scripts/Sem_05.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f444a6f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd # работа с таблицами \n",
    "import numpy as np # математические функции и матрицы\n",
    "import matplotlib.pyplot as plt # графики\n",
    "import seaborn as sns # еще более классные графики\n",
    "import statsmodels.api as sm # стандартные регрессионные модели\n",
    "import statsmodels.formula.api as smf # аналогичные модели с синтаксисом в стиле R\n",
    "import statsmodels.graphics.gofplots as gf # визуализация моделей\n",
    "import statsmodels.discrete.discrete_model # дискретные модели\n",
    "from statsmodels.stats.outliers_influence import summary_table # работа с выбросами\n",
    "from scipy.stats import shapiro # тест Шапиро – Уилка "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d0cfda3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# При желании можем настроить графики по своему вкусу, изменив стиль и другие параметры шрифтов и графиков\n",
    "# (https://tonysyu.github.io/raw_content/matplotlib-style-gallery/gallery.html)\n",
    "plt.style.use('seaborn')\n",
    "plt.rc('font', size=14)\n",
    "plt.rc('figure', titlesize=15)\n",
    "plt.rc('axes', labelsize=15)\n",
    "plt.rc('axes', titlesize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f1df2f39",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Импортируем данные о квартирах в Москве\n",
    "data = pd.read_excel('/Users/polinapogorelova/Desktop/econ_metrics/dataflats.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3c85bdc3",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>totsp</th>\n",
       "      <th>livesp</th>\n",
       "      <th>kitsp</th>\n",
       "      <th>dist</th>\n",
       "      <th>metrdist</th>\n",
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       "      <th>2035</th>\n",
       "      <td>2036</td>\n",
       "      <td>110.0</td>\n",
       "      <td>77</td>\n",
       "      <td>45</td>\n",
       "      <td>10.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2036</th>\n",
       "      <td>2037</td>\n",
       "      <td>95.0</td>\n",
       "      <td>60</td>\n",
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       "      <th>2037</th>\n",
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       "      <th>2039</th>\n",
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       "      <td>103.0</td>\n",
       "      <td>64</td>\n",
       "      <td>45</td>\n",
       "      <td>7.0</td>\n",
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       "         A      B  totsp  livesp  kitsp  dist  metrdist  walk  brick  floor\n",
       "0        1   81.0     58      40    6.0  12.5         7     1      1      1\n",
       "1        2   75.0     44      28    6.0  13.5         7     1      0      1\n",
       "2        3  128.0     70      42    6.0  14.5         3     1      1      1\n",
       "3        4   95.0     61      37    6.0  13.5         7     1      0      1\n",
       "4        5  330.0    104      60   11.0  10.5         7     0      1      1\n",
       "...    ...    ...    ...     ...    ...   ...       ...   ...    ...    ...\n",
       "2035  2036  110.0     77      45   10.0  12.0         5     0      0      1\n",
       "2036  2037   95.0     60      43    6.0   9.0         5     0      0      1\n",
       "2037  2038   95.0     60      46    5.0  10.5         5     1      0      1\n",
       "2038  2039  129.0     76      48   10.0  12.5         5     0      0      1\n",
       "2039  2040  103.0     64      45    7.0  15.5         5     1      0      1\n",
       "\n",
       "[2040 rows x 10 columns]"
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     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cc21bb07",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Изменив название столбцов A и B на n (номер наблюдения) и price, соответственно\n",
    "data.rename(columns={'A':'n', 'B': 'price'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7b831841",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Удалим строки, в которых есть пропуск хотя бы для одного столбца\n",
    "data.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a8136b14",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Добавим в набор данных новую переменную price_sq (стоимость 1 кв м квартиры в Москве)\n",
    "data['price_sq'] = data['price']/data['totsp']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5c6456b3",
   "metadata": {},
   "outputs": [
    {
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       "      <td>77</td>\n",
       "      <td>45</td>\n",
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      "text/plain": [
       "         n  price  totsp  livesp  kitsp  dist  metrdist  walk  brick  floor  \\\n",
       "0        1   81.0     58      40    6.0  12.5         7     1      1      1   \n",
       "1        2   75.0     44      28    6.0  13.5         7     1      0      1   \n",
       "2        3  128.0     70      42    6.0  14.5         3     1      1      1   \n",
       "3        4   95.0     61      37    6.0  13.5         7     1      0      1   \n",
       "4        5  330.0    104      60   11.0  10.5         7     0      1      1   \n",
       "...    ...    ...    ...     ...    ...   ...       ...   ...    ...    ...   \n",
       "2035  2036  110.0     77      45   10.0  12.0         5     0      0      1   \n",
       "2036  2037   95.0     60      43    6.0   9.0         5     0      0      1   \n",
       "2037  2038   95.0     60      46    5.0  10.5         5     1      0      1   \n",
       "2038  2039  129.0     76      48   10.0  12.5         5     0      0      1   \n",
       "2039  2040  103.0     64      45    7.0  15.5         5     1      0      1   \n",
       "\n",
       "      price_sq  \n",
       "0     1.396552  \n",
       "1     1.704545  \n",
       "2     1.828571  \n",
       "3     1.557377  \n",
       "4     3.173077  \n",
       "...        ...  \n",
       "2035  1.428571  \n",
       "2036  1.583333  \n",
       "2037  1.583333  \n",
       "2038  1.697368  \n",
       "2039  1.609375  \n",
       "\n",
       "[2038 rows x 11 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a16b5b15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>price_sq</td>     <th>  R-squared:         </th> <td>   0.279</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.278</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   393.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 09 Oct 2022</td> <th>  Prob (F-statistic):</th> <td>2.94e-145</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:13:34</td>     <th>  Log-Likelihood:    </th> <td> -717.45</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  2038</td>      <th>  AIC:               </th> <td>   1441.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  2035</td>      <th>  BIC:               </th> <td>   1458.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    1.5395</td> <td>    0.057</td> <td>   26.994</td> <td> 0.000</td> <td>    1.428</td> <td>    1.651</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>livesp</th>    <td>    0.0149</td> <td>    0.001</td> <td>   15.117</td> <td> 0.000</td> <td>    0.013</td> <td>    0.017</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dist</th>      <td>   -0.0465</td> <td>    0.002</td> <td>  -20.177</td> <td> 0.000</td> <td>   -0.051</td> <td>   -0.042</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>806.418</td> <th>  Durbin-Watson:     </th> <td>   2.020</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>6015.853</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.676</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>10.721</td>  <th>  Cond. No.          </th> <td>    361.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               price_sq   R-squared:                       0.279\n",
       "Model:                            OLS   Adj. R-squared:                  0.278\n",
       "Method:                 Least Squares   F-statistic:                     393.7\n",
       "Date:                Sun, 09 Oct 2022   Prob (F-statistic):          2.94e-145\n",
       "Time:                        19:13:34   Log-Likelihood:                -717.45\n",
       "No. Observations:                2038   AIC:                             1441.\n",
       "Df Residuals:                    2035   BIC:                             1458.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.5395      0.057     26.994      0.000       1.428       1.651\n",
       "livesp         0.0149      0.001     15.117      0.000       0.013       0.017\n",
       "dist          -0.0465      0.002    -20.177      0.000      -0.051      -0.042\n",
       "==============================================================================\n",
       "Omnibus:                      806.418   Durbin-Watson:                   2.020\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6015.853\n",
       "Skew:                           1.676   Prob(JB):                         0.00\n",
       "Kurtosis:                      10.721   Cond. No.                         361.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# С помощью МНК оценим модель регрессии для стоимости 1 кв м квартиры, используя в качестве объясянющих переменных \n",
    "# livesp (жилая площадь) и dist (расстояние до центра в км)\n",
    "ols_1 = smf.ols('price_sq ~ livesp + dist', data=data).fit()\n",
    "ols_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "aa031993",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Спрогнозируем модельные значения для имеющихся наблюдений\n",
    "data['yhat'] = ols_1.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "22af620a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "      <td>1.762252</td>\n",
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       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>2038</td>\n",
       "      <td>95.0</td>\n",
       "      <td>60</td>\n",
       "      <td>46</td>\n",
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       "      <td>1.583333</td>\n",
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       "      <th>2038</th>\n",
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       "<p>2038 rows × 12 columns</p>\n",
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      ],
      "text/plain": [
       "         n  price  totsp  livesp  kitsp  dist  metrdist  walk  brick  floor  \\\n",
       "0        1   81.0     58      40    6.0  12.5         7     1      1      1   \n",
       "1        2   75.0     44      28    6.0  13.5         7     1      0      1   \n",
       "2        3  128.0     70      42    6.0  14.5         3     1      1      1   \n",
       "3        4   95.0     61      37    6.0  13.5         7     1      0      1   \n",
       "4        5  330.0    104      60   11.0  10.5         7     0      1      1   \n",
       "...    ...    ...    ...     ...    ...   ...       ...   ...    ...    ...   \n",
       "2035  2036  110.0     77      45   10.0  12.0         5     0      0      1   \n",
       "2036  2037   95.0     60      43    6.0   9.0         5     0      0      1   \n",
       "2037  2038   95.0     60      46    5.0  10.5         5     1      0      1   \n",
       "2038  2039  129.0     76      48   10.0  12.5         5     0      0      1   \n",
       "2039  2040  103.0     64      45    7.0  15.5         5     1      0      1   \n",
       "\n",
       "      price_sq      yhat  \n",
       "0     1.396552  1.554726  \n",
       "1     1.704545  1.329234  \n",
       "2     1.828571  1.491539  \n",
       "3     1.557377  1.463471  \n",
       "4     3.173077  1.946048  \n",
       "...        ...       ...  \n",
       "2035  1.428571  1.652556  \n",
       "2036  1.583333  1.762252  \n",
       "2037  1.583333  1.737235  \n",
       "2038  1.697368  1.674048  \n",
       "2039  1.609375  1.489776  \n",
       "\n",
       "[2038 rows x 12 columns]"
      ]
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     "execution_count": 43,
     "metadata": {},
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   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "e46f3e17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               price_sq   R-squared:                       0.302\n",
      "Model:                            OLS   Adj. R-squared:                  0.301\n",
      "Method:                 Least Squares   F-statistic:                     293.6\n",
      "Date:                Sun, 09 Oct 2022   Prob (F-statistic):          2.46e-158\n",
      "Time:                        19:21:59   Log-Likelihood:                -684.12\n",
      "No. Observations:                2038   AIC:                             1376.\n",
      "Df Residuals:                    2034   BIC:                             1399.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.6653      0.058     28.629      0.000       1.551       1.779\n",
      "livesp         0.0146      0.001     15.075      0.000       0.013       0.017\n",
      "dist          -0.0448      0.002    -19.676      0.000      -0.049      -0.040\n",
      "metrdist      -0.0163      0.002     -8.223      0.000      -0.020      -0.012\n",
      "==============================================================================\n",
      "Omnibus:                      825.479   Durbin-Watson:                   2.021\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6653.228\n",
      "Skew:                           1.697   Prob(JB):                         0.00\n",
      "Kurtosis:                      11.175   Cond. No.                         379.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# С помощью МНК оценим альтернативную модель регрессии, включив дополнительно переменную metrdist \n",
    "# (расстояние до ближайшей станции метро (в минутах))\n",
    "ols_2 = smf.ols('price_sq ~ livesp + dist + metrdist', data=data).fit()\n",
    "print(ols_2.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "92ca1520",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  0         1\n",
      "Intercept  1.445626  1.633324\n",
      "livesp     0.013292  0.016539\n",
      "dist      -0.050302 -0.042716\n",
      "                  0         1\n",
      "Intercept  1.569613  1.761058\n",
      "livesp     0.013046  0.016243\n",
      "dist      -0.048561 -0.041066\n",
      "metrdist  -0.019516 -0.013008\n"
     ]
    }
   ],
   "source": [
    "# Построим 90%-й доверительные интервалы для оценок коэффициентов моделей ols_1 и ols_2\n",
    "print(ols_1.conf_int(alpha = 0.1))\n",
    "print(ols_2.conf_int(alpha = 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "6b64fad3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=array([[538.53546841]]), p=6.859863066294954e-106, df_denom=2.04e+03, df_num=1>\n",
      "<F test: F=array([[587.12704297]]), p=3.650897547863692e-114, df_denom=2.03e+03, df_num=1>\n"
     ]
    }
   ],
   "source": [
    "# Проверим гипотезу о равенстве коэффициента при регрессоре dist -0.1 в моделях ols_1 и ols_2\n",
    "hypotheses = '(dist = -0.1)' # формулируем гипотезу H_0\n",
    "print(ols_1.f_test(r_matrix = hypotheses)) # тестируем гипотезу с помощью F-теста\n",
    "print(ols_2.f_test(r_matrix = hypotheses)) # тестируем гипотезу с помощью F-теста"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "abd5c05d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=array([[138.87082475]]), p=4.686108267182074e-31, df_denom=2.04e+03, df_num=1>\n",
      "<F test: F=array([[130.21478616]]), p=2.800332329425247e-29, df_denom=2.03e+03, df_num=1>\n"
     ]
    }
   ],
   "source": [
    "# Проверим гипотезу о равенстве коэффициента при регрессоре dist -0.1\n",
    "hypotheses = '(livesp+dist=0)' # формулируем гипотезу H_0\n",
    "print(ols_1.f_test(r_matrix = hypotheses)) # тестируем гипотезу с помощью F-теста\n",
    "print(ols_2.f_test(r_matrix = hypotheses)) # тестируем гипотезу с помощью F-теста"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "61198e9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=array([[21.35721064]]), p=4.050825141903661e-06, df_denom=2.03e+03, df_num=1>\n"
     ]
    }
   ],
   "source": [
    "# Проверим гипотезу о равенстве коэффициента при регрессоре dist -0.1\n",
    "hypotheses = '(2*livesp+metrdist=0)' # формулируем гипотезу H_0\n",
    "print(ols_2.f_test(r_matrix = hypotheses)) # тестируем гипотезу с помощью F-теста"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "1718a1d7",
   "metadata": {},
   "outputs": [
    {
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       "      <th>walk</th>\n",
       "      <th>brick</th>\n",
       "      <th>floor</th>\n",
       "      <th>price_sq</th>\n",
       "      <th>yhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.734057</td>\n",
       "      <td>-0.896179</td>\n",
       "      <td>-0.999273</td>\n",
       "      <td>-0.803102</td>\n",
       "      <td>-1.042635</td>\n",
       "      <td>0.440190</td>\n",
       "      <td>-0.292507</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>1.448194</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.794058</td>\n",
       "      <td>-0.764332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.732358</td>\n",
       "      <td>-1.011871</td>\n",
       "      <td>-1.927887</td>\n",
       "      <td>-2.324690</td>\n",
       "      <td>-1.042635</td>\n",
       "      <td>0.736412</td>\n",
       "      <td>-0.292507</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.033961</td>\n",
       "      <td>-1.817944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.730658</td>\n",
       "      <td>0.010076</td>\n",
       "      <td>-0.203317</td>\n",
       "      <td>-0.549504</td>\n",
       "      <td>-1.042635</td>\n",
       "      <td>1.032634</td>\n",
       "      <td>-1.340648</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>1.448194</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>0.272123</td>\n",
       "      <td>-1.059574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.728959</td>\n",
       "      <td>-0.626231</td>\n",
       "      <td>-0.800284</td>\n",
       "      <td>-1.183499</td>\n",
       "      <td>-1.042635</td>\n",
       "      <td>0.736412</td>\n",
       "      <td>-0.292507</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.397157</td>\n",
       "      <td>-1.190719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.727260</td>\n",
       "      <td>3.905046</td>\n",
       "      <td>2.051889</td>\n",
       "      <td>1.732879</td>\n",
       "      <td>0.758424</td>\n",
       "      <td>-0.152253</td>\n",
       "      <td>-0.292507</td>\n",
       "      <td>-1.477963</td>\n",
       "      <td>1.448194</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>3.590225</td>\n",
       "      <td>1.064124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2033</th>\n",
       "      <td>1.724146</td>\n",
       "      <td>-0.337000</td>\n",
       "      <td>0.260990</td>\n",
       "      <td>-0.169107</td>\n",
       "      <td>0.398213</td>\n",
       "      <td>0.292079</td>\n",
       "      <td>-0.816578</td>\n",
       "      <td>-1.477963</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.715036</td>\n",
       "      <td>-0.307218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2034</th>\n",
       "      <td>1.725845</td>\n",
       "      <td>-0.626231</td>\n",
       "      <td>-0.866613</td>\n",
       "      <td>-0.422705</td>\n",
       "      <td>-1.042635</td>\n",
       "      <td>-0.596586</td>\n",
       "      <td>-0.816578</td>\n",
       "      <td>-1.477963</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.333100</td>\n",
       "      <td>0.205336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2035</th>\n",
       "      <td>1.727545</td>\n",
       "      <td>-0.626231</td>\n",
       "      <td>-0.866613</td>\n",
       "      <td>-0.042308</td>\n",
       "      <td>-1.402847</td>\n",
       "      <td>-0.152253</td>\n",
       "      <td>-0.816578</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.333100</td>\n",
       "      <td>0.088442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2036</th>\n",
       "      <td>1.729244</td>\n",
       "      <td>0.029358</td>\n",
       "      <td>0.194660</td>\n",
       "      <td>0.211290</td>\n",
       "      <td>0.398213</td>\n",
       "      <td>0.440190</td>\n",
       "      <td>-0.816578</td>\n",
       "      <td>-1.477963</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.051673</td>\n",
       "      <td>-0.206800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>1.730943</td>\n",
       "      <td>-0.471974</td>\n",
       "      <td>-0.601295</td>\n",
       "      <td>-0.169107</td>\n",
       "      <td>-0.682423</td>\n",
       "      <td>1.328856</td>\n",
       "      <td>-0.816578</td>\n",
       "      <td>0.676607</td>\n",
       "      <td>-0.690515</td>\n",
       "      <td>0.514833</td>\n",
       "      <td>-0.268832</td>\n",
       "      <td>-1.067811</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2038 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             n     price     totsp    livesp     kitsp      dist  metrdist  \\\n",
       "0    -1.734057 -0.896179 -0.999273 -0.803102 -1.042635  0.440190 -0.292507   \n",
       "1    -1.732358 -1.011871 -1.927887 -2.324690 -1.042635  0.736412 -0.292507   \n",
       "2    -1.730658  0.010076 -0.203317 -0.549504 -1.042635  1.032634 -1.340648   \n",
       "3    -1.728959 -0.626231 -0.800284 -1.183499 -1.042635  0.736412 -0.292507   \n",
       "4    -1.727260  3.905046  2.051889  1.732879  0.758424 -0.152253 -0.292507   \n",
       "...        ...       ...       ...       ...       ...       ...       ...   \n",
       "2033  1.724146 -0.337000  0.260990 -0.169107  0.398213  0.292079 -0.816578   \n",
       "2034  1.725845 -0.626231 -0.866613 -0.422705 -1.042635 -0.596586 -0.816578   \n",
       "2035  1.727545 -0.626231 -0.866613 -0.042308 -1.402847 -0.152253 -0.816578   \n",
       "2036  1.729244  0.029358  0.194660  0.211290  0.398213  0.440190 -0.816578   \n",
       "2037  1.730943 -0.471974 -0.601295 -0.169107 -0.682423  1.328856 -0.816578   \n",
       "\n",
       "          walk     brick     floor  price_sq      yhat  \n",
       "0     0.676607  1.448194  0.514833 -0.794058 -0.764332  \n",
       "1     0.676607 -0.690515  0.514833 -0.033961 -1.817944  \n",
       "2     0.676607  1.448194  0.514833  0.272123 -1.059574  \n",
       "3     0.676607 -0.690515  0.514833 -0.397157 -1.190719  \n",
       "4    -1.477963  1.448194  0.514833  3.590225  1.064124  \n",
       "...        ...       ...       ...       ...       ...  \n",
       "2033 -1.477963 -0.690515  0.514833 -0.715036 -0.307218  \n",
       "2034 -1.477963 -0.690515  0.514833 -0.333100  0.205336  \n",
       "2035  0.676607 -0.690515  0.514833 -0.333100  0.088442  \n",
       "2036 -1.477963 -0.690515  0.514833 -0.051673 -0.206800  \n",
       "2037  0.676607 -0.690515  0.514833 -0.268832 -1.067811  \n",
       "\n",
       "[2038 rows x 12 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "data_scale=data.copy()\n",
    "data_scale=pd.DataFrame(scaler.fit_transform(data_scale), columns=data_scale.columns)\n",
    "data_scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "db3269c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               price_sq   R-squared:                       0.302\n",
      "Model:                            OLS   Adj. R-squared:                  0.301\n",
      "Method:                 Least Squares   F-statistic:                     293.6\n",
      "Date:                Sun, 09 Oct 2022   Prob (F-statistic):          2.46e-158\n",
      "Time:                        19:30:32   Log-Likelihood:                -2525.2\n",
      "No. Observations:                2038   AIC:                             5058.\n",
      "Df Residuals:                    2034   BIC:                             5081.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept  -1.839e-16      0.019  -9.93e-15      1.000      -0.036       0.036\n",
      "livesp         0.2850      0.019     15.075      0.000       0.248       0.322\n",
      "dist          -0.3734      0.019    -19.676      0.000      -0.411      -0.336\n",
      "metrdist      -0.1532      0.019     -8.223      0.000      -0.190      -0.117\n",
      "==============================================================================\n",
      "Omnibus:                      825.479   Durbin-Watson:                   2.021\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6653.228\n",
      "Skew:                           1.697   Prob(JB):                         0.00\n",
      "Kurtosis:                      11.175   Cond. No.                         1.25\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Оценим модель регрессии ols_2 для шкалированных показателей\n",
    "ols_2_scale = smf.ols('price_sq ~ livesp + dist + metrdist', data=data_scale).fit()\n",
    "print(ols_2_scale.summary())"
   ]
  }
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