Het_Tests_BP_White.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#using BP and White Testing for Heteroscedasticity\n",
    "#going to use statsmodels for the OLS linear regression\n",
    "#going to use the car models fuel economy df from breakout 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.stats.api as sms\n",
    "import statsmodels.formula.api as smf\n",
    "from statsmodels.compat import lzip\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from win32com.client import Dispatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Cmpg</th>\n",
       "      <th>Eng</th>\n",
       "      <th>Inv_eng</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Acura RL 3.7L</td>\n",
       "      <td>17</td>\n",
       "      <td>3.7</td>\n",
       "      <td>0.270270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Acura TL 2wd 3.5L</td>\n",
       "      <td>18</td>\n",
       "      <td>3.5</td>\n",
       "      <td>0.285714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Acura TL 4wd 3.7L</td>\n",
       "      <td>17</td>\n",
       "      <td>3.7</td>\n",
       "      <td>0.270270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Aston Martin DB9 5.9L</td>\n",
       "      <td>13</td>\n",
       "      <td>5.9</td>\n",
       "      <td>0.169492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Aston Martin DBS 5.9L</td>\n",
       "      <td>12</td>\n",
       "      <td>5.9</td>\n",
       "      <td>0.169492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>346</th>\n",
       "      <td>Volvo XC60 Awd 3L</td>\n",
       "      <td>17</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>347</th>\n",
       "      <td>Volvo XC60 Fwd 3.2L</td>\n",
       "      <td>18</td>\n",
       "      <td>3.2</td>\n",
       "      <td>0.312500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>348</th>\n",
       "      <td>Volvo XC70 Awd 3.2L</td>\n",
       "      <td>18</td>\n",
       "      <td>3.2</td>\n",
       "      <td>0.312500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>349</th>\n",
       "      <td>Volvo XC70 Awd 3L</td>\n",
       "      <td>17</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>350</th>\n",
       "      <td>Volvo XC70 Fwd 3.2L</td>\n",
       "      <td>18</td>\n",
       "      <td>3.2</td>\n",
       "      <td>0.312500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>351 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                      Name  Cmpg  Eng   Inv_eng\n",
       "0            Acura RL 3.7L    17  3.7  0.270270\n",
       "1        Acura TL 2wd 3.5L    18  3.5  0.285714\n",
       "2        Acura TL 4wd 3.7L    17  3.7  0.270270\n",
       "3    Aston Martin DB9 5.9L    13  5.9  0.169492\n",
       "4    Aston Martin DBS 5.9L    12  5.9  0.169492\n",
       "..                     ...   ...  ...       ...\n",
       "346      Volvo XC60 Awd 3L    17  3.0  0.333333\n",
       "347    Volvo XC60 Fwd 3.2L    18  3.2  0.312500\n",
       "348    Volvo XC70 Awd 3.2L    18  3.2  0.312500\n",
       "349      Volvo XC70 Awd 3L    17  3.0  0.333333\n",
       "350    Volvo XC70 Fwd 3.2L    18  3.2  0.312500\n",
       "\n",
       "[351 rows x 4 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = ('data\\car models fuel economy.csv')\n",
    "df = pd.read_csv(file)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# #loading the jmp file into the environment as df\n",
    "# jmp = Dispatch(\"JMP.Application\")\n",
    "# doc = jmp.OpenDocument(\"data/car models fuel economy.jmp\")\n",
    "# print(doc)\n",
    "\n",
    "# doc.SaveAs(\"data/car models fuel economy.csv\")\n",
    "\n",
    "# df = pd.read_csv(\"data/car models fuel economy.csv\")\n",
    "# print(df.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Cmpg   R-squared:                       0.751\n",
      "Model:                            OLS   Adj. R-squared:                  0.751\n",
      "Method:                 Least Squares   F-statistic:                     1055.\n",
      "Date:                Sat, 20 Nov 2021   Prob (F-statistic):          1.67e-107\n",
      "Time:                        11:58:14   Log-Likelihood:                -727.57\n",
      "No. Observations:                 351   AIC:                             1459.\n",
      "Df Residuals:                     349   BIC:                             1467.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     27.7994      0.298     93.210      0.000      27.213      28.386\n",
      "Eng           -2.6717      0.082    -32.474      0.000      -2.834      -2.510\n",
      "==============================================================================\n",
      "Omnibus:                        2.519   Durbin-Watson:                   1.241\n",
      "Prob(Omnibus):                  0.284   Jarque-Bera (JB):                2.315\n",
      "Skew:                           0.128   Prob(JB):                        0.314\n",
      "Kurtosis:                       3.305   Cond. No.                         11.2\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model1 = smf.ols(formula = 'Cmpg ~ Eng', data = df).fit()\n",
    "print(model1.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid1 = model1.resid\n",
    "fitted1 = model1.fittedvalues\n",
    "#QQ plot of residuals\n",
    "fig1 = sm.qqplot(resid1,fit=True,line='45')\n",
    "#fitted v. residuals\n",
    "fig, ax = plt.subplots()\n",
    "_ = ax.scatter(fitted1, resid1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Breusch-Pagan Test for Heteroscedasticity\n",
    "bptest = sms.diagnostic.het_breuschpagan(resid1,model1.model.exog)\n",
    "# White Test for Heteroscedasticity, including squares and cross-product of exog\n",
    "white_test = sms.diagnostic.het_white(resid1,model1.model.exog)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Breusch-Pagan Test and White LM Tests for Heteroscedasticity\n",
      "            Test Type     Chi-Sq  DF   Prob>Chi-Sq\n",
      "0  Breusch-Pagan Test  13.003549   2  3.109012e-04\n",
      "1          White Test  41.592622   4  9.295589e-10\n"
     ]
    }
   ],
   "source": [
    "print('Breusch-Pagan Test and White LM Tests for Heteroscedasticity')\n",
    "df1 = pd.DataFrame({'Test Type':['Breusch-Pagan Test', 'White Test'],\n",
    "                   'Chi-Sq':[bptest[0], white_test[0]], 'DF':[2, 4],\n",
    "                   'Prob>Chi-Sq':[bptest[1], white_test[1]]})\n",
    "print(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Cmpg   R-squared:                       0.797\n",
      "Model:                            OLS   Adj. R-squared:                  0.797\n",
      "Method:                 Least Squares   F-statistic:                     1374.\n",
      "Date:                Sat, 20 Nov 2021   Prob (F-statistic):          4.56e-123\n",
      "Time:                        11:58:14   Log-Likelihood:                -691.56\n",
      "No. Observations:                 351   AIC:                             1387.\n",
      "Df Residuals:                     349   BIC:                             1395.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      9.7028      0.260     37.302      0.000       9.191      10.214\n",
      "Inv_eng       26.7067      0.720     37.071      0.000      25.290      28.124\n",
      "==============================================================================\n",
      "Omnibus:                       21.359   Durbin-Watson:                   1.126\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               26.435\n",
      "Skew:                          -0.512   Prob(JB):                     1.82e-06\n",
      "Kurtosis:                       3.872   Cond. No.                         8.65\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model2 = smf.ols(formula = 'Cmpg ~ Inv_eng', data = df).fit()\n",
    "print(model2.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid2 = model2.resid\n",
    "fitted2 = model2.fittedvalues\n",
    "#QQ plot of residuals\n",
    "fig1 = sm.qqplot(resid2,fit=True,line='45')\n",
    "#fitted v. residuals\n",
    "fig, ax = plt.subplots()\n",
    "_ = ax.scatter(fitted2, resid2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Breusch-Pagan Test for Heteroscedasticity\n",
    "bptest = sms.diagnostic.het_breuschpagan(resid2,model2.model.exog)\n",
    "# White Test for Heteroscedasticity, including squares and cross-product of exog\n",
    "white_test = sms.diagnostic.het_white(resid2,model2.model.exog)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Breusch-Pagan Test and White LM Tests for Heteroscedasticity\n",
      "            Test Type     Chi-Sq  DF  Prob>Chi-Sq\n",
      "0  Breusch-Pagan Test  10.740164   2     0.001048\n",
      "1          White Test  12.586630   4     0.001849\n"
     ]
    }
   ],
   "source": [
    "print('Breusch-Pagan Test and White LM Tests for Heteroscedasticity')\n",
    "df2 = pd.DataFrame({'Test Type':['Breusch-Pagan Test', 'White Test'],\n",
    "                   'Chi-Sq':[bptest[0], white_test[0]], 'DF':[2, 4],\n",
    "                   'Prob>Chi-Sq':[bptest[1], white_test[1]]})\n",
    "print(df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Inv_cmpg\"] = 1/df[\"Cmpg\"] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               Inv_cmpg   R-squared:                       0.681\n",
      "Model:                            OLS   Adj. R-squared:                  0.680\n",
      "Method:                 Least Squares   F-statistic:                     744.7\n",
      "Date:                Sat, 20 Nov 2021   Prob (F-statistic):           1.41e-88\n",
      "Time:                        11:58:15   Log-Likelihood:                 1257.6\n",
      "No. Observations:                 351   AIC:                            -2511.\n",
      "Df Residuals:                     349   BIC:                            -2503.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0815      0.001     80.845      0.000       0.080       0.083\n",
      "Inv_eng       -0.0762      0.003    -27.289      0.000      -0.082      -0.071\n",
      "==============================================================================\n",
      "Omnibus:                       75.526   Durbin-Watson:                   0.814\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              128.542\n",
      "Skew:                           1.236   Prob(JB):                     1.22e-28\n",
      "Kurtosis:                       4.638   Cond. No.                         8.65\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model3 = smf.ols(formula = 'Inv_cmpg ~ Inv_eng', data = df).fit()\n",
    "print(model3.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid3 = model3.resid\n",
    "fitted3 = model3.fittedvalues\n",
    "#QQ plot of residuals\n",
    "fig1 = sm.qqplot(resid3,fit=True,line='45')\n",
    "#fitted v. residuals\n",
    "fig, ax = plt.subplots()\n",
    "_ = ax.scatter(fitted3, resid3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Breusch-Pagan Test for Heteroscedasticity\n",
    "bptest = sms.diagnostic.het_breuschpagan(resid3,model3.model.exog)\n",
    "# White Test for Heteroscedasticity, including squares and cross-product of exog\n",
    "white_test = sms.diagnostic.het_white(resid3,model3.model.exog)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Breusch-Pagan Test and White LM Tests for Heteroscedasticity\n",
      "            Test Type     Chi-Sq  DF   Prob>Chi-Sq\n",
      "0  Breusch-Pagan Test  18.780202   2  1.466819e-05\n",
      "1          White Test  66.271349   4  4.067798e-15\n"
     ]
    }
   ],
   "source": [
    "print('Breusch-Pagan Test and White LM Tests for Heteroscedasticity')\n",
    "df3 = pd.DataFrame({'Test Type':['Breusch-Pagan Test', 'White Test'],\n",
    "                   'Chi-Sq':[bptest[0], white_test[0]], 'DF':[2, 4],\n",
    "                   'Prob>Chi-Sq':[bptest[1], white_test[1]]})\n",
    "print(df3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"lncmpg\"] = np.log(df[\"Cmpg\"])\n",
    "df[\"lneng\"] = np.log(df[\"Eng\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 lncmpg   R-squared:                       0.804\n",
      "Model:                            OLS   Adj. R-squared:                  0.804\n",
      "Method:                 Least Squares   F-statistic:                     1434.\n",
      "Date:                Sat, 20 Nov 2021   Prob (F-statistic):          1.23e-125\n",
      "Time:                        11:58:15   Log-Likelihood:                 339.77\n",
      "No. Observations:                 351   AIC:                            -675.5\n",
      "Df Residuals:                     349   BIC:                            -667.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.4866      0.016    217.072      0.000       3.455       3.518\n",
      "lneng         -0.5005      0.013    -37.864      0.000      -0.527      -0.475\n",
      "==============================================================================\n",
      "Omnibus:                       24.631   Durbin-Watson:                   1.038\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               28.420\n",
      "Skew:                          -0.619   Prob(JB):                     6.74e-07\n",
      "Kurtosis:                       3.640   Cond. No.                         6.50\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Breusch-Pagan Test and White LM Tests for Heteroscedasticity\n",
      "            Test Type    Chi-Sq  DF  Prob>Chi-Sq\n",
      "0  Breusch-Pagan Test  1.470245   2     0.225307\n",
      "1          White Test  9.167705   4     0.010215\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model4 = smf.ols(formula = 'lncmpg ~ lneng', data = df).fit()\n",
    "print(model4.summary())\n",
    "resid4 = model4.resid\n",
    "fitted4 = model4.fittedvalues\n",
    "#QQ plot of residuals\n",
    "fig1 = sm.qqplot(resid4,fit=True,line='45')\n",
    "#fitted v. residuals\n",
    "fig, ax = plt.subplots()\n",
    "_ = ax.scatter(fitted4, resid4)\n",
    "\n",
    "# Breusch-Pagan Test for Heteroscedasticity\n",
    "bptest = sms.diagnostic.het_breuschpagan(resid4,model4.model.exog)\n",
    "# White Test for Heteroscedasticity, including squares and cross-product of exog\n",
    "white_test = sms.diagnostic.het_white(resid4,model4.model.exog)\n",
    "\n",
    "print('Breusch-Pagan Test and White LM Tests for Heteroscedasticity')\n",
    "df4 = pd.DataFrame({'Test Type':['Breusch-Pagan Test', 'White Test'],\n",
    "                   'Chi-Sq':[bptest[0], white_test[0]], 'DF':[2, 4],\n",
    "                   'Prob>Chi-Sq':[bptest[1], white_test[1]]})\n",
    "print(df4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Breusch-Pagan Test and White LM Tests for Heteroscedasticity\n",
      "            Test Type    Chi-Sq  DF  Prob>Chi-Sq\n",
      "0  Breusch-Pagan Test  1.470245   2     0.225307\n",
      "1          White Test  9.167705   4     0.010215\n"
     ]
    }
   ],
   "source": [
    "# Breusch-Pagan Test for Heteroscedasticity\n",
    "bptest = sms.diagnostic.het_breuschpagan(resid4,model4.model.exog)\n",
    "# White Test for Heteroscedasticity, including squares and cross-product of exog\n",
    "white_test = sms.diagnostic.het_white(resid4,model4.model.exog)\n",
    "\n",
    "print('Breusch-Pagan Test and White LM Tests for Heteroscedasticity')\n",
    "df4 = pd.DataFrame({'Test Type':['Breusch-Pagan Test', 'White Test'],\n",
    "                   'Chi-Sq':[bptest[0], white_test[0]], 'DF':[2, 4],\n",
    "                   'Prob>Chi-Sq':[bptest[1], white_test[1]]})\n",
    "print(df4)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}