{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rc(\"figure\", figsize=(16, 8))\n",
    "plt.rc(\"font\", size=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "data = sm.datasets.statecrime.load_pandas()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>violent</th>\n",
       "      <th>murder</th>\n",
       "      <th>hs_grad</th>\n",
       "      <th>poverty</th>\n",
       "      <th>single</th>\n",
       "      <th>white</th>\n",
       "      <th>urban</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>state</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>459.9</td>\n",
       "      <td>7.1</td>\n",
       "      <td>82.1</td>\n",
       "      <td>17.5</td>\n",
       "      <td>29.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>48.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>632.6</td>\n",
       "      <td>3.2</td>\n",
       "      <td>91.4</td>\n",
       "      <td>9.0</td>\n",
       "      <td>25.5</td>\n",
       "      <td>68.3</td>\n",
       "      <td>44.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>423.2</td>\n",
       "      <td>5.5</td>\n",
       "      <td>84.2</td>\n",
       "      <td>16.5</td>\n",
       "      <td>25.7</td>\n",
       "      <td>80.0</td>\n",
       "      <td>80.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>530.3</td>\n",
       "      <td>6.3</td>\n",
       "      <td>82.4</td>\n",
       "      <td>18.8</td>\n",
       "      <td>26.3</td>\n",
       "      <td>78.4</td>\n",
       "      <td>39.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>473.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>80.6</td>\n",
       "      <td>14.2</td>\n",
       "      <td>27.8</td>\n",
       "      <td>62.7</td>\n",
       "      <td>89.73</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            violent  murder  hs_grad  poverty  single  white  urban\n",
       "state                                                              \n",
       "Alabama       459.9     7.1     82.1     17.5    29.0   70.0  48.65\n",
       "Alaska        632.6     3.2     91.4      9.0    25.5   68.3  44.46\n",
       "Arizona       423.2     5.5     84.2     16.5    25.7   80.0  80.07\n",
       "Arkansas      530.3     6.3     82.4     18.8    26.3   78.4  39.54\n",
       "California    473.4     5.4     80.6     14.2    27.8   62.7  89.73"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 51 entries, Alabama to Wyoming\n",
      "Data columns (total 7 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   violent  51 non-null     float64\n",
      " 1   murder   51 non-null     float64\n",
      " 2   hs_grad  51 non-null     float64\n",
      " 3   poverty  51 non-null     float64\n",
      " 4   single   51 non-null     float64\n",
      " 5   white    51 non-null     float64\n",
      " 6   urban    51 non-null     float64\n",
      "dtypes: float64(7)\n",
      "memory usage: 3.2+ KB\n"
     ]
    }
   ],
   "source": [
    "data.data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>urban</th>\n",
       "      <th>poverty</th>\n",
       "      <th>hs_grad</th>\n",
       "      <th>single</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>state</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>48.65</td>\n",
       "      <td>17.5</td>\n",
       "      <td>82.1</td>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>44.46</td>\n",
       "      <td>9.0</td>\n",
       "      <td>91.4</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>80.07</td>\n",
       "      <td>16.5</td>\n",
       "      <td>84.2</td>\n",
       "      <td>25.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>39.54</td>\n",
       "      <td>18.8</td>\n",
       "      <td>82.4</td>\n",
       "      <td>26.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>89.73</td>\n",
       "      <td>14.2</td>\n",
       "      <td>80.6</td>\n",
       "      <td>27.8</td>\n",
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      "text/plain": [
       "            urban  poverty  hs_grad  single\n",
       "state                                      \n",
       "Alabama     48.65     17.5     82.1    29.0\n",
       "Alaska      44.46      9.0     91.4    25.5\n",
       "Arizona     80.07     16.5     84.2    25.7\n",
       "Arkansas    39.54     18.8     82.4    26.3\n",
       "California  89.73     14.2     80.6    27.8"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.exog.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "state\n",
       "Alabama       7.1\n",
       "Alaska        3.2\n",
       "Arizona       5.5\n",
       "Arkansas      6.3\n",
       "California    5.4\n",
       "Name: murder, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.endog.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>urban</th>\n",
       "      <th>poverty</th>\n",
       "      <th>hs_grad</th>\n",
       "      <th>single</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>state</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>1.0</td>\n",
       "      <td>48.65</td>\n",
       "      <td>17.5</td>\n",
       "      <td>82.1</td>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>1.0</td>\n",
       "      <td>44.46</td>\n",
       "      <td>9.0</td>\n",
       "      <td>91.4</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>1.0</td>\n",
       "      <td>80.07</td>\n",
       "      <td>16.5</td>\n",
       "      <td>84.2</td>\n",
       "      <td>25.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>1.0</td>\n",
       "      <td>39.54</td>\n",
       "      <td>18.8</td>\n",
       "      <td>82.4</td>\n",
       "      <td>26.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>1.0</td>\n",
       "      <td>89.73</td>\n",
       "      <td>14.2</td>\n",
       "      <td>80.6</td>\n",
       "      <td>27.8</td>\n",
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      ],
      "text/plain": [
       "            const  urban  poverty  hs_grad  single\n",
       "state                                             \n",
       "Alabama       1.0  48.65     17.5     82.1    29.0\n",
       "Alaska        1.0  44.46      9.0     91.4    25.5\n",
       "Arizona       1.0  80.07     16.5     84.2    25.7\n",
       "Arkansas      1.0  39.54     18.8     82.4    26.3\n",
       "California    1.0  89.73     14.2     80.6    27.8"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data.exog\n",
    "X = sm.add_constant(X)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "Y = data.endog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "crime_model = sm.OLS(Y, X).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# equal to this:\n",
    "data_copy = data.data.copy()\n",
    "data_copy = sm.add_constant(data_copy)\n",
    "crime_model = sm.formula.ols(\n",
    "    \"murder ~ urban + poverty + hs_grad + single + C(const)\",\n",
    "    data=data_copy\n",
    ").fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 murder   R-squared:                       0.813\n",
      "Model:                            OLS   Adj. R-squared:                  0.797\n",
      "Method:                 Least Squares   F-statistic:                     50.08\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):           3.42e-16\n",
      "Time:                        09:07:46   Log-Likelihood:                -95.050\n",
      "No. Observations:                  51   AIC:                             200.1\n",
      "Df Residuals:                      46   BIC:                             209.8\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept    -44.1024     12.086     -3.649      0.001     -68.430     -19.774\n",
      "urban          0.0109      0.015      0.707      0.483      -0.020       0.042\n",
      "poverty        0.4121      0.140      2.939      0.005       0.130       0.694\n",
      "hs_grad        0.3059      0.117      2.611      0.012       0.070       0.542\n",
      "single         0.6374      0.070      9.065      0.000       0.496       0.779\n",
      "==============================================================================\n",
      "Omnibus:                        1.618   Durbin-Watson:                   2.507\n",
      "Prob(Omnibus):                  0.445   Jarque-Bera (JB):                0.831\n",
      "Skew:                          -0.220   Prob(JB):                        0.660\n",
      "Kurtosis:                       3.445   Cond. No.                     5.80e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.8e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8132403052312949\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.rsquared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept   -44.102416\n",
      "urban         0.010888\n",
      "poverty       0.412150\n",
      "hs_grad       0.305927\n",
      "single        0.637375\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(crime_model.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eval_env: 1\n",
      "eval_env: 1\n",
      "eval_env: 1\n",
      "eval_env: 1\n",
      "eval_env: 1\n"
     ]
    },
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      "text/plain": [
       "<Figure size 1152x576 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = sm.graphics.plot_partregress_grid(crime_model)\n",
    "fig.tight_layout(pad=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
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     "metadata": {
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    }
   ],
   "source": [
    "fig = sm.graphics.plot_fit(crime_model, \"single\")\n",
    "fig.tight_layout(pad=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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