lect06-ancova.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis of Covariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Single-factor-Analysis\" data-toc-modified-id=\"Single-factor-Analysis-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Single-factor Analysis</a></span><ul class=\"toc-item\"><li><span><a href=\"#ANOVA-model\" data-toc-modified-id=\"ANOVA-model-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>ANOVA model</a></span></li><li><span><a href=\"#ANCOVA-model\" data-toc-modified-id=\"ANCOVA-model-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>ANCOVA model</a></span></li><li><span><a href=\"#Partial-F-test-for-treatment-effects\" data-toc-modified-id=\"Partial-F-test-for-treatment-effects-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Partial F-test for treatment effects</a></span></li><li><span><a href=\"#Covariance-of-estimators\" data-toc-modified-id=\"Covariance-of-estimators-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Covariance of estimators</a></span></li></ul></li><li><span><a href=\"#Two-factor--Analysis\" data-toc-modified-id=\"Two-factor--Analysis-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Two-factor  Analysis</a></span><ul class=\"toc-item\"><li><span><a href=\"#Model-fitting\" data-toc-modified-id=\"Model-fitting-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Model fitting</a></span></li><li><span><a href=\"#Covariance-matrix-of-estimators\" data-toc-modified-id=\"Covariance-matrix-of-estimators-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Covariance matrix of estimators</a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Enabling interactive shell outputs ...\n",
      "   Use command pass; to disable cell text outputs\n"
     ]
    }
   ],
   "source": [
    "print('\\nEnabling interactive shell outputs ...')\n",
    "print('   Use command pass; to disable cell text outputs')\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore') \n",
    "warnings.simplefilter(action=\"ignore\",category=UserWarning)\n",
    "warnings.simplefilter(action=\"ignore\",category=FutureWarning)\n",
    "\n",
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm\n",
    "\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_formats = {'png', 'retina'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single-factor Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .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>PromotionSold</th>\n",
       "      <th>PreviousSold</th>\n",
       "      <th>Promotion</th>\n",
       "      <th>Store</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>38</td>\n",
       "      <td>21</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39</td>\n",
       "      <td>26</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>45</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>33</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>43</td>\n",
       "      <td>34</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>38</td>\n",
       "      <td>26</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>38</td>\n",
       "      <td>29</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>27</td>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>34</td>\n",
       "      <td>25</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>24</td>\n",
       "      <td>23</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>32</td>\n",
       "      <td>29</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>31</td>\n",
       "      <td>30</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>21</td>\n",
       "      <td>16</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    PromotionSold  PreviousSold  Promotion  Store\n",
       "0              38            21          1      1\n",
       "1              39            26          1      2\n",
       "2              36            22          1      3\n",
       "3              45            28          1      4\n",
       "4              33            19          1      5\n",
       "5              43            34          2      1\n",
       "6              38            26          2      2\n",
       "7              38            29          2      3\n",
       "8              27            18          2      4\n",
       "9              34            25          2      5\n",
       "10             24            23          3      1\n",
       "11             32            29          3      2\n",
       "12             31            30          3      3\n",
       "13             21            16          3      4\n",
       "14             28            29          3      5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cracker_data = pd.read_excel('data/lect06-ancova.xlsx', sheet_name='Cracker')\n",
    "cracker_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def codingfunc(x):\n",
    "    if x == 1:\n",
    "        return (1,0)\n",
    "    elif x == 2:\n",
    "        return (0,1)\n",
    "    else:\n",
    "        return (-1,-1)\n",
    "\n",
    "cracker_data[['I1', 'I2']] = pd.DataFrame(cracker_data['Promotion'].apply(codingfunc).tolist(), \n",
    "                                           index=cracker_data.index)\n",
    "cracker_data.PreviousSold -= cracker_data.PreviousSold.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PromotionSold</th>\n",
       "      <th>PreviousSold</th>\n",
       "      <th>Promotion</th>\n",
       "      <th>Store</th>\n",
       "      <th>I1</th>\n",
       "      <th>I2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>38</td>\n",
       "      <td>-4.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36</td>\n",
       "      <td>-3.0</td>\n",
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       "      <td>3</td>\n",
       "      <td>1</td>\n",
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       "      <th>3</th>\n",
       "      <td>45</td>\n",
       "      <td>3.0</td>\n",
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       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>33</td>\n",
       "      <td>-6.0</td>\n",
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       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>43</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>38</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>38</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>27</td>\n",
       "      <td>-7.0</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>34</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>24</td>\n",
       "      <td>-2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>32</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>31</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>21</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>28</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    PromotionSold  PreviousSold  Promotion  Store  I1  I2\n",
       "0              38          -4.0          1      1   1   0\n",
       "1              39           1.0          1      2   1   0\n",
       "2              36          -3.0          1      3   1   0\n",
       "3              45           3.0          1      4   1   0\n",
       "4              33          -6.0          1      5   1   0\n",
       "5              43           9.0          2      1   0   1\n",
       "6              38           1.0          2      2   0   1\n",
       "7              38           4.0          2      3   0   1\n",
       "8              27          -7.0          2      4   0   1\n",
       "9              34           0.0          2      5   0   1\n",
       "10             24          -2.0          3      1  -1  -1\n",
       "11             32           4.0          3      2  -1  -1\n",
       "12             31           5.0          3      3  -1  -1\n",
       "13             21          -9.0          3      4  -1  -1\n",
       "14             28           4.0          3      5  -1  -1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cracker_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ANOVA model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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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(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Promotion)</th>\n",
       "      <td>2.0</td>\n",
       "      <td>338.8</td>\n",
       "      <td>169.400000</td>\n",
       "      <td>6.608583</td>\n",
       "      <td>0.011612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>12.0</td>\n",
       "      <td>307.6</td>\n",
       "      <td>25.633333</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(Promotion)   2.0   338.8  169.400000  6.608583  0.011612\n",
       "Residual      12.0   307.6   25.633333       NaN       NaN"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "\n",
    "\n",
    "formula = 'PromotionSold ~ C(Promotion)'\n",
    "\n",
    "\n",
    "cracker_lm = ols(formula, data=cracker_data).fit()\n",
    "aov_table = anova_lm(cracker_lm) \n",
    "aov_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ANCOVA model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>     <td>0.924</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>   <td>PromotionSold</td>         <td>AIC:</td>          <td>64.7350</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 09:55</td>        <td>BIC:</td>          <td>67.5672</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>15</td>          <td>Log-Likelihood:</td>    <td>-28.368</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>3</td>           <td>F-statistic:</td>       <td>57.78</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>11</td>        <td>Prob (F-statistic):</td> <td>5.08e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.940</td>            <td>Scale:</td>         <td>3.5065</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>33.8000</td>  <td>0.4835</td>  <td>69.9079</td> <td>0.0000</td> <td>32.7358</td> <td>34.8642</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I1</th>           <td>6.0174</td>   <td>0.7083</td>  <td>8.4961</td>  <td>0.0000</td> <td>4.4585</td>  <td>7.5763</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I2</th>           <td>0.9420</td>   <td>0.6987</td>  <td>1.3483</td>  <td>0.2047</td> <td>-0.5958</td> <td>2.4798</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PreviousSold</th> <td>0.8986</td>   <td>0.1026</td>  <td>8.7592</td>  <td>0.0000</td> <td>0.6728</td>  <td>1.1243</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>3.304</td>  <td>Durbin-Watson:</td>   <td>2.497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td> <td>0.192</td> <td>Jarque-Bera (JB):</td> <td>1.380</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>0.337</td>     <td>Prob(JB):</td>     <td>0.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>   <td>1.675</td>  <td>Condition No.:</td>     <td>9</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                 Results: Ordinary least squares\n",
       "=================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.924   \n",
       "Dependent Variable: PromotionSold    AIC:                64.7350 \n",
       "Date:               2021-10-14 09:55 BIC:                67.5672 \n",
       "No. Observations:   15               Log-Likelihood:     -28.368 \n",
       "Df Model:           3                F-statistic:        57.78   \n",
       "Df Residuals:       11               Prob (F-statistic): 5.08e-07\n",
       "R-squared:          0.940            Scale:              3.5065  \n",
       "------------------------------------------------------------------\n",
       "               Coef.   Std.Err.     t     P>|t|    [0.025   0.975]\n",
       "------------------------------------------------------------------\n",
       "Intercept     33.8000    0.4835  69.9079  0.0000  32.7358  34.8642\n",
       "I1             6.0174    0.7083   8.4961  0.0000   4.4585   7.5763\n",
       "I2             0.9420    0.6987   1.3483  0.2047  -0.5958   2.4798\n",
       "PreviousSold   0.8986    0.1026   8.7592  0.0000   0.6728   1.1243\n",
       "-----------------------------------------------------------------\n",
       "Omnibus:              3.304        Durbin-Watson:           2.497\n",
       "Prob(Omnibus):        0.192        Jarque-Bera (JB):        1.380\n",
       "Skew:                 0.337        Prob(JB):                0.502\n",
       "Kurtosis:             1.675        Condition No.:           9    \n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "formula = 'PromotionSold ~ I1 + I2 + PreviousSold'\n",
    "cracker_lm = ols(formula, data=cracker_data).fit()\n",
    "cracker_lm.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE (ANCOVA): 3.51\n"
     ]
    }
   ],
   "source": [
    "print('MSE (ANCOVA): {:.2f}'.format(cracker_lm.mse_resid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_linreg_residuals(model):\n",
    "\n",
    "    kws = dict(color='blue', marker='o', markersize=7, alpha=0.5)\n",
    "    sns1_kws = dict(marker='o', s=70, alpha=0.5)\n",
    "    sns2_kws = dict(marker='o', s=7, alpha=0.5)\n",
    "    \n",
    "    x = model.resid\n",
    "    yhat = model.fittedvalues\n",
    "    \n",
    "    fig = plt.figure(figsize=(9, 7))\n",
    "\n",
    "    ax1 = fig.add_subplot(221)\n",
    "    ax2 = fig.add_subplot(222)\n",
    "    ax3 = fig.add_subplot(223)\n",
    "    ax4 = fig.add_subplot(224)\n",
    "\n",
    "    ax1.scatter(yhat, x, **sns1_kws)\n",
    "    ax1.set_title('Residuals vs. Fitted values')\n",
    "    \n",
    "    n=len(x)\n",
    "    #sns.residplot(np.linspace(1,n,n), x, ax=ax2, scatter_kws=sns1_kws)\n",
    "    #ax2.set_title('Sequence plot')\n",
    "    ax2.scatter(yhat+x, yhat, **sns1_kws)\n",
    "    ax2.set_title('Actual vs. Fitted values')\n",
    "      \n",
    "    # Box plot\n",
    "    ax3.boxplot(x,showmeans=True)\n",
    "    ax3.set_title('Boxplot')\n",
    "\n",
    "    # qq plot\n",
    "    sm.graphics.qqplot(x,line='q', ax=ax4, **kws)\n",
    "    ax4.set_title('Normal Q-Q plot')\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 648x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 495,
       "width": 639
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_linreg_residuals(cracker_lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial F-test for treatment effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>    <td>0.241</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>   <td>PromotionSold</td>         <td>AIC:</td>         <td>97.7757</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 10:03</td>        <td>BIC:</td>         <td>99.1918</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>15</td>          <td>Log-Likelihood:</td>   <td>-46.888</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>1</td>           <td>F-statistic:</td>      <td>5.439</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>13</td>        <td>Prob (F-statistic):</td> <td>0.0364</td> \n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.295</td>            <td>Scale:</td>        <td>35.056</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>33.8000</td>  <td>1.5287</td>  <td>22.1098</td> <td>0.0000</td> <td>30.4974</td> <td>37.1026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PreviousSold</th> <td>0.7278</td>   <td>0.3121</td>  <td>2.3322</td>  <td>0.0364</td> <td>0.0536</td>  <td>1.4019</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>     <td>2.085</td>  <td>Durbin-Watson:</td>   <td>0.378</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td>  <td>0.353</td> <td>Jarque-Bera (JB):</td> <td>1.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>-0.194</td>     <td>Prob(JB):</td>     <td>0.599</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>    <td>1.780</td>  <td>Condition No.:</td>     <td>5</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                Results: Ordinary least squares\n",
       "================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.241  \n",
       "Dependent Variable: PromotionSold    AIC:                97.7757\n",
       "Date:               2021-10-14 10:03 BIC:                99.1918\n",
       "No. Observations:   15               Log-Likelihood:     -46.888\n",
       "Df Model:           1                F-statistic:        5.439  \n",
       "Df Residuals:       13               Prob (F-statistic): 0.0364 \n",
       "R-squared:          0.295            Scale:              35.056 \n",
       "----------------------------------------------------------------\n",
       "                  Coef.  Std.Err.    t    P>|t|   [0.025  0.975]\n",
       "----------------------------------------------------------------\n",
       "Intercept        33.8000   1.5287 22.1098 0.0000 30.4974 37.1026\n",
       "PreviousSold      0.7278   0.3121  2.3322 0.0364  0.0536  1.4019\n",
       "----------------------------------------------------------------\n",
       "Omnibus:              2.085        Durbin-Watson:          0.378\n",
       "Prob(Omnibus):        0.353        Jarque-Bera (JB):       1.024\n",
       "Skew:                 -0.194       Prob(JB):               0.599\n",
       "Kurtosis:             1.780        Condition No.:          5    \n",
       "================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cracker_reduced_lm = ols('PromotionSold ~ PreviousSold', data=cracker_data).fit()\n",
    "cracker_reduced_lm.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SSE_k (reduced model): 455.72 \n",
      "SSE (full model): 38.57 \n",
      "MSE (full model): 3.51 \n"
     ]
    }
   ],
   "source": [
    "print('SSE_k (reduced model): {:.2f} '.format(cracker_reduced_lm.ssr))\n",
    "print('SSE (full model): {:.2f} '.format(cracker_lm.ssr))\n",
    "print('MSE (full model): {:.2f} '.format(cracker_lm.mse_resid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test statistic: 59.48, P-value: 0.0000\n",
      "Critical value at 0.05: 3.98 \n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "k=2\n",
    "partial_F0 = ((cracker_reduced_lm.ssr-cracker_lm.ssr)/k)/cracker_lm.mse_resid\n",
    "print('Test statistic: {:.2f}, P-value: {:.4f}'.format(partial_F0, \n",
    "                                                       stats.f.sf(partial_F0, k, cracker_lm.df_resid)))\n",
    "print('Critical value at 0.05: {:.2f} '.format(stats.f.isf(0.05, k, cracker_lm.df_resid)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Your Turn -- Activity I: Monofilament"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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>Strength</th>\n",
       "      <th>Diameter</th>\n",
       "      <th>Machine</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>36</td>\n",
       "      <td>20</td>\n",
       "      <td>M1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>41</td>\n",
       "      <td>25</td>\n",
       "      <td>M1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>39</td>\n",
       "      <td>24</td>\n",
       "      <td>M1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>42</td>\n",
       "      <td>25</td>\n",
       "      <td>M1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>49</td>\n",
       "      <td>32</td>\n",
       "      <td>M1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40</td>\n",
       "      <td>22</td>\n",
       "      <td>M2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>48</td>\n",
       "      <td>28</td>\n",
       "      <td>M2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>39</td>\n",
       "      <td>22</td>\n",
       "      <td>M2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>45</td>\n",
       "      <td>30</td>\n",
       "      <td>M2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>44</td>\n",
       "      <td>28</td>\n",
       "      <td>M2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>35</td>\n",
       "      <td>21</td>\n",
       "      <td>M3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>37</td>\n",
       "      <td>23</td>\n",
       "      <td>M3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>42</td>\n",
       "      <td>26</td>\n",
       "      <td>M3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>34</td>\n",
       "      <td>21</td>\n",
       "      <td>M3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>32</td>\n",
       "      <td>15</td>\n",
       "      <td>M3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Strength  Diameter Machine\n",
       "0         36        20      M1\n",
       "1         41        25      M1\n",
       "2         39        24      M1\n",
       "3         42        25      M1\n",
       "4         49        32      M1\n",
       "5         40        22      M2\n",
       "6         48        28      M2\n",
       "7         39        22      M2\n",
       "8         45        30      M2\n",
       "9         44        28      M2\n",
       "10        35        21      M3\n",
       "11        37        23      M3\n",
       "12        42        26      M3\n",
       "13        34        21      M3\n",
       "14        32        15      M3"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fiber_data = pd.read_excel('data/lect06-ancova.xlsx', sheet_name='Filament')\n",
    "fiber_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def codingfunc(x):\n",
    "    if x == 'M1':\n",
    "        return (1,0)\n",
    "    elif x == 'M2':\n",
    "        return (0,1)\n",
    "    else:\n",
    "        return (-1,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strength</th>\n",
       "      <th>Diameter</th>\n",
       "      <th>Machine</th>\n",
       "      <th>I1</th>\n",
       "      <th>I2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>36</td>\n",
       "      <td>-4.133333</td>\n",
       "      <td>M1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
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       "      <td>41</td>\n",
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       "      <td>M1</td>\n",
       "      <td>1</td>\n",
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       "      <th>2</th>\n",
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       "      <th>4</th>\n",
       "      <td>49</td>\n",
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       "      <td>M1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40</td>\n",
       "      <td>-2.133333</td>\n",
       "      <td>M2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>48</td>\n",
       "      <td>3.866667</td>\n",
       "      <td>M2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>39</td>\n",
       "      <td>-2.133333</td>\n",
       "      <td>M2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>45</td>\n",
       "      <td>5.866667</td>\n",
       "      <td>M2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>44</td>\n",
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       "      <td>M2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>35</td>\n",
       "      <td>-3.133333</td>\n",
       "      <td>M3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>37</td>\n",
       "      <td>-1.133333</td>\n",
       "      <td>M3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>42</td>\n",
       "      <td>1.866667</td>\n",
       "      <td>M3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>34</td>\n",
       "      <td>-3.133333</td>\n",
       "      <td>M3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>32</td>\n",
       "      <td>-9.133333</td>\n",
       "      <td>M3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Strength  Diameter Machine  I1  I2\n",
       "0         36 -4.133333      M1   1   0\n",
       "1         41  0.866667      M1   1   0\n",
       "2         39 -0.133333      M1   1   0\n",
       "3         42  0.866667      M1   1   0\n",
       "4         49  7.866667      M1   1   0\n",
       "5         40 -2.133333      M2   0   1\n",
       "6         48  3.866667      M2   0   1\n",
       "7         39 -2.133333      M2   0   1\n",
       "8         45  5.866667      M2   0   1\n",
       "9         44  3.866667      M2   0   1\n",
       "10        35 -3.133333      M3  -1  -1\n",
       "11        37 -1.133333      M3  -1  -1\n",
       "12        42  1.866667      M3  -1  -1\n",
       "13        34 -3.133333      M3  -1  -1\n",
       "14        32 -9.133333      M3  -1  -1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fiber_data[['I1', 'I2']] = pd.DataFrame(fiber_data['Machine'].apply(codingfunc).tolist(), \n",
    "                                           index=fiber_data.index)\n",
    "fiber_data.Diameter -= fiber_data.Diameter.mean()\n",
    "fiber_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "        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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Machine)</th>\n",
       "      <td>2.0</td>\n",
       "      <td>140.4</td>\n",
       "      <td>70.200000</td>\n",
       "      <td>4.08932</td>\n",
       "      <td>0.044232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>12.0</td>\n",
       "      <td>206.0</td>\n",
       "      <td>17.166667</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(Machine)   2.0   140.4  70.200000  4.08932  0.044232\n",
       "Residual    12.0   206.0  17.166667      NaN       NaN"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ANOVA table\n",
    "formula = 'Strength ~ C(Machine)'\n",
    "\n",
    "fiber_lm = ols(formula, data=fiber_data).fit()\n",
    "aov_table2 = anova_lm(fiber_lm) \n",
    "aov_table2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>     <td>0.897</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>     <td>Strength</td>            <td>AIC:</td>          <td>59.9229</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 10:32</td>        <td>BIC:</td>          <td>62.7551</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>15</td>          <td>Log-Likelihood:</td>    <td>-25.961</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>3</td>           <td>F-statistic:</td>       <td>41.72</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>11</td>        <td>Prob (F-statistic):</td> <td>2.66e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.919</td>            <td>Scale:</td>         <td>2.5442</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>40.2000</td>  <td>0.4118</td>  <td>97.6109</td> <td>0.0000</td> <td>39.2935</td> <td>41.1065</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I1</th>        <td>0.1824</td>   <td>0.5950</td>  <td>0.3066</td>  <td>0.7649</td> <td>-1.1272</td> <td>1.4920</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I2</th>        <td>1.2192</td>   <td>0.6201</td>  <td>1.9661</td>  <td>0.0750</td> <td>-0.1456</td> <td>2.5841</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Diameter</th>  <td>0.9540</td>   <td>0.1140</td>  <td>8.3648</td>  <td>0.0000</td> <td>0.7030</td>  <td>1.2050</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>0.909</td>  <td>Durbin-Watson:</td>   <td>1.931</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td> <td>0.635</td> <td>Jarque-Bera (JB):</td> <td>0.818</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>0.463</td>     <td>Prob(JB):</td>     <td>0.664</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>   <td>2.327</td>  <td>Condition No.:</td>     <td>7</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                 Results: Ordinary least squares\n",
       "=================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.897   \n",
       "Dependent Variable: Strength         AIC:                59.9229 \n",
       "Date:               2021-10-14 10:32 BIC:                62.7551 \n",
       "No. Observations:   15               Log-Likelihood:     -25.961 \n",
       "Df Model:           3                F-statistic:        41.72   \n",
       "Df Residuals:       11               Prob (F-statistic): 2.66e-06\n",
       "R-squared:          0.919            Scale:              2.5442  \n",
       "------------------------------------------------------------------\n",
       "               Coef.   Std.Err.     t     P>|t|    [0.025   0.975]\n",
       "------------------------------------------------------------------\n",
       "Intercept     40.2000    0.4118  97.6109  0.0000  39.2935  41.1065\n",
       "I1             0.1824    0.5950   0.3066  0.7649  -1.1272   1.4920\n",
       "I2             1.2192    0.6201   1.9661  0.0750  -0.1456   2.5841\n",
       "Diameter       0.9540    0.1140   8.3648  0.0000   0.7030   1.2050\n",
       "-----------------------------------------------------------------\n",
       "Omnibus:              0.909        Durbin-Watson:           1.931\n",
       "Prob(Omnibus):        0.635        Jarque-Bera (JB):        0.818\n",
       "Skew:                 0.463        Prob(JB):                0.664\n",
       "Kurtosis:             2.327        Condition No.:           7    \n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ANCOVA table\n",
    "formula = 'Strength ~ I1 + I2 + Diameter'\n",
    "\n",
    "fiber_lm = ols(formula, data=fiber_data).fit()\n",
    "fiber_lm.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>     <td>0.872</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>     <td>Strength</td>            <td>AIC:</td>          <td>61.7493</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 10:32</td>        <td>BIC:</td>          <td>63.1654</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>15</td>          <td>Log-Likelihood:</td>    <td>-28.875</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>1</td>           <td>F-statistic:</td>       <td>96.12</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>13</td>        <td>Prob (F-statistic):</td> <td>2.26e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.881</td>            <td>Scale:</td>         <td>3.1746</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>40.2000</td>  <td>0.4600</td>  <td>87.3831</td> <td>0.0000</td> <td>39.2061</td> <td>41.1939</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Diameter</th>  <td>1.0797</td>   <td>0.1101</td>  <td>9.8039</td>  <td>0.0000</td> <td>0.8418</td>  <td>1.3177</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>0.495</td>  <td>Durbin-Watson:</td>   <td>1.387</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td> <td>0.781</td> <td>Jarque-Bera (JB):</td> <td>0.362</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>0.331</td>     <td>Prob(JB):</td>     <td>0.834</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>   <td>2.623</td>  <td>Condition No.:</td>     <td>4</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                 Results: Ordinary least squares\n",
       "=================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.872   \n",
       "Dependent Variable: Strength         AIC:                61.7493 \n",
       "Date:               2021-10-14 10:32 BIC:                63.1654 \n",
       "No. Observations:   15               Log-Likelihood:     -28.875 \n",
       "Df Model:           1                F-statistic:        96.12   \n",
       "Df Residuals:       13               Prob (F-statistic): 2.26e-07\n",
       "R-squared:          0.881            Scale:              3.1746  \n",
       "------------------------------------------------------------------\n",
       "               Coef.   Std.Err.     t     P>|t|    [0.025   0.975]\n",
       "------------------------------------------------------------------\n",
       "Intercept     40.2000    0.4600  87.3831  0.0000  39.2061  41.1939\n",
       "Diameter       1.0797    0.1101   9.8039  0.0000   0.8418   1.3177\n",
       "-----------------------------------------------------------------\n",
       "Omnibus:              0.495        Durbin-Watson:           1.387\n",
       "Prob(Omnibus):        0.781        Jarque-Bera (JB):        0.362\n",
       "Skew:                 0.331        Prob(JB):                0.834\n",
       "Kurtosis:             2.623        Condition No.:           4    \n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fiber_reduced_lm = ols('Strength ~ Diameter', data=fiber_data).fit()\n",
    "fiber_reduced_lm.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SSE_k (reduced model): 41.27 \n",
      "SSE (full model): 27.99 \n",
      "MSE (full model): 2.54 \n"
     ]
    }
   ],
   "source": [
    "print('SSE_k (reduced model): {:.2f} '.format(fiber_reduced_lm.ssr))\n",
    "print('SSE (full model): {:.2f} '.format(fiber_lm.ssr))\n",
    "print('MSE (full model): {:.2f} '.format(fiber_lm.mse_resid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test statistic: 2.61, P-value: 0.1181\n",
      "Critical value at 0.05: 3.98 \n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "k=2\n",
    "partial_F0 = ((fiber_reduced_lm.ssr-fiber_lm.ssr)/k)/fiber_lm.mse_resid\n",
    "print('Test statistic: {:.2f}, P-value: {:.4f}'.format(partial_F0, \n",
    "                                                       stats.f.sf(partial_F0, k, fiber_lm.df_resid)))\n",
    "print('Critical value at 0.05: {:.2f} '.format(stats.f.isf(0.05, k, fiber_lm.df_resid)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x214c125d460>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 411x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 351,
       "width": 402
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.lmplot(data=fiber_data, x=\"Diameter\", y=\"Strength\", hue=\"Machine\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance of estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2338,  0.    ,  0.    ,  0.    ],\n",
       "       [-0.    ,  0.5016, -0.2603,  0.0189],\n",
       "       [ 0.    , -0.2603,  0.4882, -0.0147],\n",
       "       [ 0.    ,  0.0189, -0.0147,  0.0105]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from numpy.linalg import inv\n",
    "\n",
    "Xreg = sm.add_constant(cracker_data[['I1','I2','PreviousSold']]) \n",
    "Covmat = cracker_lm.mse_resid*inv(Xreg.T@Xreg)\n",
    "np.set_printoptions(precision=4)\n",
    "Covmat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-factor  Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "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>Sales</th>\n",
       "      <th>Plot</th>\n",
       "      <th>Variety</th>\n",
       "      <th>Moisture</th>\n",
       "      <th>Rep</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>98</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>77</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>64</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>55</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>75</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>65</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>87</td>\n",
       "      <td>13</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>78</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>71</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>80</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>86</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>82</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>46</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>55</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>76</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>68</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>43</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>47</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>62</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>70</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Sales  Plot  Variety  Moisture  Rep\n",
       "0      98    15        1         1    1\n",
       "1      60     4        1         1    2\n",
       "2      77     7        1         1    3\n",
       "3      80     9        1         1    4\n",
       "4      95    14        1         1    5\n",
       "5      64     5        1         1    6\n",
       "6      55     4        2         1    1\n",
       "7      60     5        2         1    2\n",
       "8      75     8        2         1    3\n",
       "9      65     7        2         1    4\n",
       "10     87    13        2         1    5\n",
       "11     78    11        2         1    6\n",
       "12     71    10        1         2    1\n",
       "13     80    12        1         2    2\n",
       "14     86    14        1         2    3\n",
       "15     82    13        1         2    4\n",
       "16     46     2        1         2    5\n",
       "17     55     3        1         2    6\n",
       "18     76    11        2         2    1\n",
       "19     68    10        2         2    2\n",
       "20     43     2        2         2    3\n",
       "21     47     3        2         2    4\n",
       "22     62     7        2         2    5\n",
       "23     70     9        2         2    6"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flower_data = pd.read_excel('data/lect06-ancova.xlsx', sheet_name='Flower')\n",
    "flower_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "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",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales</th>\n",
       "      <th>Plot</th>\n",
       "      <th>Variety</th>\n",
       "      <th>Moisture</th>\n",
       "      <th>Rep</th>\n",
       "      <th>I1</th>\n",
       "      <th>I2</th>\n",
       "      <th>I1I2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>98</td>\n",
       "      <td>6.75</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>-4.25</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>77</td>\n",
       "      <td>-1.25</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80</td>\n",
       "      <td>0.75</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95</td>\n",
       "      <td>5.75</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>64</td>\n",
       "      <td>-3.25</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>55</td>\n",
       "      <td>-4.25</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "      <td>-3.25</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>75</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>65</td>\n",
       "      <td>-1.25</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>87</td>\n",
       "      <td>4.75</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>78</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>71</td>\n",
       "      <td>1.75</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>80</td>\n",
       "      <td>3.75</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>86</td>\n",
       "      <td>5.75</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>82</td>\n",
       "      <td>4.75</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>46</td>\n",
       "      <td>-6.25</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>55</td>\n",
       "      <td>-5.25</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>76</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>68</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>43</td>\n",
       "      <td>-6.25</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>47</td>\n",
       "      <td>-5.25</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>62</td>\n",
       "      <td>-1.25</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>70</td>\n",
       "      <td>0.75</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Sales  Plot  Variety  Moisture  Rep  I1  I2  I1I2\n",
       "0      98  6.75        1         1    1   1   1     1\n",
       "1      60 -4.25        1         1    2   1   1     1\n",
       "2      77 -1.25        1         1    3   1   1     1\n",
       "3      80  0.75        1         1    4   1   1     1\n",
       "4      95  5.75        1         1    5   1   1     1\n",
       "5      64 -3.25        1         1    6   1   1     1\n",
       "6      55 -4.25        2         1    1  -1   1    -1\n",
       "7      60 -3.25        2         1    2  -1   1    -1\n",
       "8      75 -0.25        2         1    3  -1   1    -1\n",
       "9      65 -1.25        2         1    4  -1   1    -1\n",
       "10     87  4.75        2         1    5  -1   1    -1\n",
       "11     78  2.75        2         1    6  -1   1    -1\n",
       "12     71  1.75        1         2    1   1  -1    -1\n",
       "13     80  3.75        1         2    2   1  -1    -1\n",
       "14     86  5.75        1         2    3   1  -1    -1\n",
       "15     82  4.75        1         2    4   1  -1    -1\n",
       "16     46 -6.25        1         2    5   1  -1    -1\n",
       "17     55 -5.25        1         2    6   1  -1    -1\n",
       "18     76  2.75        2         2    1  -1  -1     1\n",
       "19     68  1.75        2         2    2  -1  -1     1\n",
       "20     43 -6.25        2         2    3  -1  -1     1\n",
       "21     47 -5.25        2         2    4  -1  -1     1\n",
       "22     62 -1.25        2         2    5  -1  -1     1\n",
       "23     70  0.75        2         2    6  -1  -1     1"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def codingfunc(x):\n",
    "    if x == 1:\n",
    "        return 1\n",
    "    else:\n",
    "        return -1\n",
    "      \n",
    "flower_data['I1'] = flower_data['Variety'].apply(codingfunc)\n",
    "flower_data['I2'] = flower_data['Moisture'].apply(codingfunc)\n",
    "flower_data['I1I2'] = flower_data['I1']*flower_data['I2'] \n",
    "flower_data.Plot -= flower_data.Plot.mean()\n",
    "flower_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>     <td>0.972</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>       <td>Sales</td>             <td>AIC:</td>         <td>116.6316</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 13:21</td>        <td>BIC:</td>         <td>122.5218</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>24</td>          <td>Log-Likelihood:</td>    <td>-53.316</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>4</td>           <td>F-statistic:</td>       <td>197.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>19</td>        <td>Prob (F-statistic):</td> <td>3.43e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.977</td>            <td>Scale:</td>         <td>6.2885</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>70.0000</td>  <td>0.5119</td>  <td>136.7511</td> <td>0.0000</td> <td>68.9286</td> <td>71.0714</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I1</th>        <td>2.0423</td>   <td>0.5211</td>   <td>3.9194</td>  <td>0.0009</td> <td>0.9517</td>  <td>3.1330</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I2</th>        <td>3.6808</td>   <td>0.5129</td>   <td>7.1763</td>  <td>0.0000</td> <td>2.6072</td>  <td>4.7543</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I1I2</th>      <td>0.8192</td>   <td>0.5129</td>   <td>1.5972</td>  <td>0.1267</td> <td>-0.2543</td> <td>1.8928</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Plot</th>      <td>3.2769</td>   <td>0.1300</td>   <td>25.2034</td> <td>0.0000</td> <td>3.0048</td>  <td>3.5490</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>4.855</td>  <td>Durbin-Watson:</td>   <td>1.974</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td> <td>0.088</td> <td>Jarque-Bera (JB):</td> <td>3.784</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>0.973</td>     <td>Prob(JB):</td>     <td>0.151</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>   <td>2.979</td>  <td>Condition No.:</td>     <td>4</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                 Results: Ordinary least squares\n",
       "=================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.972   \n",
       "Dependent Variable: Sales            AIC:                116.6316\n",
       "Date:               2021-10-14 13:21 BIC:                122.5218\n",
       "No. Observations:   24               Log-Likelihood:     -53.316 \n",
       "Df Model:           4                F-statistic:        197.4   \n",
       "Df Residuals:       19               Prob (F-statistic): 3.43e-15\n",
       "R-squared:          0.977            Scale:              6.2885  \n",
       "------------------------------------------------------------------\n",
       "              Coef.   Std.Err.     t      P>|t|    [0.025   0.975]\n",
       "------------------------------------------------------------------\n",
       "Intercept    70.0000    0.5119  136.7511  0.0000  68.9286  71.0714\n",
       "I1            2.0423    0.5211    3.9194  0.0009   0.9517   3.1330\n",
       "I2            3.6808    0.5129    7.1763  0.0000   2.6072   4.7543\n",
       "I1I2          0.8192    0.5129    1.5972  0.1267  -0.2543   1.8928\n",
       "Plot          3.2769    0.1300   25.2034  0.0000   3.0048   3.5490\n",
       "-----------------------------------------------------------------\n",
       "Omnibus:              4.855        Durbin-Watson:           1.974\n",
       "Prob(Omnibus):        0.088        Jarque-Bera (JB):        3.784\n",
       "Skew:                 0.973        Prob(JB):                0.151\n",
       "Kurtosis:             2.979        Condition No.:           4    \n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "formula = 'Sales ~ I1 + I2 + I1I2 + Plot'\n",
    "flower_lm = ols(formula, data=flower_data).fit()\n",
    "flower_lm.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>OLS</td>         <td>Adj. R-squared:</td>     <td>0.969</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>       <td>Sales</td>             <td>AIC:</td>         <td>117.6552</td>\n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2021-10-14 13:21</td>        <td>BIC:</td>         <td>122.3674</td>\n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>         <td>24</td>          <td>Log-Likelihood:</td>    <td>-54.828</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>3</td>           <td>F-statistic:</td>       <td>243.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>           <td>20</td>        <td>Prob (F-statistic):</td> <td>6.60e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "      <td>R-squared:</td>            <td>0.973</td>            <td>Scale:</td>         <td>6.7762</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>70.0000</td>  <td>0.5314</td>  <td>131.7381</td> <td>0.0000</td> <td>68.8916</td> <td>71.1084</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I1</th>        <td>2.0522</td>   <td>0.5409</td>   <td>3.7942</td>  <td>0.0011</td> <td>0.9240</td>  <td>3.1805</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I2</th>        <td>3.6841</td>   <td>0.5324</td>   <td>6.9194</td>  <td>0.0000</td> <td>2.5735</td>  <td>4.7947</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Plot</th>      <td>3.2637</td>   <td>0.1347</td>   <td>24.2307</td> <td>0.0000</td> <td>2.9828</td>  <td>3.5447</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td>Omnibus:</td>    <td>2.838</td>  <td>Durbin-Watson:</td>   <td>1.731</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Prob(Omnibus):</td> <td>0.242</td> <td>Jarque-Bera (JB):</td> <td>2.435</td>\n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Skew:</td>     <td>0.715</td>     <td>Prob(JB):</td>     <td>0.296</td>\n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Kurtosis:</td>   <td>2.373</td>  <td>Condition No.:</td>     <td>4</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "                 Results: Ordinary least squares\n",
       "=================================================================\n",
       "Model:              OLS              Adj. R-squared:     0.969   \n",
       "Dependent Variable: Sales            AIC:                117.6552\n",
       "Date:               2021-10-14 13:21 BIC:                122.3674\n",
       "No. Observations:   24               Log-Likelihood:     -54.828 \n",
       "Df Model:           3                F-statistic:        243.5   \n",
       "Df Residuals:       20               Prob (F-statistic): 6.60e-16\n",
       "R-squared:          0.973            Scale:              6.7762  \n",
       "------------------------------------------------------------------\n",
       "              Coef.   Std.Err.     t      P>|t|    [0.025   0.975]\n",
       "------------------------------------------------------------------\n",
       "Intercept    70.0000    0.5314  131.7381  0.0000  68.8916  71.1084\n",
       "I1            2.0522    0.5409    3.7942  0.0011   0.9240   3.1805\n",
       "I2            3.6841    0.5324    6.9194  0.0000   2.5735   4.7947\n",
       "Plot          3.2637    0.1347   24.2307  0.0000   2.9828   3.5447\n",
       "-----------------------------------------------------------------\n",
       "Omnibus:              2.838        Durbin-Watson:           1.731\n",
       "Prob(Omnibus):        0.242        Jarque-Bera (JB):        2.435\n",
       "Skew:                 0.715        Prob(JB):                0.296\n",
       "Kurtosis:             2.373        Condition No.:           4    \n",
       "=================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'Sales ~ I1 + I2 + Plot'\n",
    "flower_lm = ols(formula, data=flower_data).fit()\n",
    "flower_lm.summary2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example has one coefficient for each factor and the coded variables  \n",
    "are uncorrelated. So the significance of a factor can be determined from \n",
    "that of the coefficient.\n",
    "\n",
    "\n",
    "Significance of factor can be generally determined from partial f-tests.  \n",
    "The reduced models are obtained by removing coefficients related to each  \n",
    "factor at the time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance matrix of estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.2823  0.      0.      0.      0.    ]\n",
      " [ 0.      0.2926  0.0034 -0.0034 -0.0137]\n",
      " [ 0.      0.0034  0.2835 -0.0011 -0.0046]\n",
      " [ 0.     -0.0034 -0.0011  0.2835  0.0046]\n",
      " [ 0.     -0.0137 -0.0046  0.0046  0.0182]]\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from numpy.linalg import inv\n",
    "\n",
    "Xreg = sm.add_constant(flower_data[['I1', 'I2', 'I1I2', 'Plot']])\n",
    "Covmat = flower_lm.mse_resid*inv(Xreg.T@Xreg)\n",
    "np.set_printoptions(precision=4)\n",
    "print(Covmat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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