545746)"
- ]
- },
- "execution_count": 47,
- "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"
- },
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- "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"
- },
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- "title_cell": "Table of Contents",
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