logistic-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hospital Readmission Prevention\n",
    "\n",
    "This code was taken from an example of loan default application explained in the class of 45980 Big Data at Tepper School, Carnegie Mellon University taught by Dr. Amr Farahat. The data used for this is a cleaned version of the data available from the website - https://doi.org/10.1155/2014/781670\n",
    "\n",
    "The cleaned and raw data are both available on the repository\n",
    "\n",
    "The concept used in this algorithm is logistic regression and calculating the probability of readmission is explained below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Importing the Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load the Datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = pd.read_csv(\"Dataset/readmission_train.csv\")\n",
    "test_data = pd.read_csv(\"Dataset/readmission_test.csv\")\n",
    "\n",
    "# train and test split\n",
    "y_train = train_data[\"readmission\"]\n",
    "X_train = train_data.drop(\"readmission\", axis=1)\n",
    "y_test = test_data[\"readmission\"]\n",
    "X_test = test_data.drop(\"readmission\", axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting a logistic regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Hp\\AppData\\Local\\Temp\\ipykernel_20388\\564504020.py:3: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.\n",
      "  a = pd.DataFrame(X_train.corr())\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numberEmergency</th>\n",
       "      <th>numberInpatient</th>\n",
       "      <th>insulin</th>\n",
       "      <th>metformin</th>\n",
       "      <th>numberDiagnoses</th>\n",
       "      <th>diagAnemia</th>\n",
       "      <th>diagAsthma</th>\n",
       "      <th>diagAthlerosclerosis</th>\n",
       "      <th>diagCellulitis</th>\n",
       "      <th>diagCKD</th>\n",
       "      <th>diagDyspnea</th>\n",
       "      <th>diagHeartFailure</th>\n",
       "      <th>diagHypertension</th>\n",
       "      <th>diagHypertensiveCKD</th>\n",
       "      <th>diagPneumonia</th>\n",
       "      <th>diagSkinUlcer</th>\n",
       "      <th>timeInHospital</th>\n",
       "      <th>numNonLabProcedures</th>\n",
       "      <th>numMedications</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>numberEmergency</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.263135</td>\n",
       "      <td>0.044120</td>\n",
       "      <td>-0.007924</td>\n",
       "      <td>0.054522</td>\n",
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       "      <td>0.019523</td>\n",
       "      <td>-0.038603</td>\n",
       "      <td>0.009968</td>\n",
       "      <td>0.032091</td>\n",
       "      <td>0.007955</td>\n",
       "      <td>-0.007619</td>\n",
       "      <td>-0.025371</td>\n",
       "      <td>0.029686</td>\n",
       "      <td>-0.003759</td>\n",
       "      <td>0.004687</td>\n",
       "      <td>-0.010916</td>\n",
       "      <td>-0.035311</td>\n",
       "      <td>0.015310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numberInpatient</th>\n",
       "      <td>0.263135</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.074493</td>\n",
       "      <td>-0.069363</td>\n",
       "      <td>0.103253</td>\n",
       "      <td>-0.010376</td>\n",
       "      <td>-0.001201</td>\n",
       "      <td>-0.056811</td>\n",
       "      <td>0.000987</td>\n",
       "      <td>0.084466</td>\n",
       "      <td>-0.024945</td>\n",
       "      <td>0.073758</td>\n",
       "      <td>-0.081380</td>\n",
       "      <td>0.098688</td>\n",
       "      <td>0.002665</td>\n",
       "      <td>0.039279</td>\n",
       "      <td>0.070520</td>\n",
       "      <td>-0.065898</td>\n",
       "      <td>0.066684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>insulin</th>\n",
       "      <td>0.044120</td>\n",
       "      <td>0.074493</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.032876</td>\n",
       "      <td>0.077813</td>\n",
       "      <td>-0.014202</td>\n",
       "      <td>0.020576</td>\n",
       "      <td>-0.052817</td>\n",
       "      <td>0.032062</td>\n",
       "      <td>0.021988</td>\n",
       "      <td>-0.056395</td>\n",
       "      <td>0.016746</td>\n",
       "      <td>-0.071227</td>\n",
       "      <td>0.035131</td>\n",
       "      <td>0.039097</td>\n",
       "      <td>0.035985</td>\n",
       "      <td>0.097233</td>\n",
       "      <td>0.015254</td>\n",
       "      <td>0.210029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>metformin</th>\n",
       "      <td>-0.007924</td>\n",
       "      <td>-0.069363</td>\n",
       "      <td>-0.032876</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.069568</td>\n",
       "      <td>0.010804</td>\n",
       "      <td>0.042947</td>\n",
       "      <td>-0.015875</td>\n",
       "      <td>0.036785</td>\n",
       "      <td>-0.089101</td>\n",
       "      <td>0.017816</td>\n",
       "      <td>-0.077188</td>\n",
       "      <td>0.080196</td>\n",
       "      <td>-0.108662</td>\n",
       "      <td>-0.003381</td>\n",
       "      <td>-0.001456</td>\n",
       "      <td>-0.005356</td>\n",
       "      <td>-0.042431</td>\n",
       "      <td>0.070382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numberDiagnoses</th>\n",
       "      <td>0.054522</td>\n",
       "      <td>0.103253</td>\n",
       "      <td>0.077813</td>\n",
       "      <td>-0.069568</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.022955</td>\n",
       "      <td>-0.011619</td>\n",
       "      <td>-0.028811</td>\n",
       "      <td>0.025940</td>\n",
       "      <td>0.094173</td>\n",
       "      <td>-0.036277</td>\n",
       "      <td>0.164767</td>\n",
       "      <td>-0.254362</td>\n",
       "      <td>0.069238</td>\n",
       "      <td>0.065287</td>\n",
       "      <td>0.054470</td>\n",
       "      <td>0.219679</td>\n",
       "      <td>0.074678</td>\n",
       "      <td>0.262856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAnemia</th>\n",
       "      <td>-0.007535</td>\n",
       "      <td>-0.010376</td>\n",
       "      <td>-0.014202</td>\n",
       "      <td>0.010804</td>\n",
       "      <td>0.022955</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.020798</td>\n",
       "      <td>-0.034673</td>\n",
       "      <td>-0.024957</td>\n",
       "      <td>-0.015852</td>\n",
       "      <td>-0.028351</td>\n",
       "      <td>-0.040184</td>\n",
       "      <td>-0.033625</td>\n",
       "      <td>-0.016966</td>\n",
       "      <td>-0.027561</td>\n",
       "      <td>-0.020873</td>\n",
       "      <td>0.003619</td>\n",
       "      <td>0.055043</td>\n",
       "      <td>0.039295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAsthma</th>\n",
       "      <td>0.019523</td>\n",
       "      <td>-0.001201</td>\n",
       "      <td>0.020576</td>\n",
       "      <td>0.042947</td>\n",
       "      <td>-0.011619</td>\n",
       "      <td>-0.020798</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.032332</td>\n",
       "      <td>-0.019567</td>\n",
       "      <td>-0.021843</td>\n",
       "      <td>0.005194</td>\n",
       "      <td>-0.006992</td>\n",
       "      <td>-0.003253</td>\n",
       "      <td>-0.030641</td>\n",
       "      <td>0.035584</td>\n",
       "      <td>-0.021335</td>\n",
       "      <td>0.007312</td>\n",
       "      <td>-0.055690</td>\n",
       "      <td>0.037264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAthlerosclerosis</th>\n",
       "      <td>-0.038603</td>\n",
       "      <td>-0.056811</td>\n",
       "      <td>-0.052817</td>\n",
       "      <td>-0.015875</td>\n",
       "      <td>-0.028811</td>\n",
       "      <td>-0.034673</td>\n",
       "      <td>-0.032332</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.067614</td>\n",
       "      <td>-0.048066</td>\n",
       "      <td>0.044318</td>\n",
       "      <td>-0.014969</td>\n",
       "      <td>0.035625</td>\n",
       "      <td>-0.056549</td>\n",
       "      <td>-0.068290</td>\n",
       "      <td>-0.063368</td>\n",
       "      <td>-0.111946</td>\n",
       "      <td>0.344275</td>\n",
       "      <td>0.091699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagCellulitis</th>\n",
       "      <td>0.009968</td>\n",
       "      <td>0.000987</td>\n",
       "      <td>0.032062</td>\n",
       "      <td>0.036785</td>\n",
       "      <td>0.025940</td>\n",
       "      <td>-0.024957</td>\n",
       "      <td>-0.019567</td>\n",
       "      <td>-0.067614</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.010495</td>\n",
       "      <td>-0.042650</td>\n",
       "      <td>-0.035768</td>\n",
       "      <td>-0.039195</td>\n",
       "      <td>-0.025505</td>\n",
       "      <td>-0.041301</td>\n",
       "      <td>0.191703</td>\n",
       "      <td>0.071726</td>\n",
       "      <td>-0.038095</td>\n",
       "      <td>0.010768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagCKD</th>\n",
       "      <td>0.032091</td>\n",
       "      <td>0.084466</td>\n",
       "      <td>0.021988</td>\n",
       "      <td>-0.089101</td>\n",
       "      <td>0.094173</td>\n",
       "      <td>-0.015852</td>\n",
       "      <td>-0.021843</td>\n",
       "      <td>-0.048066</td>\n",
       "      <td>-0.010495</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.022176</td>\n",
       "      <td>0.023142</td>\n",
       "      <td>-0.068533</td>\n",
       "      <td>0.220902</td>\n",
       "      <td>-0.011995</td>\n",
       "      <td>-0.018233</td>\n",
       "      <td>0.000447</td>\n",
       "      <td>0.016328</td>\n",
       "      <td>0.039034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagDyspnea</th>\n",
       "      <td>0.007955</td>\n",
       "      <td>-0.024945</td>\n",
       "      <td>-0.056395</td>\n",
       "      <td>0.017816</td>\n",
       "      <td>-0.036277</td>\n",
       "      <td>-0.028351</td>\n",
       "      <td>0.005194</td>\n",
       "      <td>0.044318</td>\n",
       "      <td>-0.042650</td>\n",
       "      <td>-0.022176</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.051062</td>\n",
       "      <td>0.063928</td>\n",
       "      <td>-0.027955</td>\n",
       "      <td>-0.038705</td>\n",
       "      <td>-0.038546</td>\n",
       "      <td>-0.163390</td>\n",
       "      <td>-0.071067</td>\n",
       "      <td>-0.096716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHeartFailure</th>\n",
       "      <td>-0.007619</td>\n",
       "      <td>0.073758</td>\n",
       "      <td>0.016746</td>\n",
       "      <td>-0.077188</td>\n",
       "      <td>0.164767</td>\n",
       "      <td>-0.040184</td>\n",
       "      <td>-0.006992</td>\n",
       "      <td>-0.014969</td>\n",
       "      <td>-0.035768</td>\n",
       "      <td>0.023142</td>\n",
       "      <td>-0.051062</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.102339</td>\n",
       "      <td>0.018061</td>\n",
       "      <td>0.038548</td>\n",
       "      <td>-0.038662</td>\n",
       "      <td>0.057377</td>\n",
       "      <td>-0.068332</td>\n",
       "      <td>0.077534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHypertension</th>\n",
       "      <td>-0.025371</td>\n",
       "      <td>-0.081380</td>\n",
       "      <td>-0.071227</td>\n",
       "      <td>0.080196</td>\n",
       "      <td>-0.254362</td>\n",
       "      <td>-0.033625</td>\n",
       "      <td>-0.003253</td>\n",
       "      <td>0.035625</td>\n",
       "      <td>-0.039195</td>\n",
       "      <td>-0.068533</td>\n",
       "      <td>0.063928</td>\n",
       "      <td>-0.102339</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.090151</td>\n",
       "      <td>-0.051083</td>\n",
       "      <td>-0.057918</td>\n",
       "      <td>-0.142214</td>\n",
       "      <td>-0.012836</td>\n",
       "      <td>-0.081889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHypertensiveCKD</th>\n",
       "      <td>0.029686</td>\n",
       "      <td>0.098688</td>\n",
       "      <td>0.035131</td>\n",
       "      <td>-0.108662</td>\n",
       "      <td>0.069238</td>\n",
       "      <td>-0.016966</td>\n",
       "      <td>-0.030641</td>\n",
       "      <td>-0.056549</td>\n",
       "      <td>-0.025505</td>\n",
       "      <td>0.220902</td>\n",
       "      <td>-0.027955</td>\n",
       "      <td>0.018061</td>\n",
       "      <td>-0.090151</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.022786</td>\n",
       "      <td>-0.016086</td>\n",
       "      <td>0.030560</td>\n",
       "      <td>0.043684</td>\n",
       "      <td>0.049943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagPneumonia</th>\n",
       "      <td>-0.003759</td>\n",
       "      <td>0.002665</td>\n",
       "      <td>0.039097</td>\n",
       "      <td>-0.003381</td>\n",
       "      <td>0.065287</td>\n",
       "      <td>-0.027561</td>\n",
       "      <td>0.035584</td>\n",
       "      <td>-0.068290</td>\n",
       "      <td>-0.041301</td>\n",
       "      <td>-0.011995</td>\n",
       "      <td>-0.038705</td>\n",
       "      <td>0.038548</td>\n",
       "      <td>-0.051083</td>\n",
       "      <td>-0.022786</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.022413</td>\n",
       "      <td>0.076723</td>\n",
       "      <td>-0.092866</td>\n",
       "      <td>0.054934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagSkinUlcer</th>\n",
       "      <td>0.004687</td>\n",
       "      <td>0.039279</td>\n",
       "      <td>0.035985</td>\n",
       "      <td>-0.001456</td>\n",
       "      <td>0.054470</td>\n",
       "      <td>-0.020873</td>\n",
       "      <td>-0.021335</td>\n",
       "      <td>-0.063368</td>\n",
       "      <td>0.191703</td>\n",
       "      <td>-0.018233</td>\n",
       "      <td>-0.038546</td>\n",
       "      <td>-0.038662</td>\n",
       "      <td>-0.057918</td>\n",
       "      <td>-0.016086</td>\n",
       "      <td>-0.022413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.098890</td>\n",
       "      <td>0.013882</td>\n",
       "      <td>0.036110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>timeInHospital</th>\n",
       "      <td>-0.010916</td>\n",
       "      <td>0.070520</td>\n",
       "      <td>0.097233</td>\n",
       "      <td>-0.005356</td>\n",
       "      <td>0.219679</td>\n",
       "      <td>0.003619</td>\n",
       "      <td>0.007312</td>\n",
       "      <td>-0.111946</td>\n",
       "      <td>0.071726</td>\n",
       "      <td>0.000447</td>\n",
       "      <td>-0.163390</td>\n",
       "      <td>0.057377</td>\n",
       "      <td>-0.142214</td>\n",
       "      <td>0.030560</td>\n",
       "      <td>0.076723</td>\n",
       "      <td>0.098890</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.192761</td>\n",
       "      <td>0.463207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numNonLabProcedures</th>\n",
       "      <td>-0.035311</td>\n",
       "      <td>-0.065898</td>\n",
       "      <td>0.015254</td>\n",
       "      <td>-0.042431</td>\n",
       "      <td>0.074678</td>\n",
       "      <td>0.055043</td>\n",
       "      <td>-0.055690</td>\n",
       "      <td>0.344275</td>\n",
       "      <td>-0.038095</td>\n",
       "      <td>0.016328</td>\n",
       "      <td>-0.071067</td>\n",
       "      <td>-0.068332</td>\n",
       "      <td>-0.012836</td>\n",
       "      <td>0.043684</td>\n",
       "      <td>-0.092866</td>\n",
       "      <td>0.013882</td>\n",
       "      <td>0.192761</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.388542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numMedications</th>\n",
       "      <td>0.015310</td>\n",
       "      <td>0.066684</td>\n",
       "      <td>0.210029</td>\n",
       "      <td>0.070382</td>\n",
       "      <td>0.262856</td>\n",
       "      <td>0.039295</td>\n",
       "      <td>0.037264</td>\n",
       "      <td>0.091699</td>\n",
       "      <td>0.010768</td>\n",
       "      <td>0.039034</td>\n",
       "      <td>-0.096716</td>\n",
       "      <td>0.077534</td>\n",
       "      <td>-0.081889</td>\n",
       "      <td>0.049943</td>\n",
       "      <td>0.054934</td>\n",
       "      <td>0.036110</td>\n",
       "      <td>0.463207</td>\n",
       "      <td>0.388542</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      numberEmergency  numberInpatient   insulin  metformin  \\\n",
       "numberEmergency              1.000000         0.263135  0.044120  -0.007924   \n",
       "numberInpatient              0.263135         1.000000  0.074493  -0.069363   \n",
       "insulin                      0.044120         0.074493  1.000000  -0.032876   \n",
       "metformin                   -0.007924        -0.069363 -0.032876   1.000000   \n",
       "numberDiagnoses              0.054522         0.103253  0.077813  -0.069568   \n",
       "diagAnemia                  -0.007535        -0.010376 -0.014202   0.010804   \n",
       "diagAsthma                   0.019523        -0.001201  0.020576   0.042947   \n",
       "diagAthlerosclerosis        -0.038603        -0.056811 -0.052817  -0.015875   \n",
       "diagCellulitis               0.009968         0.000987  0.032062   0.036785   \n",
       "diagCKD                      0.032091         0.084466  0.021988  -0.089101   \n",
       "diagDyspnea                  0.007955        -0.024945 -0.056395   0.017816   \n",
       "diagHeartFailure            -0.007619         0.073758  0.016746  -0.077188   \n",
       "diagHypertension            -0.025371        -0.081380 -0.071227   0.080196   \n",
       "diagHypertensiveCKD          0.029686         0.098688  0.035131  -0.108662   \n",
       "diagPneumonia               -0.003759         0.002665  0.039097  -0.003381   \n",
       "diagSkinUlcer                0.004687         0.039279  0.035985  -0.001456   \n",
       "timeInHospital              -0.010916         0.070520  0.097233  -0.005356   \n",
       "numNonLabProcedures         -0.035311        -0.065898  0.015254  -0.042431   \n",
       "numMedications               0.015310         0.066684  0.210029   0.070382   \n",
       "\n",
       "                      numberDiagnoses  diagAnemia  diagAsthma  \\\n",
       "numberEmergency              0.054522   -0.007535    0.019523   \n",
       "numberInpatient              0.103253   -0.010376   -0.001201   \n",
       "insulin                      0.077813   -0.014202    0.020576   \n",
       "metformin                   -0.069568    0.010804    0.042947   \n",
       "numberDiagnoses              1.000000    0.022955   -0.011619   \n",
       "diagAnemia                   0.022955    1.000000   -0.020798   \n",
       "diagAsthma                  -0.011619   -0.020798    1.000000   \n",
       "diagAthlerosclerosis        -0.028811   -0.034673   -0.032332   \n",
       "diagCellulitis               0.025940   -0.024957   -0.019567   \n",
       "diagCKD                      0.094173   -0.015852   -0.021843   \n",
       "diagDyspnea                 -0.036277   -0.028351    0.005194   \n",
       "diagHeartFailure             0.164767   -0.040184   -0.006992   \n",
       "diagHypertension            -0.254362   -0.033625   -0.003253   \n",
       "diagHypertensiveCKD          0.069238   -0.016966   -0.030641   \n",
       "diagPneumonia                0.065287   -0.027561    0.035584   \n",
       "diagSkinUlcer                0.054470   -0.020873   -0.021335   \n",
       "timeInHospital               0.219679    0.003619    0.007312   \n",
       "numNonLabProcedures          0.074678    0.055043   -0.055690   \n",
       "numMedications               0.262856    0.039295    0.037264   \n",
       "\n",
       "                      diagAthlerosclerosis  diagCellulitis   diagCKD  \\\n",
       "numberEmergency                  -0.038603        0.009968  0.032091   \n",
       "numberInpatient                  -0.056811        0.000987  0.084466   \n",
       "insulin                          -0.052817        0.032062  0.021988   \n",
       "metformin                        -0.015875        0.036785 -0.089101   \n",
       "numberDiagnoses                  -0.028811        0.025940  0.094173   \n",
       "diagAnemia                       -0.034673       -0.024957 -0.015852   \n",
       "diagAsthma                       -0.032332       -0.019567 -0.021843   \n",
       "diagAthlerosclerosis              1.000000       -0.067614 -0.048066   \n",
       "diagCellulitis                   -0.067614        1.000000 -0.010495   \n",
       "diagCKD                          -0.048066       -0.010495  1.000000   \n",
       "diagDyspnea                       0.044318       -0.042650 -0.022176   \n",
       "diagHeartFailure                 -0.014969       -0.035768  0.023142   \n",
       "diagHypertension                  0.035625       -0.039195 -0.068533   \n",
       "diagHypertensiveCKD              -0.056549       -0.025505  0.220902   \n",
       "diagPneumonia                    -0.068290       -0.041301 -0.011995   \n",
       "diagSkinUlcer                    -0.063368        0.191703 -0.018233   \n",
       "timeInHospital                   -0.111946        0.071726  0.000447   \n",
       "numNonLabProcedures               0.344275       -0.038095  0.016328   \n",
       "numMedications                    0.091699        0.010768  0.039034   \n",
       "\n",
       "                      diagDyspnea  diagHeartFailure  diagHypertension  \\\n",
       "numberEmergency          0.007955         -0.007619         -0.025371   \n",
       "numberInpatient         -0.024945          0.073758         -0.081380   \n",
       "insulin                 -0.056395          0.016746         -0.071227   \n",
       "metformin                0.017816         -0.077188          0.080196   \n",
       "numberDiagnoses         -0.036277          0.164767         -0.254362   \n",
       "diagAnemia              -0.028351         -0.040184         -0.033625   \n",
       "diagAsthma               0.005194         -0.006992         -0.003253   \n",
       "diagAthlerosclerosis     0.044318         -0.014969          0.035625   \n",
       "diagCellulitis          -0.042650         -0.035768         -0.039195   \n",
       "diagCKD                 -0.022176          0.023142         -0.068533   \n",
       "diagDyspnea              1.000000         -0.051062          0.063928   \n",
       "diagHeartFailure        -0.051062          1.000000         -0.102339   \n",
       "diagHypertension         0.063928         -0.102339          1.000000   \n",
       "diagHypertensiveCKD     -0.027955          0.018061         -0.090151   \n",
       "diagPneumonia           -0.038705          0.038548         -0.051083   \n",
       "diagSkinUlcer           -0.038546         -0.038662         -0.057918   \n",
       "timeInHospital          -0.163390          0.057377         -0.142214   \n",
       "numNonLabProcedures     -0.071067         -0.068332         -0.012836   \n",
       "numMedications          -0.096716          0.077534         -0.081889   \n",
       "\n",
       "                      diagHypertensiveCKD  diagPneumonia  diagSkinUlcer  \\\n",
       "numberEmergency                  0.029686      -0.003759       0.004687   \n",
       "numberInpatient                  0.098688       0.002665       0.039279   \n",
       "insulin                          0.035131       0.039097       0.035985   \n",
       "metformin                       -0.108662      -0.003381      -0.001456   \n",
       "numberDiagnoses                  0.069238       0.065287       0.054470   \n",
       "diagAnemia                      -0.016966      -0.027561      -0.020873   \n",
       "diagAsthma                      -0.030641       0.035584      -0.021335   \n",
       "diagAthlerosclerosis            -0.056549      -0.068290      -0.063368   \n",
       "diagCellulitis                  -0.025505      -0.041301       0.191703   \n",
       "diagCKD                          0.220902      -0.011995      -0.018233   \n",
       "diagDyspnea                     -0.027955      -0.038705      -0.038546   \n",
       "diagHeartFailure                 0.018061       0.038548      -0.038662   \n",
       "diagHypertension                -0.090151      -0.051083      -0.057918   \n",
       "diagHypertensiveCKD              1.000000      -0.022786      -0.016086   \n",
       "diagPneumonia                   -0.022786       1.000000      -0.022413   \n",
       "diagSkinUlcer                   -0.016086      -0.022413       1.000000   \n",
       "timeInHospital                   0.030560       0.076723       0.098890   \n",
       "numNonLabProcedures              0.043684      -0.092866       0.013882   \n",
       "numMedications                   0.049943       0.054934       0.036110   \n",
       "\n",
       "                      timeInHospital  numNonLabProcedures  numMedications  \n",
       "numberEmergency            -0.010916            -0.035311        0.015310  \n",
       "numberInpatient             0.070520            -0.065898        0.066684  \n",
       "insulin                     0.097233             0.015254        0.210029  \n",
       "metformin                  -0.005356            -0.042431        0.070382  \n",
       "numberDiagnoses             0.219679             0.074678        0.262856  \n",
       "diagAnemia                  0.003619             0.055043        0.039295  \n",
       "diagAsthma                  0.007312            -0.055690        0.037264  \n",
       "diagAthlerosclerosis       -0.111946             0.344275        0.091699  \n",
       "diagCellulitis              0.071726            -0.038095        0.010768  \n",
       "diagCKD                     0.000447             0.016328        0.039034  \n",
       "diagDyspnea                -0.163390            -0.071067       -0.096716  \n",
       "diagHeartFailure            0.057377            -0.068332        0.077534  \n",
       "diagHypertension           -0.142214            -0.012836       -0.081889  \n",
       "diagHypertensiveCKD         0.030560             0.043684        0.049943  \n",
       "diagPneumonia               0.076723            -0.092866        0.054934  \n",
       "diagSkinUlcer               0.098890             0.013882        0.036110  \n",
       "timeInHospital              1.000000             0.192761        0.463207  \n",
       "numNonLabProcedures         0.192761             1.000000        0.388542  \n",
       "numMedications              0.463207             0.388542        1.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking the correlation between the elements\n",
    "\n",
    "a = pd.DataFrame(X_train.corr())\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>numberEmergency</th>\n",
       "      <th>numberInpatient</th>\n",
       "      <th>insulin</th>\n",
       "      <th>metformin</th>\n",
       "      <th>numberDiagnoses</th>\n",
       "      <th>diagAnemia</th>\n",
       "      <th>diagAsthma</th>\n",
       "      <th>diagAthlerosclerosis</th>\n",
       "      <th>diagCellulitis</th>\n",
       "      <th>diagCKD</th>\n",
       "      <th>diagDyspnea</th>\n",
       "      <th>diagHeartFailure</th>\n",
       "      <th>diagHypertension</th>\n",
       "      <th>diagHypertensiveCKD</th>\n",
       "      <th>diagPneumonia</th>\n",
       "      <th>diagSkinUlcer</th>\n",
       "      <th>timeInHospital</th>\n",
       "      <th>numNonLabProcedures</th>\n",
       "      <th>numMedications</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>numberEmergency</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numberInpatient</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>insulin</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>metformin</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numberDiagnoses</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAnemia</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAsthma</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagAthlerosclerosis</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagCellulitis</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagCKD</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagDyspnea</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHeartFailure</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHypertension</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagHypertensiveCKD</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagPneumonia</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagSkinUlcer</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>timeInHospital</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.463207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numNonLabProcedures</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numMedications</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.463207</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      numberEmergency  numberInpatient  insulin  metformin  \\\n",
       "numberEmergency                   1.0              NaN      NaN        NaN   \n",
       "numberInpatient                   NaN              1.0      NaN        NaN   \n",
       "insulin                           NaN              NaN      1.0        NaN   \n",
       "metformin                         NaN              NaN      NaN        1.0   \n",
       "numberDiagnoses                   NaN              NaN      NaN        NaN   \n",
       "diagAnemia                        NaN              NaN      NaN        NaN   \n",
       "diagAsthma                        NaN              NaN      NaN        NaN   \n",
       "diagAthlerosclerosis              NaN              NaN      NaN        NaN   \n",
       "diagCellulitis                    NaN              NaN      NaN        NaN   \n",
       "diagCKD                           NaN              NaN      NaN        NaN   \n",
       "diagDyspnea                       NaN              NaN      NaN        NaN   \n",
       "diagHeartFailure                  NaN              NaN      NaN        NaN   \n",
       "diagHypertension                  NaN              NaN      NaN        NaN   \n",
       "diagHypertensiveCKD               NaN              NaN      NaN        NaN   \n",
       "diagPneumonia                     NaN              NaN      NaN        NaN   \n",
       "diagSkinUlcer                     NaN              NaN      NaN        NaN   \n",
       "timeInHospital                    NaN              NaN      NaN        NaN   \n",
       "numNonLabProcedures               NaN              NaN      NaN        NaN   \n",
       "numMedications                    NaN              NaN      NaN        NaN   \n",
       "\n",
       "                      numberDiagnoses  diagAnemia  diagAsthma  \\\n",
       "numberEmergency                   NaN         NaN         NaN   \n",
       "numberInpatient                   NaN         NaN         NaN   \n",
       "insulin                           NaN         NaN         NaN   \n",
       "metformin                         NaN         NaN         NaN   \n",
       "numberDiagnoses                   1.0         NaN         NaN   \n",
       "diagAnemia                        NaN         1.0         NaN   \n",
       "diagAsthma                        NaN         NaN         1.0   \n",
       "diagAthlerosclerosis              NaN         NaN         NaN   \n",
       "diagCellulitis                    NaN         NaN         NaN   \n",
       "diagCKD                           NaN         NaN         NaN   \n",
       "diagDyspnea                       NaN         NaN         NaN   \n",
       "diagHeartFailure                  NaN         NaN         NaN   \n",
       "diagHypertension                  NaN         NaN         NaN   \n",
       "diagHypertensiveCKD               NaN         NaN         NaN   \n",
       "diagPneumonia                     NaN         NaN         NaN   \n",
       "diagSkinUlcer                     NaN         NaN         NaN   \n",
       "timeInHospital                    NaN         NaN         NaN   \n",
       "numNonLabProcedures               NaN         NaN         NaN   \n",
       "numMedications                    NaN         NaN         NaN   \n",
       "\n",
       "                      diagAthlerosclerosis  diagCellulitis  diagCKD  \\\n",
       "numberEmergency                        NaN             NaN      NaN   \n",
       "numberInpatient                        NaN             NaN      NaN   \n",
       "insulin                                NaN             NaN      NaN   \n",
       "metformin                              NaN             NaN      NaN   \n",
       "numberDiagnoses                        NaN             NaN      NaN   \n",
       "diagAnemia                             NaN             NaN      NaN   \n",
       "diagAsthma                             NaN             NaN      NaN   \n",
       "diagAthlerosclerosis                   1.0             NaN      NaN   \n",
       "diagCellulitis                         NaN             1.0      NaN   \n",
       "diagCKD                                NaN             NaN      1.0   \n",
       "diagDyspnea                            NaN             NaN      NaN   \n",
       "diagHeartFailure                       NaN             NaN      NaN   \n",
       "diagHypertension                       NaN             NaN      NaN   \n",
       "diagHypertensiveCKD                    NaN             NaN      NaN   \n",
       "diagPneumonia                          NaN             NaN      NaN   \n",
       "diagSkinUlcer                          NaN             NaN      NaN   \n",
       "timeInHospital                         NaN             NaN      NaN   \n",
       "numNonLabProcedures                    NaN             NaN      NaN   \n",
       "numMedications                         NaN             NaN      NaN   \n",
       "\n",
       "                      diagDyspnea  diagHeartFailure  diagHypertension  \\\n",
       "numberEmergency               NaN               NaN               NaN   \n",
       "numberInpatient               NaN               NaN               NaN   \n",
       "insulin                       NaN               NaN               NaN   \n",
       "metformin                     NaN               NaN               NaN   \n",
       "numberDiagnoses               NaN               NaN               NaN   \n",
       "diagAnemia                    NaN               NaN               NaN   \n",
       "diagAsthma                    NaN               NaN               NaN   \n",
       "diagAthlerosclerosis          NaN               NaN               NaN   \n",
       "diagCellulitis                NaN               NaN               NaN   \n",
       "diagCKD                       NaN               NaN               NaN   \n",
       "diagDyspnea                   1.0               NaN               NaN   \n",
       "diagHeartFailure              NaN               1.0               NaN   \n",
       "diagHypertension              NaN               NaN               1.0   \n",
       "diagHypertensiveCKD           NaN               NaN               NaN   \n",
       "diagPneumonia                 NaN               NaN               NaN   \n",
       "diagSkinUlcer                 NaN               NaN               NaN   \n",
       "timeInHospital                NaN               NaN               NaN   \n",
       "numNonLabProcedures           NaN               NaN               NaN   \n",
       "numMedications                NaN               NaN               NaN   \n",
       "\n",
       "                      diagHypertensiveCKD  diagPneumonia  diagSkinUlcer  \\\n",
       "numberEmergency                       NaN            NaN            NaN   \n",
       "numberInpatient                       NaN            NaN            NaN   \n",
       "insulin                               NaN            NaN            NaN   \n",
       "metformin                             NaN            NaN            NaN   \n",
       "numberDiagnoses                       NaN            NaN            NaN   \n",
       "diagAnemia                            NaN            NaN            NaN   \n",
       "diagAsthma                            NaN            NaN            NaN   \n",
       "diagAthlerosclerosis                  NaN            NaN            NaN   \n",
       "diagCellulitis                        NaN            NaN            NaN   \n",
       "diagCKD                               NaN            NaN            NaN   \n",
       "diagDyspnea                           NaN            NaN            NaN   \n",
       "diagHeartFailure                      NaN            NaN            NaN   \n",
       "diagHypertension                      NaN            NaN            NaN   \n",
       "diagHypertensiveCKD                   1.0            NaN            NaN   \n",
       "diagPneumonia                         NaN            1.0            NaN   \n",
       "diagSkinUlcer                         NaN            NaN            1.0   \n",
       "timeInHospital                        NaN            NaN            NaN   \n",
       "numNonLabProcedures                   NaN            NaN            NaN   \n",
       "numMedications                        NaN            NaN            NaN   \n",
       "\n",
       "                      timeInHospital  numNonLabProcedures  numMedications  \n",
       "numberEmergency                  NaN                  NaN             NaN  \n",
       "numberInpatient                  NaN                  NaN             NaN  \n",
       "insulin                          NaN                  NaN             NaN  \n",
       "metformin                        NaN                  NaN             NaN  \n",
       "numberDiagnoses                  NaN                  NaN             NaN  \n",
       "diagAnemia                       NaN                  NaN             NaN  \n",
       "diagAsthma                       NaN                  NaN             NaN  \n",
       "diagAthlerosclerosis             NaN                  NaN             NaN  \n",
       "diagCellulitis                   NaN                  NaN             NaN  \n",
       "diagCKD                          NaN                  NaN             NaN  \n",
       "diagDyspnea                      NaN                  NaN             NaN  \n",
       "diagHeartFailure                 NaN                  NaN             NaN  \n",
       "diagHypertension                 NaN                  NaN             NaN  \n",
       "diagHypertensiveCKD              NaN                  NaN             NaN  \n",
       "diagPneumonia                    NaN                  NaN             NaN  \n",
       "diagSkinUlcer                    NaN                  NaN             NaN  \n",
       "timeInHospital              1.000000                  NaN        0.463207  \n",
       "numNonLabProcedures              NaN                  1.0             NaN  \n",
       "numMedications              0.463207                  NaN        1.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# finding values that are highly correlated to remove them from the model to avoid multicollinearity\n",
    "min_age = 0.4\n",
    "max_age = 1.0\n",
    "filtered_df = a[(a >= min_age) & (a <= max_age)]\n",
    "filtered_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.337959\n",
      "         Iterations 8\n"
     ]
    }
   ],
   "source": [
    "# Logistic Regression Model\n",
    "\n",
    "# the elements timeInHospital and numMedications seem to be highly colinear, hence will be removed from the model\n",
    "logreg_mod_sm = smf.logit(\n",
    "    data=train_data,\n",
    "    formula=\"readmission ~ age+numberEmergency+numberInpatient+insulin+metformin+numberDiagnoses+diagAnemia+diagAsthma+diagAthlerosclerosis+diagCellulitis+diagCKD+diagDyspnea+diagHeartFailure+diagHypertension+diagHypertensiveCKD+diagPneumonia+diagSkinUlcer+numNonLabProcedures\",\n",
    ")\n",
    "\n",
    "logreg_sm = logreg_mod_sm.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>readmission</td>   <th>  No. Observations:  </th>  <td> 71236</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td> 71209</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>    26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 10 Jul 2023</td> <th>  Pseudo R-squ.:     </th>  <td>0.03583</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>09:52:55</td>     <th>  Log-Likelihood:    </th> <td> -24075.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -24970.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th>  <td> 0.000</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>            <td>   -3.9381</td> <td>    0.585</td> <td>   -6.729</td> <td> 0.000</td> <td>   -5.085</td> <td>   -2.791</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[10-20)]</th>       <td>    0.6382</td> <td>    0.618</td> <td>    1.033</td> <td> 0.302</td> <td>   -0.573</td> <td>    1.849</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[20-30)]</th>       <td>    1.2945</td> <td>    0.592</td> <td>    2.185</td> <td> 0.029</td> <td>    0.133</td> <td>    2.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[30-40)]</th>       <td>    1.3071</td> <td>    0.589</td> <td>    2.220</td> <td> 0.026</td> <td>    0.153</td> <td>    2.461</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[40-50)]</th>       <td>    1.2101</td> <td>    0.587</td> <td>    2.061</td> <td> 0.039</td> <td>    0.059</td> <td>    2.361</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[50-60)]</th>       <td>    1.1541</td> <td>    0.587</td> <td>    1.967</td> <td> 0.049</td> <td>    0.004</td> <td>    2.304</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[60-70)]</th>       <td>    1.3171</td> <td>    0.586</td> <td>    2.246</td> <td> 0.025</td> <td>    0.168</td> <td>    2.467</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[70-80)]</th>       <td>    1.3916</td> <td>    0.586</td> <td>    2.373</td> <td> 0.018</td> <td>    0.242</td> <td>    2.541</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[80-90)]</th>       <td>    1.3739</td> <td>    0.587</td> <td>    2.342</td> <td> 0.019</td> <td>    0.224</td> <td>    2.524</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[90-100)]</th>      <td>    1.2311</td> <td>    0.591</td> <td>    2.085</td> <td> 0.037</td> <td>    0.074</td> <td>    2.389</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberEmergency</th>      <td>    0.0322</td> <td>    0.010</td> <td>    3.348</td> <td> 0.001</td> <td>    0.013</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberInpatient</th>      <td>    0.2559</td> <td>    0.008</td> <td>   32.939</td> <td> 0.000</td> <td>    0.241</td> <td>    0.271</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>insulin</th>              <td>    0.1232</td> <td>    0.025</td> <td>    4.967</td> <td> 0.000</td> <td>    0.075</td> <td>    0.172</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>metformin</th>            <td>   -0.0376</td> <td>    0.032</td> <td>   -1.161</td> <td> 0.245</td> <td>   -0.101</td> <td>    0.026</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberDiagnoses</th>      <td>    0.0432</td> <td>    0.007</td> <td>    5.974</td> <td> 0.000</td> <td>    0.029</td> <td>    0.057</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagAnemia</th>           <td>   -0.0922</td> <td>    0.073</td> <td>   -1.264</td> <td> 0.206</td> <td>   -0.235</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagAsthma</th>           <td>   -0.1604</td> <td>    0.082</td> <td>   -1.963</td> <td> 0.050</td> <td>   -0.321</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagAthlerosclerosis</th> <td>   -0.1503</td> <td>    0.043</td> <td>   -3.516</td> <td> 0.000</td> <td>   -0.234</td> <td>   -0.067</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagCellulitis</th>       <td>   -0.0859</td> <td>    0.062</td> <td>   -1.387</td> <td> 0.165</td> <td>   -0.207</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagCKD</th>              <td>    0.1453</td> <td>    0.056</td> <td>    2.575</td> <td> 0.010</td> <td>    0.035</td> <td>    0.256</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagDyspnea</th>          <td>   -0.2542</td> <td>    0.064</td> <td>   -4.000</td> <td> 0.000</td> <td>   -0.379</td> <td>   -0.130</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHeartFailure</th>     <td>    0.0893</td> <td>    0.031</td> <td>    2.847</td> <td> 0.004</td> <td>    0.028</td> <td>    0.151</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHypertension</th>     <td>   -0.1952</td> <td>    0.044</td> <td>   -4.438</td> <td> 0.000</td> <td>   -0.281</td> <td>   -0.109</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHypertensiveCKD</th>  <td>    0.2083</td> <td>    0.048</td> <td>    4.348</td> <td> 0.000</td> <td>    0.114</td> <td>    0.302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagPneumonia</th>        <td>   -0.1844</td> <td>    0.056</td> <td>   -3.300</td> <td> 0.001</td> <td>   -0.294</td> <td>   -0.075</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagSkinUlcer</th>        <td>    0.1871</td> <td>    0.061</td> <td>    3.054</td> <td> 0.002</td> <td>    0.067</td> <td>    0.307</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numNonLabProcedures</th>  <td>   -0.0134</td> <td>    0.008</td> <td>   -1.691</td> <td> 0.091</td> <td>   -0.029</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:            readmission   No. Observations:                71236\n",
       "Model:                          Logit   Df Residuals:                    71209\n",
       "Method:                           MLE   Df Model:                           26\n",
       "Date:                Mon, 10 Jul 2023   Pseudo R-squ.:                 0.03583\n",
       "Time:                        09:52:55   Log-Likelihood:                -24075.\n",
       "converged:                       True   LL-Null:                       -24970.\n",
       "Covariance Type:            nonrobust   LLR p-value:                     0.000\n",
       "========================================================================================\n",
       "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------\n",
       "Intercept               -3.9381      0.585     -6.729      0.000      -5.085      -2.791\n",
       "age[T.[10-20)]           0.6382      0.618      1.033      0.302      -0.573       1.849\n",
       "age[T.[20-30)]           1.2945      0.592      2.185      0.029       0.133       2.456\n",
       "age[T.[30-40)]           1.3071      0.589      2.220      0.026       0.153       2.461\n",
       "age[T.[40-50)]           1.2101      0.587      2.061      0.039       0.059       2.361\n",
       "age[T.[50-60)]           1.1541      0.587      1.967      0.049       0.004       2.304\n",
       "age[T.[60-70)]           1.3171      0.586      2.246      0.025       0.168       2.467\n",
       "age[T.[70-80)]           1.3916      0.586      2.373      0.018       0.242       2.541\n",
       "age[T.[80-90)]           1.3739      0.587      2.342      0.019       0.224       2.524\n",
       "age[T.[90-100)]          1.2311      0.591      2.085      0.037       0.074       2.389\n",
       "numberEmergency          0.0322      0.010      3.348      0.001       0.013       0.051\n",
       "numberInpatient          0.2559      0.008     32.939      0.000       0.241       0.271\n",
       "insulin                  0.1232      0.025      4.967      0.000       0.075       0.172\n",
       "metformin               -0.0376      0.032     -1.161      0.245      -0.101       0.026\n",
       "numberDiagnoses          0.0432      0.007      5.974      0.000       0.029       0.057\n",
       "diagAnemia              -0.0922      0.073     -1.264      0.206      -0.235       0.051\n",
       "diagAsthma              -0.1604      0.082     -1.963      0.050      -0.321      -0.000\n",
       "diagAthlerosclerosis    -0.1503      0.043     -3.516      0.000      -0.234      -0.067\n",
       "diagCellulitis          -0.0859      0.062     -1.387      0.165      -0.207       0.035\n",
       "diagCKD                  0.1453      0.056      2.575      0.010       0.035       0.256\n",
       "diagDyspnea             -0.2542      0.064     -4.000      0.000      -0.379      -0.130\n",
       "diagHeartFailure         0.0893      0.031      2.847      0.004       0.028       0.151\n",
       "diagHypertension        -0.1952      0.044     -4.438      0.000      -0.281      -0.109\n",
       "diagHypertensiveCKD      0.2083      0.048      4.348      0.000       0.114       0.302\n",
       "diagPneumonia           -0.1844      0.056     -3.300      0.001      -0.294      -0.075\n",
       "diagSkinUlcer            0.1871      0.061      3.054      0.002       0.067       0.307\n",
       "numNonLabProcedures     -0.0134      0.008     -1.691      0.091      -0.029       0.002\n",
       "========================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg_sm.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the summary, we see that the p value of age[T.[10-20)], metformin and diagAnemia are higher than 0.05, which make is non-significant values, hence the model will be re-run by eliminating these elements.\n",
    "\n",
    "The age can't be removed as the logit function breaks the age down into different variables on it's own. This can be ignored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.337980\n",
      "         Iterations 8\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>readmission</td>   <th>  No. Observations:  </th>  <td> 71236</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td> 71211</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>    24</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 10 Jul 2023</td> <th>  Pseudo R-squ.:     </th>  <td>0.03577</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>09:53:01</td>     <th>  Log-Likelihood:    </th> <td> -24076.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -24970.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th>  <td> 0.000</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>            <td>   -3.9397</td> <td>    0.585</td> <td>   -6.732</td> <td> 0.000</td> <td>   -5.087</td> <td>   -2.793</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[10-20)]</th>       <td>    0.6344</td> <td>    0.618</td> <td>    1.027</td> <td> 0.304</td> <td>   -0.576</td> <td>    1.845</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[20-30)]</th>       <td>    1.2882</td> <td>    0.592</td> <td>    2.174</td> <td> 0.030</td> <td>    0.127</td> <td>    2.449</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[30-40)]</th>       <td>    1.2970</td> <td>    0.589</td> <td>    2.203</td> <td> 0.028</td> <td>    0.143</td> <td>    2.451</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[40-50)]</th>       <td>    1.1978</td> <td>    0.587</td> <td>    2.041</td> <td> 0.041</td> <td>    0.047</td> <td>    2.348</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[50-60)]</th>       <td>    1.1409</td> <td>    0.587</td> <td>    1.945</td> <td> 0.052</td> <td>   -0.009</td> <td>    2.291</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[60-70)]</th>       <td>    1.3033</td> <td>    0.586</td> <td>    2.223</td> <td> 0.026</td> <td>    0.154</td> <td>    2.453</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[70-80)]</th>       <td>    1.3780</td> <td>    0.586</td> <td>    2.350</td> <td> 0.019</td> <td>    0.229</td> <td>    2.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[80-90)]</th>       <td>    1.3621</td> <td>    0.587</td> <td>    2.322</td> <td> 0.020</td> <td>    0.212</td> <td>    2.512</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age[T.[90-100)]</th>      <td>    1.2216</td> <td>    0.591</td> <td>    2.069</td> <td> 0.039</td> <td>    0.064</td> <td>    2.379</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberEmergency</th>      <td>    0.0321</td> <td>    0.010</td> <td>    3.341</td> <td> 0.001</td> <td>    0.013</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberInpatient</th>      <td>    0.2564</td> <td>    0.008</td> <td>   33.055</td> <td> 0.000</td> <td>    0.241</td> <td>    0.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>insulin</th>              <td>    0.1245</td> <td>    0.025</td> <td>    5.020</td> <td> 0.000</td> <td>    0.076</td> <td>    0.173</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numberDiagnoses</th>      <td>    0.0434</td> <td>    0.007</td> <td>    6.009</td> <td> 0.000</td> <td>    0.029</td> <td>    0.058</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagAsthma</th>           <td>   -0.1618</td> <td>    0.082</td> <td>   -1.981</td> <td> 0.048</td> <td>   -0.322</td> <td>   -0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagAthlerosclerosis</th> <td>   -0.1464</td> <td>    0.043</td> <td>   -3.431</td> <td> 0.001</td> <td>   -0.230</td> <td>   -0.063</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagCellulitis</th>       <td>   -0.0860</td> <td>    0.062</td> <td>   -1.390</td> <td> 0.164</td> <td>   -0.207</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagCKD</th>              <td>    0.1511</td> <td>    0.056</td> <td>    2.685</td> <td> 0.007</td> <td>    0.041</td> <td>    0.261</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagDyspnea</th>          <td>   -0.2526</td> <td>    0.064</td> <td>   -3.975</td> <td> 0.000</td> <td>   -0.377</td> <td>   -0.128</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHeartFailure</th>     <td>    0.0936</td> <td>    0.031</td> <td>    2.991</td> <td> 0.003</td> <td>    0.032</td> <td>    0.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHypertension</th>     <td>   -0.1954</td> <td>    0.044</td> <td>   -4.448</td> <td> 0.000</td> <td>   -0.282</td> <td>   -0.109</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagHypertensiveCKD</th>  <td>    0.2153</td> <td>    0.048</td> <td>    4.515</td> <td> 0.000</td> <td>    0.122</td> <td>    0.309</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagPneumonia</th>        <td>   -0.1822</td> <td>    0.056</td> <td>   -3.262</td> <td> 0.001</td> <td>   -0.292</td> <td>   -0.073</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>diagSkinUlcer</th>        <td>    0.1900</td> <td>    0.061</td> <td>    3.104</td> <td> 0.002</td> <td>    0.070</td> <td>    0.310</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>numNonLabProcedures</th>  <td>   -0.0137</td> <td>    0.008</td> <td>   -1.736</td> <td> 0.083</td> <td>   -0.029</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:            readmission   No. Observations:                71236\n",
       "Model:                          Logit   Df Residuals:                    71211\n",
       "Method:                           MLE   Df Model:                           24\n",
       "Date:                Mon, 10 Jul 2023   Pseudo R-squ.:                 0.03577\n",
       "Time:                        09:53:01   Log-Likelihood:                -24076.\n",
       "converged:                       True   LL-Null:                       -24970.\n",
       "Covariance Type:            nonrobust   LLR p-value:                     0.000\n",
       "========================================================================================\n",
       "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------\n",
       "Intercept               -3.9397      0.585     -6.732      0.000      -5.087      -2.793\n",
       "age[T.[10-20)]           0.6344      0.618      1.027      0.304      -0.576       1.845\n",
       "age[T.[20-30)]           1.2882      0.592      2.174      0.030       0.127       2.449\n",
       "age[T.[30-40)]           1.2970      0.589      2.203      0.028       0.143       2.451\n",
       "age[T.[40-50)]           1.1978      0.587      2.041      0.041       0.047       2.348\n",
       "age[T.[50-60)]           1.1409      0.587      1.945      0.052      -0.009       2.291\n",
       "age[T.[60-70)]           1.3033      0.586      2.223      0.026       0.154       2.453\n",
       "age[T.[70-80)]           1.3780      0.586      2.350      0.019       0.229       2.527\n",
       "age[T.[80-90)]           1.3621      0.587      2.322      0.020       0.212       2.512\n",
       "age[T.[90-100)]          1.2216      0.591      2.069      0.039       0.064       2.379\n",
       "numberEmergency          0.0321      0.010      3.341      0.001       0.013       0.051\n",
       "numberInpatient          0.2564      0.008     33.055      0.000       0.241       0.272\n",
       "insulin                  0.1245      0.025      5.020      0.000       0.076       0.173\n",
       "numberDiagnoses          0.0434      0.007      6.009      0.000       0.029       0.058\n",
       "diagAsthma              -0.1618      0.082     -1.981      0.048      -0.322      -0.002\n",
       "diagAthlerosclerosis    -0.1464      0.043     -3.431      0.001      -0.230      -0.063\n",
       "diagCellulitis          -0.0860      0.062     -1.390      0.164      -0.207       0.035\n",
       "diagCKD                  0.1511      0.056      2.685      0.007       0.041       0.261\n",
       "diagDyspnea             -0.2526      0.064     -3.975      0.000      -0.377      -0.128\n",
       "diagHeartFailure         0.0936      0.031      2.991      0.003       0.032       0.155\n",
       "diagHypertension        -0.1954      0.044     -4.448      0.000      -0.282      -0.109\n",
       "diagHypertensiveCKD      0.2153      0.048      4.515      0.000       0.122       0.309\n",
       "diagPneumonia           -0.1822      0.056     -3.262      0.001      -0.292      -0.073\n",
       "diagSkinUlcer            0.1900      0.061      3.104      0.002       0.070       0.310\n",
       "numNonLabProcedures     -0.0137      0.008     -1.736      0.083      -0.029       0.002\n",
       "========================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg_mod_sm = smf.logit(\n",
    "    data=train_data,\n",
    "    formula=\"readmission ~ age+numberEmergency+numberInpatient+insulin+numberDiagnoses+diagAsthma+diagAthlerosclerosis+diagCellulitis+diagCKD+diagDyspnea+diagHeartFailure+diagHypertension+diagHypertensiveCKD+diagPneumonia+diagSkinUlcer+numNonLabProcedures\",\n",
    ")\n",
    "logreg_sm = logreg_mod_sm.fit()\n",
    "logreg_sm.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the value of the probability of the patient being readmitted, from the details mentioned about the data, we see the following - \n",
    "\n",
    "1) The telehealth interventions will reduce the incidence of 30-day unplanned readmissions in the treated population by 25%\n",
    "2) Cost of admission - $35000\n",
    "3) Cost of admission with telehealth - $1200 + $35000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.137142857142857\n"
     ]
    }
   ],
   "source": [
    "# Probabilities of admission\n",
    "\n",
    "p = Symbol(\"p\")\n",
    "tele_admitted = 0.75 * (p)\n",
    "tele_notadmitted = 1 - tele_admitted\n",
    "admitted = p\n",
    "not_admitted = 1 - admitted\n",
    "\n",
    "# costs of admission\n",
    "\n",
    "cost_admission = 35000\n",
    "cost_telehealth = 1200\n",
    "cost_noadmission = 0\n",
    "\n",
    "# calculating the probability of admisssion -\n",
    "\n",
    "x = (\n",
    "    cost_admission * p\n",
    "    + (1 - p) * cost_noadmission\n",
    "    - tele_admitted * (cost_admission + cost_telehealth)\n",
    "    - (1 - tele_admitted) * (cost_telehealth)\n",
    ")\n",
    "my_threshold = solve(x, p)\n",
    "my_threshold = my_threshold[0]\n",
    "print(my_threshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22856,  4290],\n",
       "       [ 2336,  1048]], dtype=int64)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_prob_logreg_sm = logreg_sm.predict(X_test)\n",
    "class_logreg_sm = (pred_prob_logreg_sm > my_threshold).astype(int)\n",
    "cm_logreg_sm = confusion_matrix(y_test, class_logreg_sm)\n",
    "\n",
    "cm_logreg_sm  # The confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "TN = cm_logreg_sm[\n",
    "    0, 0\n",
    "]  # number of people who weren't provided with telehealth and didn't get admitted\n",
    "TP = cm_logreg_sm[\n",
    "    1, 1\n",
    "]  # number of people who were provided with telehealth and did get admitted\n",
    "FN = cm_logreg_sm[\n",
    "    1, 0\n",
    "]  # number of people who were provided with telehealth and didn't get admitted\n",
    "FP = cm_logreg_sm[\n",
    "    0, 1\n",
    "]  # number of people who weren't provided with telehealth and did get admitted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:  0.78\n",
      "Sensitivity:  0.31\n",
      "Specificity:  0.84\n"
     ]
    }
   ],
   "source": [
    "accuracy = (cm_logreg_sm[0, 0] + cm_logreg_sm[1, 1]) / sum(sum(cm_logreg_sm))\n",
    "sensitivity = (cm_logreg_sm[1, 1]) / (cm_logreg_sm[1, 0] + cm_logreg_sm[1, 1])\n",
    "specificity = (cm_logreg_sm[0, 0]) / (cm_logreg_sm[0, 0] + cm_logreg_sm[0, 1])\n",
    "print(\"Accuracy: \", round(accuracy, 2))\n",
    "print(\"Sensitivity: \", round(sensitivity, 2))\n",
    "print(\"Specificity: \", round(specificity, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The cost of admission is $ 115361200.0\n",
      "The cost of admission per patient is $ 3778.617753029807\n"
     ]
    }
   ],
   "source": [
    "x = (\n",
    "    (FP * cost_telehealth)\n",
    "    + (FN * cost_admission)\n",
    "    + (TP * 0.75) * (cost_admission + cost_telehealth)\n",
    ")  # this multiplies the\n",
    "# confusion matrix elements and their respective costs. The people who were admitted into the hospital while using telehealth\n",
    "# reduces by 25% as per the question. Hence, multiplied by 0.75\n",
    "print(\"The cost of admission is $\", x)\n",
    "print(\"The cost of admission per patient is $\", x / 30530)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The cost of admission is $ 118440000\n",
      "The cost of admission per patient is $ 3879.462823452342\n"
     ]
    }
   ],
   "source": [
    "counts = test_data[\n",
    "    \"readmission\"\n",
    "].value_counts()  # counting the people who were readmitted into the hospital\n",
    "y = counts[1] * 35000  # this is the cost of admission\n",
    "print(\"The cost of admission is $\", y)\n",
    "print(\"The cost of admission per patient is $\", y / 30530)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The profit of using telehealth is $ 100.84507042253522\n"
     ]
    }
   ],
   "source": [
    "print(\"The profit of using telehealth is $\", ((y - x) / 30530))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alternative method, using Scikit-learn\n",
    "\n",
    "Notes from Class by professor: \n",
    "1. The scikit-learn package does not produce p-values or confidence intervals on parameters. It is designed for prediction rather than inference (similar to most ML packages). So identifying which variables are non-significant and eliminating them from the model is difficult in scikit-learn. Instead it uses, by default, a method called \"regularization\" which reduces model complexity and overfitting.\n",
    "2. While in general you should use the default paramters of the LogisticRegression class, I have deviated from these parameters below in order to reproduce the same results of the statsmodels package. In particular, I have disabled regularizatoin by setting the penalty parameter to \"none\" and used the same non-linear optimizer \"newton-cg\" used by statsmodels. P.S.: If you're using version 1.2 or higher of scikit-learn, you should specify \"None\" instead of \"none\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "could not convert string to float: '[0-10)'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32mc:\\Users\\Hp\\OneDrive\\Documents\\Hospital-Readmission-Prevention\\logistic-regression.ipynb Cell 22\u001b[0m in \u001b[0;36m5\n\u001b[0;32m      <a href='vscode-notebook-cell:/c%3A/Users/Hp/OneDrive/Documents/Hospital-Readmission-Prevention/logistic-regression.ipynb#X40sZmlsZQ%3D%3D?line=0'>1</a>\u001b[0m logreg_mod_sklearn \u001b[39m=\u001b[39m LogisticRegression(\n\u001b[0;32m      <a href='vscode-notebook-cell:/c%3A/Users/Hp/OneDrive/Documents/Hospital-Readmission-Prevention/logistic-regression.ipynb#X40sZmlsZQ%3D%3D?line=1'>2</a>\u001b[0m     penalty\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mnone\u001b[39m\u001b[39m\"\u001b[39m, max_iter\u001b[39m=\u001b[39m\u001b[39m1000\u001b[39m, solver\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mnewton-cg\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[0;32m      <a href='vscode-notebook-cell:/c%3A/Users/Hp/OneDrive/Documents/Hospital-Readmission-Prevention/logistic-regression.ipynb#X40sZmlsZQ%3D%3D?line=2'>3</a>\u001b[0m )\n\u001b[1;32m----> <a href='vscode-notebook-cell:/c%3A/Users/Hp/OneDrive/Documents/Hospital-Readmission-Prevention/logistic-regression.ipynb#X40sZmlsZQ%3D%3D?line=4'>5</a>\u001b[0m logreg_sklearn \u001b[39m=\u001b[39m logreg_mod_sklearn\u001b[39m.\u001b[39;49mfit(X_train, y_train)\n",
      "File \u001b[1;32mc:\\Users\\Hp\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:1138\u001b[0m, in \u001b[0;36mLogisticRegression.fit\u001b[1;34m(self, X, y, sample_weight)\u001b[0m\n\u001b[0;32m   1135\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m   1136\u001b[0m     _dtype \u001b[39m=\u001b[39m [np\u001b[39m.\u001b[39mfloat64, np\u001b[39m.\u001b[39mfloat32]\n\u001b[1;32m-> 1138\u001b[0m X, y \u001b[39m=\u001b[39m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_validate_data(\n\u001b[0;32m   1139\u001b[0m     X,\n\u001b[0;32m   1140\u001b[0m     y,\n\u001b[0;32m   1141\u001b[0m     accept_sparse\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mcsr\u001b[39;49m\u001b[39m\"\u001b[39;49m,\n\u001b[0;32m   1142\u001b[0m     dtype\u001b[39m=\u001b[39;49m_dtype,\n\u001b[0;32m   1143\u001b[0m     order\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mC\u001b[39;49m\u001b[39m\"\u001b[39;49m,\n\u001b[0;32m   1144\u001b[0m     accept_large_sparse\u001b[39m=\u001b[39;49msolver \u001b[39mnot\u001b[39;49;00m \u001b[39min\u001b[39;49;00m [\u001b[39m\"\u001b[39;49m\u001b[39mliblinear\u001b[39;49m\u001b[39m\"\u001b[39;49m, \u001b[39m\"\u001b[39;49m\u001b[39msag\u001b[39;49m\u001b[39m\"\u001b[39;49m, \u001b[39m\"\u001b[39;49m\u001b[39msaga\u001b[39;49m\u001b[39m\"\u001b[39;49m],\n\u001b[0;32m   1145\u001b[0m )\n\u001b[0;32m   1146\u001b[0m check_classification_targets(y)\n\u001b[0;32m   1147\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mclasses_ \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39munique(y)\n",
      "File \u001b[1;32mc:\\Users\\Hp\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\base.py:596\u001b[0m, in \u001b[0;36mBaseEstimator._validate_data\u001b[1;34m(self, X, y, reset, validate_separately, **check_params)\u001b[0m\n\u001b[0;32m    594\u001b[0m         y \u001b[39m=\u001b[39m check_array(y, input_name\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39my\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mcheck_y_params)\n\u001b[0;32m    595\u001b[0m     \u001b[39melse\u001b[39;00m:\n\u001b[1;32m--> 596\u001b[0m         X, y \u001b[39m=\u001b[39m check_X_y(X, y, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mcheck_params)\n\u001b[0;32m    597\u001b[0m     out \u001b[39m=\u001b[39m X, y\n\u001b[0;32m    599\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m no_val_X \u001b[39mand\u001b[39;00m check_params\u001b[39m.\u001b[39mget(\u001b[39m\"\u001b[39m\u001b[39mensure_2d\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39mTrue\u001b[39;00m):\n",
      "File \u001b[1;32mc:\\Users\\Hp\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\utils\\validation.py:1074\u001b[0m, in \u001b[0;36mcheck_X_y\u001b[1;34m(X, y, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, multi_output, ensure_min_samples, ensure_min_features, y_numeric, estimator)\u001b[0m\n\u001b[0;32m   1069\u001b[0m         estimator_name \u001b[39m=\u001b[39m _check_estimator_name(estimator)\n\u001b[0;32m   1070\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m   1071\u001b[0m         \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m{\u001b[39;00mestimator_name\u001b[39m}\u001b[39;00m\u001b[39m requires y to be passed, but the target y is None\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[0;32m   1072\u001b[0m     )\n\u001b[1;32m-> 1074\u001b[0m X \u001b[39m=\u001b[39m check_array(\n\u001b[0;32m   1075\u001b[0m     X,\n\u001b[0;32m   1076\u001b[0m     accept_sparse\u001b[39m=\u001b[39;49maccept_sparse,\n\u001b[0;32m   1077\u001b[0m     accept_large_sparse\u001b[39m=\u001b[39;49maccept_large_sparse,\n\u001b[0;32m   1078\u001b[0m     dtype\u001b[39m=\u001b[39;49mdtype,\n\u001b[0;32m   1079\u001b[0m     order\u001b[39m=\u001b[39;49morder,\n\u001b[0;32m   1080\u001b[0m     copy\u001b[39m=\u001b[39;49mcopy,\n\u001b[0;32m   1081\u001b[0m     force_all_finite\u001b[39m=\u001b[39;49mforce_all_finite,\n\u001b[0;32m   1082\u001b[0m     ensure_2d\u001b[39m=\u001b[39;49mensure_2d,\n\u001b[0;32m   1083\u001b[0m     allow_nd\u001b[39m=\u001b[39;49mallow_nd,\n\u001b[0;32m   1084\u001b[0m     ensure_min_samples\u001b[39m=\u001b[39;49mensure_min_samples,\n\u001b[0;32m   1085\u001b[0m     ensure_min_features\u001b[39m=\u001b[39;49mensure_min_features,\n\u001b[0;32m   1086\u001b[0m     estimator\u001b[39m=\u001b[39;49mestimator,\n\u001b[0;32m   1087\u001b[0m     input_name\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mX\u001b[39;49m\u001b[39m\"\u001b[39;49m,\n\u001b[0;32m   1088\u001b[0m )\n\u001b[0;32m   1090\u001b[0m y \u001b[39m=\u001b[39m _check_y(y, multi_output\u001b[39m=\u001b[39mmulti_output, y_numeric\u001b[39m=\u001b[39my_numeric, estimator\u001b[39m=\u001b[39mestimator)\n\u001b[0;32m   1092\u001b[0m check_consistent_length(X, y)\n",
      "File \u001b[1;32mc:\\Users\\Hp\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\utils\\validation.py:856\u001b[0m, in \u001b[0;36mcheck_array\u001b[1;34m(array, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, estimator, input_name)\u001b[0m\n\u001b[0;32m    854\u001b[0m         array \u001b[39m=\u001b[39m array\u001b[39m.\u001b[39mastype(dtype, casting\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39munsafe\u001b[39m\u001b[39m\"\u001b[39m, copy\u001b[39m=\u001b[39m\u001b[39mFalse\u001b[39;00m)\n\u001b[0;32m    855\u001b[0m     \u001b[39melse\u001b[39;00m:\n\u001b[1;32m--> 856\u001b[0m         array \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39;49masarray(array, order\u001b[39m=\u001b[39;49morder, dtype\u001b[39m=\u001b[39;49mdtype)\n\u001b[0;32m    857\u001b[0m \u001b[39mexcept\u001b[39;00m ComplexWarning \u001b[39mas\u001b[39;00m complex_warning:\n\u001b[0;32m    858\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m    859\u001b[0m         \u001b[39m\"\u001b[39m\u001b[39mComplex data not supported\u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(array)\n\u001b[0;32m    860\u001b[0m     ) \u001b[39mfrom\u001b[39;00m \u001b[39mcomplex_warning\u001b[39;00m\n",
      "File \u001b[1;32mc:\\Users\\Hp\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\pandas\\core\\generic.py:2070\u001b[0m, in \u001b[0;36mNDFrame.__array__\u001b[1;34m(self, dtype)\u001b[0m\n\u001b[0;32m   2069\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m__array__\u001b[39m(\u001b[39mself\u001b[39m, dtype: npt\u001b[39m.\u001b[39mDTypeLike \u001b[39m|\u001b[39m \u001b[39mNone\u001b[39;00m \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m) \u001b[39m-\u001b[39m\u001b[39m>\u001b[39m np\u001b[39m.\u001b[39mndarray:\n\u001b[1;32m-> 2070\u001b[0m     \u001b[39mreturn\u001b[39;00m np\u001b[39m.\u001b[39;49masarray(\u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_values, dtype\u001b[39m=\u001b[39;49mdtype)\n",
      "\u001b[1;31mValueError\u001b[0m: could not convert string to float: '[0-10)'"
     ]
    }
   ],
   "source": [
    "logreg_mod_sklearn = LogisticRegression(\n",
    "    penalty=\"none\", max_iter=1000, solver=\"newton-cg\"\n",
    ")\n",
    "\n",
    "logreg_sklearn = logreg_mod_sklearn.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "logreg_mod_sklearn.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "logreg_mod_sklearn.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_prob_logreg_sklearn = logreg_mod_sklearn.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class_logreg_sklearn = (pred_prob_logreg_sklearn[:, 1] > my_threshold).astype(int)\n",
    "cm_logreg_sklearn = confusion_matrix(y_test, class_logreg_sklearn)  # confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "accuracy = (cm_logreg_sklearn[0, 0] + cm_logreg_sklearn[1, 1]) / sum(\n",
    "    sum(cm_logreg_sklearn)\n",
    ")\n",
    "sensitivity = (cm_logreg_sklearn[1, 1]) / (\n",
    "    cm_logreg_sklearn[1, 0] + cm_logreg_sklearn[1, 1]\n",
    ")\n",
    "specificity = (cm_logreg_sklearn[0, 0]) / (\n",
    "    cm_logreg_sklearn[0, 0] + cm_logreg_sklearn[0, 1]\n",
    ")\n",
    "print(\"Accuracy: \", round(accuracy, 2))\n",
    "print(\"Sensitivity: \", round(sensitivity, 2))\n",
    "print(\"Specificity: \", round(specificity, 2))"
   ]
  }
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