Two Way ANOVA Test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# load packages\n",
    "import scipy.stats as stats\n",
    "import os\n",
    "from statsmodels.formula.api import ols\n",
    "import statsmodels.api as sm\n",
    "\n",
    "import statsmodels.stats.multicomp\n",
    "from statsmodels.graphics.api import interaction_plot, abline_plot\n",
    "\n",
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "import random\n",
    "import math\n",
    "import statistics \n",
    "\n",
    "os.getcwd()\n",
    "os.chdir('D:\\Qurantine\\Blog\\ANOVA Test')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "####Load Data\n",
    "individualDetails=pd.read_csv('./individualDetails.csv',parse_dates=[2])\n",
    "stateDensity=pd.read_csv('./stateDensity.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\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>id</th>\n",
       "      <th>government_id</th>\n",
       "      <th>diagnosed_date</th>\n",
       "      <th>age</th>\n",
       "      <th>gender</th>\n",
       "      <th>detected_city</th>\n",
       "      <th>detected_district</th>\n",
       "      <th>State</th>\n",
       "      <th>nationality</th>\n",
       "      <th>current_status</th>\n",
       "      <th>status_change_date</th>\n",
       "      <th>notes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>KL-TS-P1</td>\n",
       "      <td>2020-01-30</td>\n",
       "      <td>20</td>\n",
       "      <td>F</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>KL-AL-P1</td>\n",
       "      <td>2020-02-02</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>KL-KS-P1</td>\n",
       "      <td>2020-03-02</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>DL-P1</td>\n",
       "      <td>2020-02-03</td>\n",
       "      <td>45</td>\n",
       "      <td>M</td>\n",
       "      <td>East Delhi (Mayur Vihar)</td>\n",
       "      <td>East Delhi</td>\n",
       "      <td>Delhi</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>15-03-2020</td>\n",
       "      <td>Travelled from Austria, Italy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>TS-P1</td>\n",
       "      <td>2020-02-03</td>\n",
       "      <td>24</td>\n",
       "      <td>M</td>\n",
       "      <td>Hyderabad</td>\n",
       "      <td>Hyderabad</td>\n",
       "      <td>Telangana</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>02-03-2020</td>\n",
       "      <td>Travelled from Dubai to Bangalore on 20th Feb,...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id government_id diagnosed_date  age gender             detected_city  \\\n",
       "0   0      KL-TS-P1     2020-01-30   20      F                  Thrissur   \n",
       "1   1      KL-AL-P1     2020-02-02  NaN    NaN                 Alappuzha   \n",
       "2   2      KL-KS-P1     2020-03-02  NaN    NaN                 Kasaragod   \n",
       "3   3         DL-P1     2020-02-03   45      M  East Delhi (Mayur Vihar)   \n",
       "4   4         TS-P1     2020-02-03   24      M                 Hyderabad   \n",
       "\n",
       "  detected_district      State nationality current_status status_change_date  \\\n",
       "0          Thrissur     Kerala       India      Recovered         14-02-2020   \n",
       "1         Alappuzha     Kerala       India      Recovered         14-02-2020   \n",
       "2         Kasaragod     Kerala       India      Recovered         14-02-2020   \n",
       "3        East Delhi      Delhi       India      Recovered         15-03-2020   \n",
       "4         Hyderabad  Telangana       India      Recovered         02-03-2020   \n",
       "\n",
       "                                               notes  \n",
       "0                               Travelled from Wuhan  \n",
       "1                               Travelled from Wuhan  \n",
       "2                               Travelled from Wuhan  \n",
       "3                      Travelled from Austria, Italy  \n",
       "4  Travelled from Dubai to Bangalore on 20th Feb,...  "
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "individualDetails.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 12)"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "individualDetails[individualDetails['age']==0].shape # There's nobody with age=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                             int64\n",
       "government_id                 object\n",
       "diagnosed_date        datetime64[ns]\n",
       "age                           object\n",
       "gender                        object\n",
       "detected_city                 object\n",
       "detected_district             object\n",
       "State                         object\n",
       "nationality                   object\n",
       "current_status                object\n",
       "status_change_date            object\n",
       "notes                         object\n",
       "dtype: object"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "individualDetails.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"\n",
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:7: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "# Transform data in legit format\n",
    "for index , row in individualDetails.iterrows():\n",
    "    if not pd.isnull(row['age']):\n",
    "        if len(row['age'].split('-'))>1:\n",
    "                    individualDetails['age'][index]=round((int(row['age'].split('-')[0])+int(row['age'].split('-')[1]))/2)\n",
    "        elif len(row['age'].split('.'))>1:    \n",
    "            individualDetails['age'][index]=round(float(row['age']))\n",
    "        else:\n",
    "            pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                        0\n",
       "government_id         24893\n",
       "diagnosed_date            0\n",
       "age                   25544\n",
       "gender                22577\n",
       "detected_city         25543\n",
       "detected_district      7650\n",
       "State                     0\n",
       "nationality           25183\n",
       "current_status            0\n",
       "status_change_date      110\n",
       "notes                  1335\n",
       "dtype: int64"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check for missing values\n",
    "individualDetails.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage of missing values in age & gender columns respectively : 91.58838293295088 % 80.95016134815346 %\n"
     ]
    }
   ],
   "source": [
    "print('Percentage of missing values in age & gender columns respectively :', \\\n",
    "      (individualDetails['age'].isna().sum()/individualDetails.shape[0])*100,'%',\\\n",
    "      (individualDetails['gender'].isna().sum()/individualDetails.shape[0])*100,'%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9158838293295087"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "25544/individualDetails.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "#We see that there're 25544 missing entires in age column i.e.almost 92% of overall Data Size. So in lieu of imputing\n",
    "#missing values with median or Mode , I'll impute it with mean. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "ageMedianPerState=individualDetails[~individualDetails['age'].isna()]\n",
    "ageMedianPerState['age']=ageMedianPerState['age'].astype(str).astype(int)\n",
    "\n",
    "ageMedianPerState=ageMedianPerState.groupby('State')[['age']].median().reset_index()\n",
    "ageMedianPerState['age']=ageMedianPerState['age'].apply(lambda x:math.ceil(x))\n",
    "\n",
    "#Find the most frequent infected gender by COVID-19 for each state\n",
    "genderModePerState=individualDetails.groupby(['State'])['gender'].agg(pd.Series.mode).to_frame().reset_index()\n",
    "#Drop Arunachal Pradesh , Since this has got no informatio about gender overall\n",
    "genderModePerState=genderModePerState[genderModePerState['State']!='Arunachal Pradesh']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "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>State</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Andaman and Nicobar Islands</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Andhra Pradesh</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Assam</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Bihar</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Chandigarh</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         State  age\n",
       "0  Andaman and Nicobar Islands   53\n",
       "1               Andhra Pradesh   37\n",
       "2                        Assam   52\n",
       "3                        Bihar   31\n",
       "4                   Chandigarh   26"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ageMedianPerState.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>State</th>\n",
       "      <th>gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Andaman and Nicobar Islands</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Andhra Pradesh</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Assam</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bihar</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Chandigarh</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         State gender\n",
       "0  Andaman and Nicobar Islands      M\n",
       "1               Andhra Pradesh      M\n",
       "3                        Assam      M\n",
       "4                        Bihar      M\n",
       "5                   Chandigarh      M"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "genderModePerState.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:7: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  import sys\n",
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:10: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    }
   ],
   "source": [
    "#Impute missing values in age & gender columns now\n",
    "for index,row in individualDetails.iterrows():\n",
    "    if row['State']=='Arunachal Pradesh':     \n",
    "        individualDetails.drop([index],inplace=True)\n",
    "        continue\n",
    "    if pd.isnull(row['age']):\n",
    "        individualDetails['age'][index]=list(ageMedianPerState['age'][ageMedianPerState['State']=='West Bengal'].values)[0]\n",
    "    if pd.isnull(row['gender']):\n",
    "        if len(genderModePerState['gender'][genderModePerState['State']==row['State']].values)>0:\n",
    "            individualDetails['gender'][index]=(genderModePerState['gender'][genderModePerState['State']==row['State']].values[0])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "id                        0\n",
       "government_id         24892\n",
       "diagnosed_date            0\n",
       "age                       0\n",
       "gender                    0\n",
       "detected_city         25542\n",
       "detected_district      7650\n",
       "State                     0\n",
       "nationality           25183\n",
       "current_status            0\n",
       "status_change_date      110\n",
       "notes                  1335\n",
       "dtype: int64"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "individualDetails.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Merge individualDetails & stateDensity dataframes\n",
    "data=pd.merge(individualDetails,stateDensity,on='State',how='left').reset_index(drop=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "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>id</th>\n",
       "      <th>government_id</th>\n",
       "      <th>diagnosed_date</th>\n",
       "      <th>age</th>\n",
       "      <th>gender</th>\n",
       "      <th>detected_city</th>\n",
       "      <th>detected_district</th>\n",
       "      <th>State</th>\n",
       "      <th>nationality</th>\n",
       "      <th>current_status</th>\n",
       "      <th>status_change_date</th>\n",
       "      <th>notes</th>\n",
       "      <th>density_Group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>KL-TS-P1</td>\n",
       "      <td>2020-01-30</td>\n",
       "      <td>20</td>\n",
       "      <td>F</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>KL-AL-P1</td>\n",
       "      <td>2020-02-02</td>\n",
       "      <td>50</td>\n",
       "      <td>M</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>KL-KS-P1</td>\n",
       "      <td>2020-03-02</td>\n",
       "      <td>50</td>\n",
       "      <td>M</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>DL-P1</td>\n",
       "      <td>2020-02-03</td>\n",
       "      <td>45</td>\n",
       "      <td>M</td>\n",
       "      <td>East Delhi (Mayur Vihar)</td>\n",
       "      <td>East Delhi</td>\n",
       "      <td>Delhi</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>15-03-2020</td>\n",
       "      <td>Travelled from Austria, Italy</td>\n",
       "      <td>Dense4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>TS-P1</td>\n",
       "      <td>2020-02-03</td>\n",
       "      <td>24</td>\n",
       "      <td>M</td>\n",
       "      <td>Hyderabad</td>\n",
       "      <td>Hyderabad</td>\n",
       "      <td>Telangana</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>02-03-2020</td>\n",
       "      <td>Travelled from Dubai to Bangalore on 20th Feb,...</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id government_id diagnosed_date age gender             detected_city  \\\n",
       "0   0      KL-TS-P1     2020-01-30  20      F                  Thrissur   \n",
       "1   1      KL-AL-P1     2020-02-02  50      M                 Alappuzha   \n",
       "2   2      KL-KS-P1     2020-03-02  50      M                 Kasaragod   \n",
       "3   3         DL-P1     2020-02-03  45      M  East Delhi (Mayur Vihar)   \n",
       "4   4         TS-P1     2020-02-03  24      M                 Hyderabad   \n",
       "\n",
       "  detected_district      State nationality current_status status_change_date  \\\n",
       "0          Thrissur     Kerala       India      Recovered         14-02-2020   \n",
       "1         Alappuzha     Kerala       India      Recovered         14-02-2020   \n",
       "2         Kasaragod     Kerala       India      Recovered         14-02-2020   \n",
       "3        East Delhi      Delhi       India      Recovered         15-03-2020   \n",
       "4         Hyderabad  Telangana       India      Recovered         02-03-2020   \n",
       "\n",
       "                                               notes density_Group  \n",
       "0                               Travelled from Wuhan        Dense3  \n",
       "1                               Travelled from Wuhan        Dense3  \n",
       "2                               Travelled from Wuhan        Dense3  \n",
       "3                      Travelled from Austria, Italy        Dense4  \n",
       "4  Travelled from Dubai to Bangalore on 20th Feb,...           NaN  "
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head() # we see that there're NAs in density group coumn for Telangana & Manipur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(27889, 13)"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Kerala', 'Delhi', 'Telangana', 'Rajasthan', 'Haryana',\n",
       "       'Uttar Pradesh', 'Ladakh', 'Tamil Nadu', 'Jammu and Kashmir',\n",
       "       'Karnataka', 'Maharashtra', 'Punjab', 'Andhra Pradesh',\n",
       "       'Uttarakhand', 'Odisha', 'Puducherry', 'West Bengal', 'Chandigarh',\n",
       "       'Chhattisgarh', 'Gujarat', 'Himachal Pradesh', 'Madhya Pradesh',\n",
       "       'Bihar', 'Manipur', 'Mizoram', 'Goa',\n",
       "       'Andaman and Nicobar Islands', 'Jharkhand', 'Assam', 'Tripura',\n",
       "       'Meghalaya'], dtype=object)"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['State'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data[data['State']=='Telangana']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.dropna(subset=['density_Group'],inplace=True) #Drop Telangana & Manipur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.reset_index(drop=True,inplace=True) #resetting index , since just now we've dropped few records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \n",
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\pandas\\core\\indexing.py:670: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self._setitem_with_indexer(indexer, value)\n",
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:10: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  # Remove the CWD from sys.path while we load stuff.\n",
      "C:\\Users\\PraveenKumar\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "#create Age Group bucket\n",
    "data['age_Group']=0\n",
    "for index, row in data.iterrows():\n",
    "    i=float(row['age'])\n",
    "    if 0<i<=20:\n",
    "        data['age_Group'][index]='Young'\n",
    "    elif 20<i<=40:\n",
    "        data['age_Group'][index]='Adult'\n",
    "    else:\n",
    "        data['age_Group'][index]='Old'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "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>id</th>\n",
       "      <th>government_id</th>\n",
       "      <th>diagnosed_date</th>\n",
       "      <th>age</th>\n",
       "      <th>gender</th>\n",
       "      <th>detected_city</th>\n",
       "      <th>detected_district</th>\n",
       "      <th>State</th>\n",
       "      <th>nationality</th>\n",
       "      <th>current_status</th>\n",
       "      <th>status_change_date</th>\n",
       "      <th>notes</th>\n",
       "      <th>density_Group</th>\n",
       "      <th>age_Group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>KL-TS-P1</td>\n",
       "      <td>2020-01-30</td>\n",
       "      <td>20</td>\n",
       "      <td>F</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Thrissur</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "      <td>Young</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>KL-AL-P1</td>\n",
       "      <td>2020-02-02</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Alappuzha</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "      <td>Old</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>KL-KS-P1</td>\n",
       "      <td>2020-03-02</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kasaragod</td>\n",
       "      <td>Kerala</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>14-02-2020</td>\n",
       "      <td>Travelled from Wuhan</td>\n",
       "      <td>Dense3</td>\n",
       "      <td>Old</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>DL-P1</td>\n",
       "      <td>2020-02-03</td>\n",
       "      <td>45</td>\n",
       "      <td>M</td>\n",
       "      <td>East Delhi (Mayur Vihar)</td>\n",
       "      <td>East Delhi</td>\n",
       "      <td>Delhi</td>\n",
       "      <td>India</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>15-03-2020</td>\n",
       "      <td>Travelled from Austria, Italy</td>\n",
       "      <td>Dense4</td>\n",
       "      <td>Old</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2020-03-03</td>\n",
       "      <td>69</td>\n",
       "      <td>M</td>\n",
       "      <td>Jaipur</td>\n",
       "      <td>Italians*</td>\n",
       "      <td>Rajasthan</td>\n",
       "      <td>Italy</td>\n",
       "      <td>Recovered</td>\n",
       "      <td>03-03-2020</td>\n",
       "      <td>Travelled from Italy</td>\n",
       "      <td>Dense1</td>\n",
       "      <td>Old</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id government_id diagnosed_date  age gender             detected_city  \\\n",
       "0   0      KL-TS-P1     2020-01-30   20      F                  Thrissur   \n",
       "1   1      KL-AL-P1     2020-02-02  NaN    NaN                 Alappuzha   \n",
       "2   2      KL-KS-P1     2020-03-02  NaN    NaN                 Kasaragod   \n",
       "3   3         DL-P1     2020-02-03   45      M  East Delhi (Mayur Vihar)   \n",
       "4   5           NaN     2020-03-03   69      M                    Jaipur   \n",
       "\n",
       "  detected_district      State nationality current_status status_change_date  \\\n",
       "0          Thrissur     Kerala       India      Recovered         14-02-2020   \n",
       "1         Alappuzha     Kerala       India      Recovered         14-02-2020   \n",
       "2         Kasaragod     Kerala       India      Recovered         14-02-2020   \n",
       "3        East Delhi      Delhi       India      Recovered         15-03-2020   \n",
       "4         Italians*  Rajasthan       Italy      Recovered         03-03-2020   \n",
       "\n",
       "                           notes density_Group age_Group  \n",
       "0           Travelled from Wuhan        Dense3     Young  \n",
       "1           Travelled from Wuhan        Dense3       Old  \n",
       "2           Travelled from Wuhan        Dense3       Old  \n",
       "3  Travelled from Austria, Italy        Dense4       Old  \n",
       "4           Travelled from Italy        Dense1       Old  "
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "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>id</th>\n",
       "      <th>government_id</th>\n",
       "      <th>diagnosed_date</th>\n",
       "      <th>age</th>\n",
       "      <th>gender</th>\n",
       "      <th>detected_city</th>\n",
       "      <th>detected_district</th>\n",
       "      <th>State</th>\n",
       "      <th>nationality</th>\n",
       "      <th>current_status</th>\n",
       "      <th>status_change_date</th>\n",
       "      <th>notes</th>\n",
       "      <th>density_Group</th>\n",
       "      <th>age_Group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [id, government_id, diagnosed_date, age, gender, detected_city, detected_district, State, nationality, current_status, status_change_date, notes, density_Group, age_Group]\n",
       "Index: []"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['age_Group']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Merge the data to get dataset with each person mapped with their age group and their respective state density group\n",
    "patient_Count=data.groupby(['diagnosed_date','density_Group'])[['diagnosed_date']].count().\\\n",
    "                        rename(columns={'diagnosed_date':'Count'}).reset_index()\n",
    "data=pd.merge(data,patient_Count,on=['diagnosed_date','density_Group'],how='inner')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Rearrange Dataframe\n",
    "newData=data.groupby(['density_Group','age_Group'])['Count'].apply(list).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "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>density_Group</th>\n",
       "      <th>age_Group</th>\n",
       "      <th>Count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>[1, 2, 5, 4, 4, 6, 16, 16, 16, 7, 7, 23, 23, 2...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Old</td>\n",
       "      <td>[1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 5, 5, 5, 5, 4, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Young</td>\n",
       "      <td>[4, 6, 18, 18, 27, 27, 32, 11, 41, 84, 191, 19...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Dense2</td>\n",
       "      <td>Adult</td>\n",
       "      <td>[6, 5, 5, 5, 5, 9, 6, 8, 7, 7, 7, 10, 10, 10, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Dense2</td>\n",
       "      <td>Old</td>\n",
       "      <td>[14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 1...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  density_Group age_Group                                              Count\n",
       "0        Dense1     Adult  [1, 2, 5, 4, 4, 6, 16, 16, 16, 7, 7, 23, 23, 2...\n",
       "1        Dense1       Old  [1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 5, 5, 5, 5, 4, ...\n",
       "2        Dense1     Young  [4, 6, 18, 18, 27, 27, 32, 11, 41, 84, 191, 19...\n",
       "3        Dense2     Adult  [6, 5, 5, 5, 5, 9, 6, 8, 7, 7, 7, 10, 10, 10, ...\n",
       "4        Dense2       Old  [14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 1..."
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newData.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 3)"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newData.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Select random samples of each category\n",
    "np.random.seed(1234)\n",
    "AnovaData=pd.DataFrame(columns=['density_Group','age_Group','Count'])\n",
    "for index,row in newData.iterrows():\n",
    "    count=17\n",
    "    tempDf=pd.DataFrame(index=range(0,count),columns=['density_Group','age_Group','Count'])\n",
    "    \n",
    "    tempDf['age_Group']=newData['age_Group'][index]\n",
    "    tempDf['density_Group']=newData['density_Group'][index]\n",
    "    tempDf['Count']=random.sample(list(newData['Count'][index]),count)\n",
    "    AnovaData=pd.concat([AnovaData,tempDf],axis=0)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "AnovaData.to_csv('AnovaData.csv',index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qRleffBV4z6TrWaLG32T08usB4Evt52pG85/7gcPtdnPrH0Z/7OSrwJeBHZMew0njeSU/ulrmovbEPQL8A/Dc1v68tn6kbb9o0nW3un4dmGvH4p8YXXkxNccB+HPgK8CDwN8xuiJjXR8D4HZG7xH8gNHZ640recwZzWsfaT9vWQdjOMJoDn3h3/RHxvq/p43hEeCqsfYzmld+/YAkdWiap2UkSUsw3CWpQ4a7JHXIcJekDhnuktQhw12SOmS4S1KH/h/BPbTvxDMNlAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x21a9a977088>"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.hist(AnovaData['Count'])\n",
    "plt.show()\n",
    "sns.kdeplot(AnovaData['Count'],cumulative=False,bw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "# AnovaData['Count']=AnovaData['Count']+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "density_Group     object\n",
       "age_Group         object\n",
       "newCount         float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x21a9ea813c8>"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Check for outliers\n",
    "sns.boxplot(x='age_Group', y='Count', \n",
    "                 data=AnovaData, \n",
    "                 palette=\"colorblind\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "AnovaData['Count']=AnovaData['Count'].astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Transformation\n",
    "AnovaData['newCount'],fitted_lambda = stats.boxcox(AnovaData['Count'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x21a9aaba588>"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "sns.kdeplot(AnovaData['newCount'],cumulative=False,bw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "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>density_Group</th>\n",
       "      <th>age_Group</th>\n",
       "      <th>Count</th>\n",
       "      <th>newCount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>206</td>\n",
       "      <td>8.182329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>5</td>\n",
       "      <td>1.821831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>36</td>\n",
       "      <td>4.754236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>32</td>\n",
       "      <td>4.553696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>262</td>\n",
       "      <td>8.729745</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  density_Group age_Group  Count  newCount\n",
       "0        Dense1     Adult    206  8.182329\n",
       "1        Dense1     Adult      5  1.821831\n",
       "2        Dense1     Adult     36  4.754236\n",
       "3        Dense1     Adult     32  4.553696\n",
       "4        Dense1     Adult    262  8.729745"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(204, 3)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "density_Group    0\n",
       "age_Group        0\n",
       "newCount         0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall model F( 5.0, 198.0) =  33.512842550732266, p =  1.0326134879241319e-24\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>newCount</td>     <th>  R-squared:         </th> <td>   0.458</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.445</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   33.51</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 13 May 2020</td> <th>  Prob (F-statistic):</th> <td>1.03e-24</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:24:15</td>     <th>  Log-Likelihood:    </th> <td> -472.72</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   204</td>      <th>  AIC:               </th> <td>   957.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   198</td>      <th>  BIC:               </th> <td>   977.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "               <td></td>                 <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                  <td>    5.8408</td> <td>    0.427</td> <td>   13.665</td> <td> 0.000</td> <td>    4.998</td> <td>    6.684</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]</th>        <td>    1.8152</td> <td>    0.427</td> <td>    4.247</td> <td> 0.000</td> <td>    0.972</td> <td>    2.658</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]</th>      <td>    0.5816</td> <td>    0.427</td> <td>    1.361</td> <td> 0.175</td> <td>   -0.261</td> <td>    1.425</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense2]</th> <td>    4.7959</td> <td>    0.494</td> <td>    9.717</td> <td> 0.000</td> <td>    3.823</td> <td>    5.769</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense3]</th> <td>   -0.7496</td> <td>    0.494</td> <td>   -1.519</td> <td> 0.130</td> <td>   -1.723</td> <td>    0.224</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense4]</th> <td>    1.2143</td> <td>    0.494</td> <td>    2.460</td> <td> 0.015</td> <td>    0.241</td> <td>    2.188</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>32.329</td> <th>  Durbin-Watson:     </th> <td>   1.919</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  44.786</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.956</td> <th>  Prob(JB):          </th> <td>1.88e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.269</td> <th>  Cond. No.          </th> <td>    5.35</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<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:               newCount   R-squared:                       0.458\n",
       "Model:                            OLS   Adj. R-squared:                  0.445\n",
       "Method:                 Least Squares   F-statistic:                     33.51\n",
       "Date:                Wed, 13 May 2020   Prob (F-statistic):           1.03e-24\n",
       "Time:                        20:24:15   Log-Likelihood:                -472.72\n",
       "No. Observations:                 204   AIC:                             957.4\n",
       "Df Residuals:                     198   BIC:                             977.3\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================================\n",
       "                                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------------\n",
       "Intercept                      5.8408      0.427     13.665      0.000       4.998       6.684\n",
       "C(age_Group)[T.Old]            1.8152      0.427      4.247      0.000       0.972       2.658\n",
       "C(age_Group)[T.Young]          0.5816      0.427      1.361      0.175      -0.261       1.425\n",
       "C(density_Group)[T.Dense2]     4.7959      0.494      9.717      0.000       3.823       5.769\n",
       "C(density_Group)[T.Dense3]    -0.7496      0.494     -1.519      0.130      -1.723       0.224\n",
       "C(density_Group)[T.Dense4]     1.2143      0.494      2.460      0.015       0.241       2.188\n",
       "==============================================================================\n",
       "Omnibus:                       32.329   Durbin-Watson:                   1.919\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               44.786\n",
       "Skew:                          -0.956   Prob(JB):                     1.88e-10\n",
       "Kurtosis:                       4.269   Cond. No.                         5.35\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the OlS model\n",
    "#Approach 1.\n",
    "model2 = ols('newCount ~ C(age_Group)+ C(density_Group)', AnovaData).fit()\n",
    "\n",
    "print(f\"Overall model F({model2.df_model: },{model2.df_resid: }) = {model2.fvalue: }, p = {model2.f_pvalue: }\")\n",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(age_Group)</th>\n",
       "      <td>116.843479</td>\n",
       "      <td>2.0</td>\n",
       "      <td>9.404867</td>\n",
       "      <td>1.253300e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(density_Group)</th>\n",
       "      <td>924.042364</td>\n",
       "      <td>3.0</td>\n",
       "      <td>49.584826</td>\n",
       "      <td>6.007121e-24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>1229.948768</td>\n",
       "      <td>198.0</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(age_Group)       116.843479    2.0   9.404867  1.253300e-04\n",
       "C(density_Group)   924.042364    3.0  49.584826  6.007121e-24\n",
       "Residual          1229.948768  198.0        NaN           NaN"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creates the ANOVA table\n",
    "res2 = sm.stats.anova_lm(model2, typ=2)\n",
    "res2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "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": [
    "#Check the Normal distribution of residuals\n",
    "res = model2.resid \n",
    "fig = sm.qqplot(res, line='s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "#As we can see that, residuals are almost normally distributed . Although points at the extreme ends can be discounted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>newCount</td>     <th>  R-squared:         </th> <td>   0.462</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   14.98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 13 May 2020</td> <th>  Prob (F-statistic):</th> <td>8.71e-21</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:31:08</td>     <th>  Log-Likelihood:    </th> <td> -472.07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   204</td>      <th>  AIC:               </th> <td>   968.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   192</td>      <th>  BIC:               </th> <td>   1008.</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>    5.5649</td> <td>    0.612</td> <td>    9.094</td> <td> 0.000</td> <td>    4.358</td> <td>    6.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]</th>                              <td>    2.5162</td> <td>    0.865</td> <td>    2.908</td> <td> 0.004</td> <td>    0.809</td> <td>    4.223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]</th>                            <td>    0.7083</td> <td>    0.865</td> <td>    0.819</td> <td> 0.414</td> <td>   -0.999</td> <td>    2.415</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense2]</th>                       <td>    5.0590</td> <td>    0.865</td> <td>    5.846</td> <td> 0.000</td> <td>    3.352</td> <td>    6.766</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense3]</th>                       <td>   -0.3141</td> <td>    0.865</td> <td>   -0.363</td> <td> 0.717</td> <td>   -2.021</td> <td>    1.393</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense4]</th>                       <td>    1.6194</td> <td>    0.865</td> <td>    1.871</td> <td> 0.063</td> <td>   -0.087</td> <td>    3.326</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense2]</th>   <td>   -0.6723</td> <td>    1.224</td> <td>   -0.549</td> <td> 0.583</td> <td>   -3.086</td> <td>    1.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense2]</th> <td>   -0.1169</td> <td>    1.224</td> <td>   -0.096</td> <td> 0.924</td> <td>   -2.531</td> <td>    2.297</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense3]</th>   <td>   -1.0047</td> <td>    1.224</td> <td>   -0.821</td> <td> 0.413</td> <td>   -3.419</td> <td>    1.409</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense3]</th> <td>   -0.3018</td> <td>    1.224</td> <td>   -0.247</td> <td> 0.805</td> <td>   -2.716</td> <td>    2.112</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense4]</th>   <td>   -1.1273</td> <td>    1.224</td> <td>   -0.921</td> <td> 0.358</td> <td>   -3.541</td> <td>    1.287</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense4]</th> <td>   -0.0881</td> <td>    1.224</td> <td>   -0.072</td> <td> 0.943</td> <td>   -2.502</td> <td>    2.326</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>34.200</td> <th>  Durbin-Watson:     </th> <td>   1.934</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  49.587</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.974</td> <th>  Prob(JB):          </th> <td>1.71e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.429</td> <th>  Cond. No.          </th> <td>    17.9</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<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:               newCount   R-squared:                       0.462\n",
       "Model:                            OLS   Adj. R-squared:                  0.431\n",
       "Method:                 Least Squares   F-statistic:                     14.98\n",
       "Date:                Wed, 13 May 2020   Prob (F-statistic):           8.71e-21\n",
       "Time:                        20:31:08   Log-Likelihood:                -472.07\n",
       "No. Observations:                 204   AIC:                             968.1\n",
       "Df Residuals:                     192   BIC:                             1008.\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================================================\n",
       "                                                       coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------------------------------------\n",
       "Intercept                                            5.5649      0.612      9.094      0.000       4.358       6.772\n",
       "C(age_Group)[T.Old]                                  2.5162      0.865      2.908      0.004       0.809       4.223\n",
       "C(age_Group)[T.Young]                                0.7083      0.865      0.819      0.414      -0.999       2.415\n",
       "C(density_Group)[T.Dense2]                           5.0590      0.865      5.846      0.000       3.352       6.766\n",
       "C(density_Group)[T.Dense3]                          -0.3141      0.865     -0.363      0.717      -2.021       1.393\n",
       "C(density_Group)[T.Dense4]                           1.6194      0.865      1.871      0.063      -0.087       3.326\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense2]      -0.6723      1.224     -0.549      0.583      -3.086       1.742\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense2]    -0.1169      1.224     -0.096      0.924      -2.531       2.297\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense3]      -1.0047      1.224     -0.821      0.413      -3.419       1.409\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense3]    -0.3018      1.224     -0.247      0.805      -2.716       2.112\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense4]      -1.1273      1.224     -0.921      0.358      -3.541       1.287\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense4]    -0.0881      1.224     -0.072      0.943      -2.502       2.326\n",
       "==============================================================================\n",
       "Omnibus:                       34.200   Durbin-Watson:                   1.934\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               49.587\n",
       "Skew:                          -0.974   Prob(JB):                     1.71e-11\n",
       "Kurtosis:                       4.429   Cond. No.                         17.9\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Approach 2.\n",
    "formula = 'newCount ~ C(age_Group) *C(density_Group)'\n",
    "model = ols(formula, AnovaData).fit()\n",
    "\n",
    "model.summary()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                  sum_sq     df        F  PR(>F)\n",
      "C(age_Group)                    116.8435    2.0   9.1781  0.0002\n",
      "C(density_Group)                924.0424    3.0  48.3893  0.0000\n",
      "C(age_Group):C(density_Group)     7.8047    6.0   0.2044  0.9751\n",
      "Residual                       1222.1441  192.0      NaN     NaN\n"
     ]
    }
   ],
   "source": [
    "aov_table = anova_lm(model, typ=2)\n",
    "print(aov_table.round(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "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": [
    "#Check the Normal distribution of residuals\n",
    "res = model2.resid \n",
    "fig = sm.qqplot(res, line='s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>newCount</td>     <th>  R-squared:         </th> <td>   0.462</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   14.98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 13 May 2020</td> <th>  Prob (F-statistic):</th> <td>8.71e-21</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:30:45</td>     <th>  Log-Likelihood:    </th> <td> -472.07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   204</td>      <th>  AIC:               </th> <td>   968.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   192</td>      <th>  BIC:               </th> <td>   1008.</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>    5.5649</td> <td>    0.612</td> <td>    9.094</td> <td> 0.000</td> <td>    4.358</td> <td>    6.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]</th>                              <td>    2.5162</td> <td>    0.865</td> <td>    2.908</td> <td> 0.004</td> <td>    0.809</td> <td>    4.223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]</th>                            <td>    0.7083</td> <td>    0.865</td> <td>    0.819</td> <td> 0.414</td> <td>   -0.999</td> <td>    2.415</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense2]</th>                       <td>    5.0590</td> <td>    0.865</td> <td>    5.846</td> <td> 0.000</td> <td>    3.352</td> <td>    6.766</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense3]</th>                       <td>   -0.3141</td> <td>    0.865</td> <td>   -0.363</td> <td> 0.717</td> <td>   -2.021</td> <td>    1.393</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(density_Group)[T.Dense4]</th>                       <td>    1.6194</td> <td>    0.865</td> <td>    1.871</td> <td> 0.063</td> <td>   -0.087</td> <td>    3.326</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense2]</th>   <td>   -0.6723</td> <td>    1.224</td> <td>   -0.549</td> <td> 0.583</td> <td>   -3.086</td> <td>    1.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense2]</th> <td>   -0.1169</td> <td>    1.224</td> <td>   -0.096</td> <td> 0.924</td> <td>   -2.531</td> <td>    2.297</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense3]</th>   <td>   -1.0047</td> <td>    1.224</td> <td>   -0.821</td> <td> 0.413</td> <td>   -3.419</td> <td>    1.409</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense3]</th> <td>   -0.3018</td> <td>    1.224</td> <td>   -0.247</td> <td> 0.805</td> <td>   -2.716</td> <td>    2.112</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Old]:C(density_Group)[T.Dense4]</th>   <td>   -1.1273</td> <td>    1.224</td> <td>   -0.921</td> <td> 0.358</td> <td>   -3.541</td> <td>    1.287</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(age_Group)[T.Young]:C(density_Group)[T.Dense4]</th> <td>   -0.0881</td> <td>    1.224</td> <td>   -0.072</td> <td> 0.943</td> <td>   -2.502</td> <td>    2.326</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>34.200</td> <th>  Durbin-Watson:     </th> <td>   1.934</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  49.587</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.974</td> <th>  Prob(JB):          </th> <td>1.71e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.429</td> <th>  Cond. No.          </th> <td>    17.9</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<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:               newCount   R-squared:                       0.462\n",
       "Model:                            OLS   Adj. R-squared:                  0.431\n",
       "Method:                 Least Squares   F-statistic:                     14.98\n",
       "Date:                Wed, 13 May 2020   Prob (F-statistic):           8.71e-21\n",
       "Time:                        20:30:45   Log-Likelihood:                -472.07\n",
       "No. Observations:                 204   AIC:                             968.1\n",
       "Df Residuals:                     192   BIC:                             1008.\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================================================\n",
       "                                                       coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------------------------------------\n",
       "Intercept                                            5.5649      0.612      9.094      0.000       4.358       6.772\n",
       "C(age_Group)[T.Old]                                  2.5162      0.865      2.908      0.004       0.809       4.223\n",
       "C(age_Group)[T.Young]                                0.7083      0.865      0.819      0.414      -0.999       2.415\n",
       "C(density_Group)[T.Dense2]                           5.0590      0.865      5.846      0.000       3.352       6.766\n",
       "C(density_Group)[T.Dense3]                          -0.3141      0.865     -0.363      0.717      -2.021       1.393\n",
       "C(density_Group)[T.Dense4]                           1.6194      0.865      1.871      0.063      -0.087       3.326\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense2]      -0.6723      1.224     -0.549      0.583      -3.086       1.742\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense2]    -0.1169      1.224     -0.096      0.924      -2.531       2.297\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense3]      -1.0047      1.224     -0.821      0.413      -3.419       1.409\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense3]    -0.3018      1.224     -0.247      0.805      -2.716       2.112\n",
       "C(age_Group)[T.Old]:C(density_Group)[T.Dense4]      -1.1273      1.224     -0.921      0.358      -3.541       1.287\n",
       "C(age_Group)[T.Young]:C(density_Group)[T.Dense4]    -0.0881      1.224     -0.072      0.943      -2.502       2.326\n",
       "==============================================================================\n",
       "Omnibus:                       34.200   Durbin-Watson:                   1.934\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               49.587\n",
       "Skew:                          -0.974   Prob(JB):                     1.71e-11\n",
       "Kurtosis:                       4.429   Cond. No.                         17.9\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###Approch 3.\n",
    "\n",
    "formula = 'newCount ~ C(age_Group) + C(density_Group) + C(age_Group):C(density_Group)'\n",
    "model = ols(formula, AnovaData).fit()\n",
    "\n",
    "model.summary()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                    sum_sq     df          F        PR(>F)\n",
      "C(age_Group)                    116.843479    2.0   9.178111  1.560282e-04\n",
      "C(density_Group)                924.042364    3.0  48.389313  2.448503e-23\n",
      "C(age_Group):C(density_Group)     7.804715    6.0   0.204355  9.751253e-01\n",
      "Residual                       1222.144053  192.0        NaN           NaN\n"
     ]
    }
   ],
   "source": [
    "aov_table = statsmodels.stats.anova.anova_lm(model, typ=2)\n",
    "print(aov_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Interpretation: The P-value obtained from ANOVA analysis for genotype, years, and interaction are statistically significant \n",
    "#(P<0.05). We conclude that type of density_Group significantly affects the corona cases outcome,\n",
    "#age_Group significantly affects the corona cases outcome outcome, and interaction of both age_Group and density_Group \n",
    "#significantly affects the corona cases outcome outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "density_Group     object\n",
       "age_Group         object\n",
       "newCount         float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "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>density_Group</th>\n",
       "      <th>age_Group</th>\n",
       "      <th>newCount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>8.182329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>1.821831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>4.754236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>4.553696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Dense1</td>\n",
       "      <td>Adult</td>\n",
       "      <td>8.729745</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  density_Group age_Group  newCount\n",
       "0        Dense1     Adult  8.182329\n",
       "1        Dense1     Adult  1.821831\n",
       "2        Dense1     Adult  4.754236\n",
       "3        Dense1     Adult  4.553696\n",
       "4        Dense1     Adult  8.729745"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AnovaData.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD, FWER=0.05 \n",
      "====================================================\n",
      "group1 group2 meandiff p-adj   lower   upper  reject\n",
      "----------------------------------------------------\n",
      "Dense1 Dense2   4.7959  0.001  3.4645  6.1273   True\n",
      "Dense1 Dense3  -0.7496 0.4656  -2.081  0.5818  False\n",
      "Dense1 Dense4   1.2143 0.0876 -0.1171  2.5457  False\n",
      "Dense2 Dense3  -5.5455  0.001 -6.8769 -4.2141   True\n",
      "Dense2 Dense4  -3.5816  0.001  -4.913 -2.2502   True\n",
      "Dense3 Dense4   1.9639  0.001  0.6325  3.2953   True\n",
      "----------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "#Post hoc test\n",
    "mc = statsmodels.stats.multicomp.MultiComparison(AnovaData['newCount'],AnovaData['density_Group'])\n",
    "mc_results = mc.tukeyhsd()\n",
    "print(mc_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD, FWER=0.05\n",
      "===================================================\n",
      "group1 group2 meandiff p-adj   lower  upper  reject\n",
      "---------------------------------------------------\n",
      " Adult    Old   1.8152 0.0041  0.4895 3.1409   True\n",
      " Adult  Young   0.5816 0.5519 -0.7441 1.9073  False\n",
      "   Old  Young  -1.2336 0.0742 -2.5593 0.0921  False\n",
      "---------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "#Post hoc test\n",
    "mc = statsmodels.stats.multicomp.MultiComparison(AnovaData['newCount'],AnovaData['age_Group'])\n",
    "mc_results = mc.tukeyhsd()\n",
    "print(mc_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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