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jamm1985/lab_5_linear_regression.ipynb

Created November 28, 2021 12:28
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Lab_5_linear_regression.ipynb",
"provenance": [],
"authorship_tag": "ABX9TyPuDhaW6Z0YtnJhZd/efLH5",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/jamm1985/5fb71795ac52f2d514844149a1d2c8b8/lab_5_linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "uXoHbRTOg1Vf"
},
"source": [
"Видео лабраторной: https://youtu.be/txDLkiesqpY\n",
"\n",
"TG: https://t.me/data_science_news\n",
"\n",
"---\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "np_jZLrjrTZ8",
"outputId": "b8aca14e-9dbc-4f81-d9fe-f4e6cccdd062"
},
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pylab as plt\n",
"plt.rcParams['figure.figsize'] = [12, 12]\n",
"\n",
"import statsmodels.api as sm\n",
"import seaborn as sns"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
" import pandas.util.testing as tm\n"
]
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "vjA2EdB9wlEd"
},
"source": [
"Документация statsmodels https://www.statsmodels.org/stable/index.html"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Lu_LS8yBuYxG"
},
"source": [
"## Цены на недвижимость в Бостоне (набор данных)\n",
"\n",
"Набор данных https://www.cs.toronto.edu/~delve/data/boston/bostonDetail.html\n",
"\n",
"Плейбук: http://www.science.smith.edu/~jcrouser/SDS293/labs/lab2-py.html "
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "-UZz9rIWtDaU",
"outputId": "6a1cd023-ed28-4a6d-8184-7c5db02597fe"
},
"source": [
"!wget http://www.science.smith.edu/~jcrouser/SDS293/data/Boston.csv"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--2021-11-10 07:16:17-- http://www.science.smith.edu/~jcrouser/SDS293/data/Boston.csv\n",
"Resolving www.science.smith.edu (www.science.smith.edu)... 131.229.72.9\n",
"Connecting to www.science.smith.edu (www.science.smith.edu)|131.229.72.9|:80... connected.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 37658 (37K) [text/csv]\n",
"Saving to: ‘Boston.csv’\n",
"\n",
"Boston.csv 100%[===================>] 36.78K --.-KB/s in 0.07s \n",
"\n",
"2021-11-10 07:16:17 (518 KB/s) - ‘Boston.csv’ saved [37658/37658]\n",
"\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "6jBJP5detISb",
"outputId": "05b0433f-6a38-4edd-d080-58cd62223020"
},
"source": [
"!head Boston.csv"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\"\",\"crim\",\"zn\",\"indus\",\"chas\",\"nox\",\"rm\",\"age\",\"dis\",\"rad\",\"tax\",\"ptratio\",\"black\",\"lstat\",\"medv\"\n",
"\"1\",0.00632,18,2.31,0,0.538,6.575,65.2,4.09,1,296,15.3,396.9,4.98,24\n",
"\"2\",0.02731,0,7.07,0,0.469,6.421,78.9,4.9671,2,242,17.8,396.9,9.14,21.6\n",
"\"3\",0.02729,0,7.07,0,0.469,7.185,61.1,4.9671,2,242,17.8,392.83,4.03,34.7\n",
"\"4\",0.03237,0,2.18,0,0.458,6.998,45.8,6.0622,3,222,18.7,394.63,2.94,33.4\n",
"\"5\",0.06905,0,2.18,0,0.458,7.147,54.2,6.0622,3,222,18.7,396.9,5.33,36.2\n",
"\"6\",0.02985,0,2.18,0,0.458,6.43,58.7,6.0622,3,222,18.7,394.12,5.21,28.7\n",
"\"7\",0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311,15.2,395.6,12.43,22.9\n",
"\"8\",0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311,15.2,396.9,19.15,27.1\n",
"\"9\",0.21124,12.5,7.87,0,0.524,5.631,100,6.0821,5,311,15.2,386.63,29.93,16.5\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 204
},
"id": "hi3Y8MgKuYHS",
"outputId": "c5b93d13-b817-4f3c-ab93-6e8126a4e544"
},
"source": [
"df = pd.read_csv('http://www.science.smith.edu/~jcrouser/SDS293/data/Boston.csv', index_col=0)\n",
"df.head()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: top;\n",
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"\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>crim</th>\n",
" <th>zn</th>\n",
" <th>indus</th>\n",
" <th>chas</th>\n",
" <th>nox</th>\n",
" <th>rm</th>\n",
" <th>age</th>\n",
" <th>dis</th>\n",
" <th>rad</th>\n",
" <th>tax</th>\n",
" <th>ptratio</th>\n",
" <th>black</th>\n",
" <th>lstat</th>\n",
" <th>medv</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.00632</td>\n",
" <td>18.0</td>\n",
" <td>2.31</td>\n",
" <td>0</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1</td>\n",
" <td>296</td>\n",
" <td>15.3</td>\n",
" <td>396.90</td>\n",
" <td>4.98</td>\n",
" <td>24.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.02731</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</td>\n",
" <td>17.8</td>\n",
" <td>396.90</td>\n",
" <td>9.14</td>\n",
" <td>21.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.02729</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
" <td>34.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.03237</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0</td>\n",
" <td>0.458</td>\n",
" <td>6.998</td>\n",
" <td>45.8</td>\n",
" <td>6.0622</td>\n",
" <td>3</td>\n",
" <td>222</td>\n",
" <td>18.7</td>\n",
" <td>394.63</td>\n",
" <td>2.94</td>\n",
" <td>33.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.06905</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0</td>\n",
" <td>0.458</td>\n",
" <td>7.147</td>\n",
" <td>54.2</td>\n",
" <td>6.0622</td>\n",
" <td>3</td>\n",
" <td>222</td>\n",
" <td>18.7</td>\n",
" <td>396.90</td>\n",
" <td>5.33</td>\n",
" <td>36.2</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" crim zn indus chas nox ... tax ptratio black lstat medv\n",
"1 0.00632 18.0 2.31 0 0.538 ... 296 15.3 396.90 4.98 24.0\n",
"2 0.02731 0.0 7.07 0 0.469 ... 242 17.8 396.90 9.14 21.6\n",
"3 0.02729 0.0 7.07 0 0.469 ... 242 17.8 392.83 4.03 34.7\n",
"4 0.03237 0.0 2.18 0 0.458 ... 222 18.7 394.63 2.94 33.4\n",
"5 0.06905 0.0 2.18 0 0.458 ... 222 18.7 396.90 5.33 36.2\n",
"\n",
"[5 rows x 14 columns]"
]
},
"metadata": {},
"execution_count": 4
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"id": "v0AQ1BA7rmT7",
"outputId": "31eee5f4-a413-4d3a-8e4a-928f72f12aaf"
},
"source": [
"df.describe()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"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>crim</th>\n",
" <th>zn</th>\n",
" <th>indus</th>\n",
" <th>chas</th>\n",
" <th>nox</th>\n",
" <th>rm</th>\n",
" <th>age</th>\n",
" <th>dis</th>\n",
" <th>rad</th>\n",
" <th>tax</th>\n",
" <th>ptratio</th>\n",
" <th>black</th>\n",
" <th>lstat</th>\n",
" <th>medv</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" <td>506.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>3.613524</td>\n",
" <td>11.363636</td>\n",
" <td>11.136779</td>\n",
" <td>0.069170</td>\n",
" <td>0.554695</td>\n",
" <td>6.284634</td>\n",
" <td>68.574901</td>\n",
" <td>3.795043</td>\n",
" <td>9.549407</td>\n",
" <td>408.237154</td>\n",
" <td>18.455534</td>\n",
" <td>356.674032</td>\n",
" <td>12.653063</td>\n",
" <td>22.532806</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>8.601545</td>\n",
" <td>23.322453</td>\n",
" <td>6.860353</td>\n",
" <td>0.253994</td>\n",
" <td>0.115878</td>\n",
" <td>0.702617</td>\n",
" <td>28.148861</td>\n",
" <td>2.105710</td>\n",
" <td>8.707259</td>\n",
" <td>168.537116</td>\n",
" <td>2.164946</td>\n",
" <td>91.294864</td>\n",
" <td>7.141062</td>\n",
" <td>9.197104</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>0.006320</td>\n",
" <td>0.000000</td>\n",
" <td>0.460000</td>\n",
" <td>0.000000</td>\n",
" <td>0.385000</td>\n",
" <td>3.561000</td>\n",
" <td>2.900000</td>\n",
" <td>1.129600</td>\n",
" <td>1.000000</td>\n",
" <td>187.000000</td>\n",
" <td>12.600000</td>\n",
" <td>0.320000</td>\n",
" <td>1.730000</td>\n",
" <td>5.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>0.082045</td>\n",
" <td>0.000000</td>\n",
" <td>5.190000</td>\n",
" <td>0.000000</td>\n",
" <td>0.449000</td>\n",
" <td>5.885500</td>\n",
" <td>45.025000</td>\n",
" <td>2.100175</td>\n",
" <td>4.000000</td>\n",
" <td>279.000000</td>\n",
" <td>17.400000</td>\n",
" <td>375.377500</td>\n",
" <td>6.950000</td>\n",
" <td>17.025000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>0.256510</td>\n",
" <td>0.000000</td>\n",
" <td>9.690000</td>\n",
" <td>0.000000</td>\n",
" <td>0.538000</td>\n",
" <td>6.208500</td>\n",
" <td>77.500000</td>\n",
" <td>3.207450</td>\n",
" <td>5.000000</td>\n",
" <td>330.000000</td>\n",
" <td>19.050000</td>\n",
" <td>391.440000</td>\n",
" <td>11.360000</td>\n",
" <td>21.200000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>3.677082</td>\n",
" <td>12.500000</td>\n",
" <td>18.100000</td>\n",
" <td>0.000000</td>\n",
" <td>0.624000</td>\n",
" <td>6.623500</td>\n",
" <td>94.075000</td>\n",
" <td>5.188425</td>\n",
" <td>24.000000</td>\n",
" <td>666.000000</td>\n",
" <td>20.200000</td>\n",
" <td>396.225000</td>\n",
" <td>16.955000</td>\n",
" <td>25.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>88.976200</td>\n",
" <td>100.000000</td>\n",
" <td>27.740000</td>\n",
" <td>1.000000</td>\n",
" <td>0.871000</td>\n",
" <td>8.780000</td>\n",
" <td>100.000000</td>\n",
" <td>12.126500</td>\n",
" <td>24.000000</td>\n",
" <td>711.000000</td>\n",
" <td>22.000000</td>\n",
" <td>396.900000</td>\n",
" <td>37.970000</td>\n",
" <td>50.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" crim zn indus ... black lstat medv\n",
"count 506.000000 506.000000 506.000000 ... 506.000000 506.000000 506.000000\n",
"mean 3.613524 11.363636 11.136779 ... 356.674032 12.653063 22.532806\n",
"std 8.601545 23.322453 6.860353 ... 91.294864 7.141062 9.197104\n",
"min 0.006320 0.000000 0.460000 ... 0.320000 1.730000 5.000000\n",
"25% 0.082045 0.000000 5.190000 ... 375.377500 6.950000 17.025000\n",
"50% 0.256510 0.000000 9.690000 ... 391.440000 11.360000 21.200000\n",
"75% 3.677082 12.500000 18.100000 ... 396.225000 16.955000 25.000000\n",
"max 88.976200 100.000000 27.740000 ... 396.900000 37.970000 50.000000\n",
"\n",
"[8 rows x 14 columns]"
]
},
"metadata": {},
"execution_count": 5
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "dqha-KNXwpja",
"outputId": "17554e8f-c984-49ce-d2f2-af85d0b5f6bb"
},
"source": [
"plt.rcParams['figure.figsize'] = [12, 12]\n",
"df.hist()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7faf1fe18dd0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1fe04d50>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f93d650>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f8edb50>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f918b90>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f864590>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f899b10>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f84ff90>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f85e050>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f8115d0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f77ded0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f740410>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f6f5910>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f6aae10>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f66e350>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7faf1f624850>]],\n",
" dtype=object)"
]
},
"metadata": {},
"execution_count": 7
},
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 864x864 with 16 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 419
},
"id": "uJBgQkTO2sQM",
"outputId": "818a5f16-59fd-4c49-e886-c986aa302944"
},
"source": [
"df[['crim','medv']]"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"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>crim</th>\n",
" <th>medv</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.00632</td>\n",
" <td>24.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.02731</td>\n",
" <td>21.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.02729</td>\n",
" <td>34.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.03237</td>\n",
" <td>33.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.06905</td>\n",
" <td>36.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>502</th>\n",
" <td>0.06263</td>\n",
" <td>22.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>503</th>\n",
" <td>0.04527</td>\n",
" <td>20.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>504</th>\n",
" <td>0.06076</td>\n",
" <td>23.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>505</th>\n",
" <td>0.10959</td>\n",
" <td>22.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>506</th>\n",
" <td>0.04741</td>\n",
" <td>11.9</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>506 rows × 2 columns</p>\n",
"</div>"
],
"text/plain": [
" crim medv\n",
"1 0.00632 24.0\n",
"2 0.02731 21.6\n",
"3 0.02729 34.7\n",
"4 0.03237 33.4\n",
"5 0.06905 36.2\n",
".. ... ...\n",
"502 0.06263 22.4\n",
"503 0.04527 20.6\n",
"504 0.06076 23.9\n",
"505 0.10959 22.0\n",
"506 0.04741 11.9\n",
"\n",
"[506 rows x 2 columns]"
]
},
"metadata": {},
"execution_count": 8
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "emIJC6FO3AlX"
},
"source": [
"**Sample mean:**\n",
"\n",
"$$E[X] = \\bar{X_n}=\\frac{1}{n}\\Sigma_{i=1}^n X_i$$\n",
"\n",
"**Sample variance:**\n",
"\n",
"$$Var[X] = s^2_{n-1}= E(X-E[X])^2= \\frac{1}{n-1}\\Sigma (X_i-\\bar{X_n})^2$$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "k0HII_LjLUdZ",
"outputId": "97e6952a-fb3a-49ef-81d2-166854e13a5e"
},
"source": [
"N=df['crim'].size\n",
"mean_crim = df['crim'].sum()/N\n",
"mean_crim"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"3.613523557312254"
]
},
"metadata": {},
"execution_count": 9
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "62HBmzRVLfVL",
"outputId": "b27a52c2-566f-475d-f453-e782f3701eb9"
},
"source": [
"df['crim'].mean()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"3.6135235573122535"
]
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "HkTP1ZutL6_e",
"outputId": "22a46cdc-471a-4bc0-9f22-272571e7c3db"
},
"source": [
"var_crim = 1/(N-1)*((df['crim'] - mean_crim)**2).sum()\n",
"var_crim"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"73.98657819906931"
]
},
"metadata": {},
"execution_count": 14
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1vR-jq__MSX-",
"outputId": "50164c41-0d7e-4ac5-e635-9c27178356d8"
},
"source": [
"df['crim'].var()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"73.98657819906929"
]
},
"metadata": {},
"execution_count": 12
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "k4nF94FCMpEy"
},
"source": [
"**Sample correlation:**\n",
"\n",
"$$\\rho = \\frac{Cov(X,Y)}{\\sqrt{Var(X)Var(Y)}} = \\frac{E[(X-E[X])(Y-E[Y])]}{s_X s_Y} = \\frac{\\frac{1}{n-1}\\Sigma_{n=1}^n((X-\\bar{X_n})(Y-\\bar{Y_n}))}{s_X s_Y} $$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "zfZ0N2uvP5dB"
},
"source": [
"mean_medv=df['medv'].mean()\n",
"var_medv=df['medv'].var()"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "4TrHYn9wMopP",
"outputId": "1f3db43d-b4e6-4548-e74b-c312a3e9b7d2"
},
"source": [
"1/(N-1)*((df['crim'] - mean_crim)*(df['medv'] - mean_medv)).sum()*1/(np.sqrt(var_crim*var_medv))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.3883046085868115"
]
},
"metadata": {},
"execution_count": 16
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 111
},
"id": "5POludaGQxtB",
"outputId": "06bfc463-d785-4482-ab57-4afd29fab450"
},
"source": [
"df[['crim','medv']].corr()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"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>crim</th>\n",
" <th>medv</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>crim</th>\n",
" <td>1.000000</td>\n",
" <td>-0.388305</td>\n",
" </tr>\n",
" <tr>\n",
" <th>medv</th>\n",
" <td>-0.388305</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" crim medv\n",
"crim 1.000000 -0.388305\n",
"medv -0.388305 1.000000"
]
},
"metadata": {},
"execution_count": 17
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 483
},
"id": "sXKyQuSpw4e9",
"outputId": "27d25c77-c560-4309-d153-a6b063271b13"
},
"source": [
"df.corr()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"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>crim</th>\n",
" <th>zn</th>\n",
" <th>indus</th>\n",
" <th>chas</th>\n",
" <th>nox</th>\n",
" <th>rm</th>\n",
" <th>age</th>\n",
" <th>dis</th>\n",
" <th>rad</th>\n",
" <th>tax</th>\n",
" <th>ptratio</th>\n",
" <th>black</th>\n",
" <th>lstat</th>\n",
" <th>medv</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>crim</th>\n",
" <td>1.000000</td>\n",
" <td>-0.200469</td>\n",
" <td>0.406583</td>\n",
" <td>-0.055892</td>\n",
" <td>0.420972</td>\n",
" <td>-0.219247</td>\n",
" <td>0.352734</td>\n",
" <td>-0.379670</td>\n",
" <td>0.625505</td>\n",
" <td>0.582764</td>\n",
" <td>0.289946</td>\n",
" <td>-0.385064</td>\n",
" <td>0.455621</td>\n",
" <td>-0.388305</td>\n",
" </tr>\n",
" <tr>\n",
" <th>zn</th>\n",
" <td>-0.200469</td>\n",
" <td>1.000000</td>\n",
" <td>-0.533828</td>\n",
" <td>-0.042697</td>\n",
" <td>-0.516604</td>\n",
" <td>0.311991</td>\n",
" <td>-0.569537</td>\n",
" <td>0.664408</td>\n",
" <td>-0.311948</td>\n",
" <td>-0.314563</td>\n",
" <td>-0.391679</td>\n",
" <td>0.175520</td>\n",
" <td>-0.412995</td>\n",
" <td>0.360445</td>\n",
" </tr>\n",
" <tr>\n",
" <th>indus</th>\n",
" <td>0.406583</td>\n",
" <td>-0.533828</td>\n",
" <td>1.000000</td>\n",
" <td>0.062938</td>\n",
" <td>0.763651</td>\n",
" <td>-0.391676</td>\n",
" <td>0.644779</td>\n",
" <td>-0.708027</td>\n",
" <td>0.595129</td>\n",
" <td>0.720760</td>\n",
" <td>0.383248</td>\n",
" <td>-0.356977</td>\n",
" <td>0.603800</td>\n",
" <td>-0.483725</td>\n",
" </tr>\n",
" <tr>\n",
" <th>chas</th>\n",
" <td>-0.055892</td>\n",
" <td>-0.042697</td>\n",
" <td>0.062938</td>\n",
" <td>1.000000</td>\n",
" <td>0.091203</td>\n",
" <td>0.091251</td>\n",
" <td>0.086518</td>\n",
" <td>-0.099176</td>\n",
" <td>-0.007368</td>\n",
" <td>-0.035587</td>\n",
" <td>-0.121515</td>\n",
" <td>0.048788</td>\n",
" <td>-0.053929</td>\n",
" <td>0.175260</td>\n",
" </tr>\n",
" <tr>\n",
" <th>nox</th>\n",
" <td>0.420972</td>\n",
" <td>-0.516604</td>\n",
" <td>0.763651</td>\n",
" <td>0.091203</td>\n",
" <td>1.000000</td>\n",
" <td>-0.302188</td>\n",
" <td>0.731470</td>\n",
" <td>-0.769230</td>\n",
" <td>0.611441</td>\n",
" <td>0.668023</td>\n",
" <td>0.188933</td>\n",
" <td>-0.380051</td>\n",
" <td>0.590879</td>\n",
" <td>-0.427321</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rm</th>\n",
" <td>-0.219247</td>\n",
" <td>0.311991</td>\n",
" <td>-0.391676</td>\n",
" <td>0.091251</td>\n",
" <td>-0.302188</td>\n",
" <td>1.000000</td>\n",
" <td>-0.240265</td>\n",
" <td>0.205246</td>\n",
" <td>-0.209847</td>\n",
" <td>-0.292048</td>\n",
" <td>-0.355501</td>\n",
" <td>0.128069</td>\n",
" <td>-0.613808</td>\n",
" <td>0.695360</td>\n",
" </tr>\n",
" <tr>\n",
" <th>age</th>\n",
" <td>0.352734</td>\n",
" <td>-0.569537</td>\n",
" <td>0.644779</td>\n",
" <td>0.086518</td>\n",
" <td>0.731470</td>\n",
" <td>-0.240265</td>\n",
" <td>1.000000</td>\n",
" <td>-0.747881</td>\n",
" <td>0.456022</td>\n",
" <td>0.506456</td>\n",
" <td>0.261515</td>\n",
" <td>-0.273534</td>\n",
" <td>0.602339</td>\n",
" <td>-0.376955</td>\n",
" </tr>\n",
" <tr>\n",
" <th>dis</th>\n",
" <td>-0.379670</td>\n",
" <td>0.664408</td>\n",
" <td>-0.708027</td>\n",
" <td>-0.099176</td>\n",
" <td>-0.769230</td>\n",
" <td>0.205246</td>\n",
" <td>-0.747881</td>\n",
" <td>1.000000</td>\n",
" <td>-0.494588</td>\n",
" <td>-0.534432</td>\n",
" <td>-0.232471</td>\n",
" <td>0.291512</td>\n",
" <td>-0.496996</td>\n",
" <td>0.249929</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rad</th>\n",
" <td>0.625505</td>\n",
" <td>-0.311948</td>\n",
" <td>0.595129</td>\n",
" <td>-0.007368</td>\n",
" <td>0.611441</td>\n",
" <td>-0.209847</td>\n",
" <td>0.456022</td>\n",
" <td>-0.494588</td>\n",
" <td>1.000000</td>\n",
" <td>0.910228</td>\n",
" <td>0.464741</td>\n",
" <td>-0.444413</td>\n",
" <td>0.488676</td>\n",
" <td>-0.381626</td>\n",
" </tr>\n",
" <tr>\n",
" <th>tax</th>\n",
" <td>0.582764</td>\n",
" <td>-0.314563</td>\n",
" <td>0.720760</td>\n",
" <td>-0.035587</td>\n",
" <td>0.668023</td>\n",
" <td>-0.292048</td>\n",
" <td>0.506456</td>\n",
" <td>-0.534432</td>\n",
" <td>0.910228</td>\n",
" <td>1.000000</td>\n",
" <td>0.460853</td>\n",
" <td>-0.441808</td>\n",
" <td>0.543993</td>\n",
" <td>-0.468536</td>\n",
" </tr>\n",
" <tr>\n",
" <th>ptratio</th>\n",
" <td>0.289946</td>\n",
" <td>-0.391679</td>\n",
" <td>0.383248</td>\n",
" <td>-0.121515</td>\n",
" <td>0.188933</td>\n",
" <td>-0.355501</td>\n",
" <td>0.261515</td>\n",
" <td>-0.232471</td>\n",
" <td>0.464741</td>\n",
" <td>0.460853</td>\n",
" <td>1.000000</td>\n",
" <td>-0.177383</td>\n",
" <td>0.374044</td>\n",
" <td>-0.507787</td>\n",
" </tr>\n",
" <tr>\n",
" <th>black</th>\n",
" <td>-0.385064</td>\n",
" <td>0.175520</td>\n",
" <td>-0.356977</td>\n",
" <td>0.048788</td>\n",
" <td>-0.380051</td>\n",
" <td>0.128069</td>\n",
" <td>-0.273534</td>\n",
" <td>0.291512</td>\n",
" <td>-0.444413</td>\n",
" <td>-0.441808</td>\n",
" <td>-0.177383</td>\n",
" <td>1.000000</td>\n",
" <td>-0.366087</td>\n",
" <td>0.333461</td>\n",
" </tr>\n",
" <tr>\n",
" <th>lstat</th>\n",
" <td>0.455621</td>\n",
" <td>-0.412995</td>\n",
" <td>0.603800</td>\n",
" <td>-0.053929</td>\n",
" <td>0.590879</td>\n",
" <td>-0.613808</td>\n",
" <td>0.602339</td>\n",
" <td>-0.496996</td>\n",
" <td>0.488676</td>\n",
" <td>0.543993</td>\n",
" <td>0.374044</td>\n",
" <td>-0.366087</td>\n",
" <td>1.000000</td>\n",
" <td>-0.737663</td>\n",
" </tr>\n",
" <tr>\n",
" <th>medv</th>\n",
" <td>-0.388305</td>\n",
" <td>0.360445</td>\n",
" <td>-0.483725</td>\n",
" <td>0.175260</td>\n",
" <td>-0.427321</td>\n",
" <td>0.695360</td>\n",
" <td>-0.376955</td>\n",
" <td>0.249929</td>\n",
" <td>-0.381626</td>\n",
" <td>-0.468536</td>\n",
" <td>-0.507787</td>\n",
" <td>0.333461</td>\n",
" <td>-0.737663</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" crim zn indus ... black lstat medv\n",
"crim 1.000000 -0.200469 0.406583 ... -0.385064 0.455621 -0.388305\n",
"zn -0.200469 1.000000 -0.533828 ... 0.175520 -0.412995 0.360445\n",
"indus 0.406583 -0.533828 1.000000 ... -0.356977 0.603800 -0.483725\n",
"chas -0.055892 -0.042697 0.062938 ... 0.048788 -0.053929 0.175260\n",
"nox 0.420972 -0.516604 0.763651 ... -0.380051 0.590879 -0.427321\n",
"rm -0.219247 0.311991 -0.391676 ... 0.128069 -0.613808 0.695360\n",
"age 0.352734 -0.569537 0.644779 ... -0.273534 0.602339 -0.376955\n",
"dis -0.379670 0.664408 -0.708027 ... 0.291512 -0.496996 0.249929\n",
"rad 0.625505 -0.311948 0.595129 ... -0.444413 0.488676 -0.381626\n",
"tax 0.582764 -0.314563 0.720760 ... -0.441808 0.543993 -0.468536\n",
"ptratio 0.289946 -0.391679 0.383248 ... -0.177383 0.374044 -0.507787\n",
"black -0.385064 0.175520 -0.356977 ... 1.000000 -0.366087 0.333461\n",
"lstat 0.455621 -0.412995 0.603800 ... -0.366087 1.000000 -0.737663\n",
"medv -0.388305 0.360445 -0.483725 ... 0.333461 -0.737663 1.000000\n",
"\n",
"[14 rows x 14 columns]"
]
},
"metadata": {},
"execution_count": 18
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 721
},
"id": "djONUoR01h4i",
"outputId": "be437d99-6978-47fa-baff-fb1f7f08723c"
},
"source": [
"import seaborn as sns\n",
"sns.heatmap(df.corr(), \n",
" xticklabels=df.corr().columns,\n",
" yticklabels=df.corr().columns)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf1f29b590>"
]
},
"metadata": {},
"execution_count": 19
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x864 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1pCkcbbdfdVQ"
},
"source": [
"## Простая линейная регрессия (Simple Linear Regression)\n",
"\n",
"Функция регрессии (regression function):\n",
"\n",
"$$r(x)=E[Y|X=x]=\\int y f_{Y|X}(y|x)dx$$\n",
"\n",
"Простая линейная регрессия предполагает, что $X_i$ одномерный, а функция регрессии имеет линейный вид: \n",
"\n",
"$$r(x)=\\beta_0+\\beta_1 x$$\n",
"\n",
"Тогда модель простой линейной регрессии будет иметь вид:\n",
"\n",
"$$Y_i=\\beta_0 + \\beta_1 X_i + \\epsilon_i$$\n",
"\n",
"где $Y_i$ - это \"зависимая переменная\" _(predictor variable, regressor, covariate, manipulated variable, \"explanatory variable\", exposure variable)_, $X_i$ - \"независимая переменная\" _(Explanatory variable, independent variable, exogenous)_, $\\epsilon_i$ - \"переменная ошибки\" _(error term, disturbance term, noise)_ неизуветсная случайная величина с математическим ожиданием $E[\\epsilon_i|X_i] = 0$ и константной дисперсией $Var(\\epsilon_i|X_i)=\\sigma^2$. Кроме этого, все $\\epsilon_i$ независимо распределены (имеют $Cov(\\epsilon_i,\\epsilon_j)=0$ для всех $i$,$j$ таких что $i\\neq j$).\n",
"\n",
"Допустим, что $\\hat{\\beta_0}$ и $\\hat{\\beta_1}$ это оценка неизвестных параметров функции регрессии $\\beta_0$ и $\\beta_1$, тогда подобранная прямая будет иметь вид:\n",
"\n",
"$$\\hat{r}(x)=\\hat{\\beta_0} + \\hat{\\beta_1}x$$ \n",
"\n",
"Подобранные (прогнозные) значения будут выражены $\\hat{Y_i}=\\hat{r}(X_i)$, а остаточная ошибка имеет вид:\n",
"\n",
"$$\\hat{\\epsilon_i}=Y_i-\\hat{Y_i}=Y_i-(\\hat{\\beta_0} + \\hat{\\beta_1}X_i)$$\n",
"\n",
"\n",
"Остаточная сумма квадтратов (Residual sum of squares, **RSS**) определяется как:\n",
"\n",
"$$RSS= \\Sigma_{i=1}^n \\hat{\\epsilon_i}^2$$\n",
"\n",
"Метод наименьших квадратов (least squares estimates) это такие знаяения $\\hat{\\beta_0}$ и $\\hat{\\beta_1}$ который минимизирует $RSS= \\Sigma_{i=1}^n \\hat{\\epsilon_i}$. Оценка методом наменьших квадратов иммет токчную аналитическую форму:\n",
"\n",
"$$\\hat{\\beta_1}=\\frac{\\Sigma_{i=1}^n (X_i-\\bar{X_n})(Y_i-\\bar{Y_i})}{\\Sigma_{i=1}^n(X_i-\\bar{X_n})^2}=\\frac{Cov(X,Y)}{Var(X)}=\\rho_{X,Y} \\frac{\\sigma_Y}{\\sigma_X}$$\n",
"\n",
"$$\\hat{\\beta_0}=\\bar{Y_n}-\\hat{\\beta_1} \\bar{X_n}$$\n",
"\n",
"И несмещённая оценка дисперсии:\n",
"\n",
"$$\\hat{\\sigma}^2=\\frac{1}{n-2} \\Sigma_{i=1}^n \\hat{\\epsilon_i}^2$$\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZBdkz9JJw0Oz"
},
"source": [
"Простая линейная регрессия на примере $$medv_i=\\hat{\\beta_0}+\\hat{\\beta_1}crim_i + \\epsilon_i$$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "qXjhE6zk1Kfn"
},
"source": [
"plt.rcParams['figure.figsize'] = [12, 8]"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 514
},
"id": "B8mQ7JVbxL7J",
"outputId": "a624d24f-1f2e-422f-b3d9-5a32ac7ec0cb"
},
"source": [
"df[['crim','medv']].plot.scatter(x='crim',\n",
"... y='medv',\n",
"... c='DarkBlue')"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf1ee69350>"
]
},
"metadata": {},
"execution_count": 27
},
{
"output_type": "display_data",
"data": {
"image/png": 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zg1isW1/4wjvU1RVUNBrSmjVBhcPFIZrFgAAAAJ2DhYAuLr30HP3xH79VGzd2a/v28zU6OqFkckThcECzs3MaGtrFYkAAAIAOQWh28MEPjuqee55efPyBD1yqT396QAMDcaVSk0ok1hOYAQAAOgjlGSXGx39SFJgl6Z57ntYTT7ygWKxbW7duIjADAAB0GEJziaeeOuF4/Mor/4o2cwAAAB2K0Fxi27ZNjsdzOasbb/wGbeYAAAA6EKG5RG/v2br44rMdz83OWh0/7rzxCQAAANoXobnE+PhP9NxzP/F7GAAAAGghhOYSbjXN0vyGJn19G5s4GgAAALQCQnOJCy880/Xcpz/9NjpnAAAAdCBCc4lXXsk6Hv/Qh/q0Z88lTR4NAAAAWgGhuUbvfOdr/R4CAAAAfEJoLtHXt1GRSPGnJRKhlhkAAKCTEZpLxGLduu++tysaDWnt2rCi0ZDuu+/t1DIDAAB0sJDfA2hFg4O9GhiIK5WaVCKxnsAMAADQ4QjNLmKx7qKwnE5PE6IBAAA6FOUZNRgeHlc8flA7dhxWPH5Qw8Pjfg8JAAAATURoriKdnlYyOaJMJqfJyawymZySyRGl09N+Dw0AAABNQmiuIpWaLOumEQ4HlEpN+jQiAAAANBs1zS7Gx3+i0dEJRaMhnT6dLzo3OzunRGK9TyMDAABAsxGaHXzwg6O6556nFx8HAlI4bBSNhjU7O6ehoV0sBgQAAOgghOYS4+M/KQrMkjQ3JxkjHT78bvX1bSQwAwAAdBhqmks89dQJx+P5vNVLL50mMAMAAHQgQnOJbds2uZ77znfSTRwJAAAAWgWhucRrXhN1Pbd2bbiJIwEAAECrIDSXOH78pOu5X/7l1zVxJAAAAGgVhOYavec9r1Vv79l+DwMAAAA+IDSX2Lx5nePx//yfz2vySAAAANAqCM0lpqay6uoKlh2/7ba/ZetsAACADkVoLpFIrJe15cfz+cr1zgAAAGhfhOYSsVi3du6M+z0MAAAAtBBCc4l0elqjo/9adjwcNurr2+jDiAAAAOA3QnOJVGpSkUj5p2XLlnPYDRAAAKBDEZpLJBLrdfp0vuz4k0+e1BNPvODDiAAAAOA3QnOJWKxbN930Rsdz27d/ScPD400eEQAAAPxGaHbwcz+3wfH47OycbrzxG7SeAwAA6DCE5hLp9LQ+8Ym/dz0/O2t1551HmjgiAAAA+I3QXMJtIeBSd955hNlmAACADkJoLpFIrFc2O1fxmlAooFRqskkjAgAAgN8IzSVisW4lkxdXvMba+XANAACAzkBoLpFOT+vgwWdcz4fDRvv2Xd7EEQEAAMBvhOYSx4+fdCzPuOOOK/Sxj21TKBTUJz85pnj8IO3nAAAAOgShuUYXXrhBn/rUMWUyOU1OZpXJ5JRMjrAgEAAAoAMQmkts3ryuwllb/MhaFgQCAAB0AEJziamprKLRYNGxNWvmP02ZTPH22jMzefX0RJo2NgAAAPiD0FxiviuGKTp2+vScjh9/UdFoqOh4NBrS1FS2iaMDAACAHwjNJWKxbh04cGXZ8bvuOup4Pa3nAAAA2h+h2cGWLRu1Zk2w7Pi+fZcrGg1p3bqIotGQhoZ2KRbr9mGEAAAAaKZQ9UvqY4zpkvS3ktYsvM6XrbX/wxhzgaS/knS2pKOS3m+tbakah56eiE6fLq9f/pmf6dZ9912tDRvWqK9vI4EZAACgQ3g503xa0lXW2kskXSrpamPMmyT9kaQD1toLJZ2SlPRwDHV54IHvOx7/r//1Uf3qr35d7373VzU6OtHkUQEAAMAvnoVmO29q4WF44T8r6SpJX144fr+ka70aQz3S6Wnt3/9UxWuy2TnPezSn09MaGztBH2gAAIAW4GlNszEmaIx5WtKLkh6V9M+SXrLW5hYu+bGkc12eu9sYc8QYcySdTns5zCKp1KRCoeqflkDAeNajeXh4XPH4Qe3YcZidBwEAAFqAp6HZWpu31l4q6TxJ2yRdtIznHrTW9ltr+2OxmGdjLJVIrFc2m6963dyc9aRzRjo9rWRyhJ0HAQAAWkhTumdYa1+S9JikN0vaYIwpLEA8T9ILzRhDrWKxbu3de1nFayKRgGedM1KpSUUixf9bwuEAOw8CAAD4yLPQbIyJGWM2LPw9KmmHpHHNh+dfWbjsRkkPeTWGer3rXT/nePzOO9+qkZH36cc/vkWDg72evPb8TPdc0bHZ2Tn6QQMAAPjIy5nmTZIeM8Y8I2lM0qPW2q9L+pik3zXG/FDzbeeGPBxDXX74w1OOx886K6qdOy/wtNVcLNatoaFd9IMGAABoIZ71abbWPiOpz+H4v2i+vrllXXjhmcs63miDg70aGIgrlZpUIrGewAwAAOAzz0LzavbYY+U9mI2RXnmleXuwxGLdhGUAAIAWwTbaJdLpad1xx5Nlx62VrrnmQdq/AQAAdCBCc4lUalIBl8/KzEye9m8AAAAdiNBcIpFYr1zOup6n/RsAAEDnITSXiMW69f73v8H1PO3fAAAAOk9NodkY8yljzC96PZhWkE5P68///LuO57q6grR/AwAA6EC1zjQflfTfjTH/bIz5pDGm38tB+SmVmlQuN+d47vbb3+zZpiYAAABoXTWFZmvt/dbad0jaKun7kv7IGPNPno7MJz09EeXzzueiUTr0AQAAdKLl1jRfKOkiSXFJ32v8cPw3NZVVKGQcz7kdBwAAQHurtab5jxdmlv8/Sc9J6rfWvtvTkfkkkVivYNA5HG/Z8jNNHg0AAABaQa0zzf8s6c3W2quttZ+31r7k5aD8FIt1a+fOhOO5Zu4I2C7S6WmNjZ2gtzUAAFjVKhbpGmO2LPx1TNL5xpjzl5631h7zamB+Saen9T//57/4PYy2MDw8rmRyRJFIQNnsnIaGdrGQEgAArErVVrb9/wt/dknql/QdSUbSf5J0RNKbvRuaP44fP6k5h+YZwaDU17ex+QNapdLpaSWTI8pkcspk5o8lkyMaGIjTsg8AAKw6FcszrLXbrbXbJZ2QtMVa22+tvUxSn6QXmjHAVvE7v9OnVGqyKWUG7VDSkEpNKhIp/vKqdzfFdvh8AACA1a3WmubXW2ufLTyw1j4nqS3/nb2vb2NZ2JOkz372ae3YcVjx+EEND4979vrDw+OKxw825bW8lEisVzZbPGVfz26K7fL5AAAAq1utofkZY8znjDFXLvz3Z5Ke8XJgfonFuvWpT72t7PjsrNXkZFaZTE7J5Igns55LSxq8fi2vxWLdGhrapWg0pHXrIopGQ8veTbGdPh8AAGB1q3W3jt+Q9FuSbl14/LeSPuvJiFrAli3n6Iwzwnr55VnH84Uyg0bX5hZKGgo1wF6+VjMMDvZqYCCuVGpSicT6ZX8M7fb5AAAAq1dNodlaO2OM+VNJ37DWft/jMfkukVivXM66nq+nzKDW121ESUMricW66w647fj5AAAAq1Otm5u8R9LTkr658PhSY8zDXg7MT7FYt6644meLjhmjsjKDRi9Qa0RJQzvh8wEAAFqFsdZ9RnXxImOOSrpK0uPW2r6FY89aa3/B4/FJkvr7++2RI0ea8VKSpPHxn+gNb/h82fEvfeld2r79fMVi3Z72IE6np+suaWhHfD4AAEAzGGOOWmv7nc7VWtM8a62dNKZoe+nqaXuVeuqpE47HT558ZXGG2csexCspaWhHfD4AAIDfag3N/2iM+XVJQWPM6yR9SNLfezcsf23btsnx+O/93t/qNa/p1oUXbmCBGgAAQAepteXcByW9UdJpSX8paVKvdtJoO08//aKKJ9XnzczklUyOqKcnwgI1AACADlJraH7Dwn8hzW+pfY2kMa8G5ad0elo33/xNuZV6h8MBTU1lWaAGAADQQWotz/gLSR+R9JykuSrXrmrVtnkuzChv3bppRT2IAQAAsHrUGprT1tqveTqSFpFIrFc+7zzNHAqZohllFqgBAAB0hlrLM/7Hwjbag8aY9xb+83RkPonFujU4eJHjufe973UNaysHAACA1aPW0Pwbki6VdLWkdy/89y6vBuW322673PH4Qw/9c8M2MgEAAMDqUWt5xlZr7es9HUkL6e09W9dd9/M6fPgHRccjkSBt5QAAADpQrTPNf2+MeYOnI2kxn/nMgLq6gkXHaCsHAADQmWoNzW+S9LQx5vvGmGeMMc8aY57xcmB+i8W6dejQ1bSVAwAAQM3lGVd7OooWNTjYS1s5AAAA1BaarbUTXg+kVdFWDgAAALWWZ3SkdHpaY2Mn6JgBAADQ4Wotz+g4w8PjuvnmbyoYNMrnre66a7u2bNlImQYAAEAHIjQ7SKendcMN31Au9+rOgLfcMqq1a8Oam7MaGtq17E1O0unpmmujq127nHsBAABg5SjPcHDnnWNFgbnglVdmlcnklEyOLKtkY3h4XPH4Qe3YcVjx+EEND4/Xfe1y7gUAAIDGMNaWh8NW09/fb48cOdKU10qnp3XuuX+q2dk512t6esL69rev19atm2q6Xzx+UJlMbvFYNBrSxMTuslniatcu514AAABYHmPMUWttv9M5ZppLpFKTkir/IrGcTU5SqUlFIsWf5nA4sPA6y7t2OfcCAABA4xCaS/T0RDQ7Wzk033339ppndhOJ9cpmi2et3UJ3tWuXcy8AAAA0DqG5xPPP/7Ti+dtu26Y9ey6t+X6xWLeGhnbVtLNgtWuXcy8AAAA0DjXNJR555EfatesB1/N/93eDestbzpXU2I4Yy7mW7hkAAACNV6mmmZZzJTZvXlfx/C/90rD+/M/fKUlKJkcUiQSUzc5VbUO3nJ0Fq13LLoUAAADNRWguMTWVVTgccO2eMTcn3XzzNyVJMzN5ZTLzx5PJEQ0MxAmzAAAAbYia5hKJxHrl89VLVoJBU/SYLhYAAADti9DsYG6uemguDdZ0sQAAAGhflGeUOH78ZMXzoZDRoUNXS5ovySiUcgwN7ZIkjY2dWAzPLNYDAABoD4TmEi+9dLri+Y98ZOvigr+BgfhiMB4dnVA8flCRSEDT07MyxigaDdW0SHC56J4BAADQXJRnlNiwYU3F83fffUzp9LSk+S4Wha20k8kRZTI5TU5mNTtrlc3OaXIyq0wmp2RyZPE5KzU8PK54/KB27DisePyghofHG3JfAAAAuCM0l+jr26hAhc9KKFS+4M9pe+ulGrVIMJ2eLgrnjQ7kAAAAcEZoLhGLdauvL+Z6PpvNFy34S6enderUTNn21ks1apGgUzinawcAAID3qGkukU5P6+mn067n/+APrlisIx4eHl/c4CSXyysSCairK6RMZr6muasrtLhIcKU7+7mFc7p2AAAAeI/QXKLarO1b33qe0ulpHT9+crFUorDBSVdXQIcPv1t9fRsX7+UWiJcG7mqLBd3CeaVAvhqxwBEAALQqQnOJnp6I8nn383fddVRf/eoPFQhImUyu6FwkEtSZZ3YtBj634Le0NrnajoJO13Z1BfRnf7ZTGzasWQzoq91yfokAAABoNmqaSzz//E8rnv/Lv/yeMpmcXnklV3au1lKJ5dQmuy0yvOGGv9H113+tLTposMARAAC0OkJzA6xdG1Y0Gqq5VCKRWF9zbbLTtTMzeZ0+nW+bgMkCRwAA0OoIzSU2b163rOu7uoL6ylfeo4mJ3UXlBOn0tMbGTjiG2VisW0NDuxSNhrRuXWQxcEsqe87Sa9euDWvNmqCi0eKqmtUeMJfzSwQAAIAfCM0lpqayMqa2a7u6gjp06Grt3HlB0QxzLRuQDA72amJit0ZHr9PExG5Jqvgca62k+f/y+fYKmG6/RLAYEAAAtAozH8ZaW39/vz1y5EhTXiudntY55/xJ1eu6uoJ66KFrtXPnBWXPj8cPFi0SjEZDmpjYXXFhoNtzJJWdC4eNQqGgwuHAYgeNdlg0R/cMAADgJ2PMUWttv9M5umeUiMW6dfHFZ+m55/6j6rVOnSsK9bmFTheSFAwapVKTrkHQ6TlLSy5Kz0WjYR0+/G6deWZXWwXMWKy7bT4WAADQXijPcPDmN/9sxfPhsNGhQ1c7Bjyn+typqVkdO/ai6/0q1fS6nevr26itWzcRMgEAAJqA0Oxg2zb30Lxv3zZ9/evv1cBA3PF8LNatAweuLDu+d+9jrh0uKtX0Uu8LAADgP8ozHDAnu48AACAASURBVJw4MeV67s47j+ozn3m64gYcW7Zs1BlnRPTyy9nFY4VyC7ewOzjYq4GBuGNNb6VzAAAA8B6h2cFnPvO067mZmbxmZua3DHTbxS+RWK9crrikIpvN69SpGaXT04rFuhcXvfX0RDQ1lV0Mw26BmHpfAAAA/xCaSzzxxAs6ebK2jULcZo8LJRXJ5IjC4YAymVnNzVldf/3XlM3OKZm8WENDz0myymTy6uoKylrp7ruv0p49l3jwUQEAAGAlqGku8cgjqZqvrdQfudCH+fDhdysUCiqbnVvcwe+ee55WJpNTJjM/Y13Y4e+WWx7Vvfe6z3IDAADAH4TmEjt3Jqpec8YZ5QvynHYAjMW6deaZXWVbRFdy663uCwYBAADgD8ozSvz8z59Z8fzatSF9+tNX6R3veO1iYB4eHlcyOaJIJFC2QNCpZVwl1RYMrtRq20BktY0XAAC0J2aaS6RSk1qzxv18LmeLAnM6Pa1kckSZTG6x/CKZHFmcLXZqGfeBD1yqaDSkNWuCZffP561nW2LXsr13K1lt4wUAAO2L0FwikVivfN79/N13by+a8Szs5rfU0t38pFfrm0dHr9PExG59+tMDmpjYrYcfvlYf+lCfIpGAenrCnvZgrhbuW81qGy8AAGhvlGeUiMW6tXPnBfrGN35Udu6ii87Unj2XFpUMVNrNr/S+S8Pw6OjEYklHMBjQxz62TXv2XOJZCUKlrbpbsexhtY0XAAC0N2aaHWzc6BzKvve9U/rN3/xmUcnA6OjEsnfsc5pF3b//Sa8+HEmVt+puRattvAAAoL0Rmkuk09O6//7vup4fGnqurGRgYCBeVH7htEvgUrWUdDSan9txO3UWqYbtwwEAQCuhPKPE8eMnNTdna76+EHa3bt1Uc6BLJNYrk8kVHZuZyXk+i+rHdtyVOotUw/bhAACgVRCaV8itZKBaqzRrbcXHtdyjHs3cjntpGUqhNtlt63E3bB8OAABaAeUZJTZvXud6LhQyi+3iKpUMVGuVlkpNqrs7XHQsGg0XlWe0Q7s1P8pQAAAAvMBMc4nnn/+p67nt2zfrhhveqN/+7T5NTWUdZ4BrmV2ttsitETO0rYDFfAAAoF0w07wMjz76r7riir9UX98XdOzYSccAW8vsarVFbrXco57Fdc3GYj4AANAumGku0de3UcZIDiXGkqRs1krK65ZbRiUZ7dlzSdH5WmdXKy1yq3aPlSyua7Zqi/nYJhsAAKwGns00G2M2G2MeM8Z81xjzj8aYWxeOn2WMedQY808Lf57p1RjqEYt1q7f3rJquvfXWb5fN9C5ndjUW63bsulHpHrXslNdqs9BuH2c71G0DAIDO4OVMc07Sf7PWHjPGnCHpqDHmUUk3SfqWtfYPjTG3SbpN0sc8HMeypNPT+t73/qOmayORoOMOdZVmV0tnVt0eF3o/l96j2k55q2UWul3qtgEAQGfwLDRba09IOrHw95eNMeOSzpV0jaQrFy67X9LjaqHQnEpNypjars3l3Be1ObVKKw20yeTFGhp6zvWxU+CtVLqxmoIo22QDAIDVpCkLAY0xCUl9kp6UtHEhUEvSv0na6PKc3caYI8aYI+l0uhnDlDQfSk2NqfnAge01Bzynsop77nm64uPSsgupcunGamrxRmcNAACwmngemo0xPZIekPRha21RPzc7v6OH45I7a+1Ba22/tbY/Fot5PcxFsVi3Pvzh/qrXdXcH1dUV1Pj4T2qqH3YKtNW4Bd7BwV7HbbtXUxClswYAAFhNPO2eYYwJaz4w/4W19isLh08aYzZZa08YYzZJetHLMdTj/PN7ql4zPZ3Xb/7miHI5q2h0/tNYqX7YKdBWUynwOpV/xGLdOnDgSt1662MKhwPK521LB1G2yQYAAKuFl90zjKQhSePW2juXnHpY0o0Lf79R0kNejaFezzxTWzlILjc/ST5fQ/xqOYVT9wqnmdUPfOBSdXUFHe/d1RVcduAdHh7X3r2PKxIJanZ2TgcObG/JRYBLuXXWAAAAaCXGujUkXumNjblC0v+W9KykwhTrPs3XNf+1pPMlTUi63lpbsV1Ff3+/PXLkiCfjLJVOT2vTps8qn1/+52Xduog++tF+7d//lOtivtJuGY888iO9970P65VXZhevWbs2rK985T3aufOCZY07Hj+oTCa3eCwaDWliYjeBFAAAoAbGmKPWWsc6XS+7Z/ydJLcVdW/z6nVX6vjxk3UFZknKZvPav/+pou4VN9/8zaLuFaVlFX19GzU3V/x6udycNm9e5/o6ThuCdHI3CjZIAQAAXmMb7TqEw6boz2g0pGg0pI9//E1li/1mZvK6997vVLzfvn2XL95DkgIB6bLLvui42YfbhiCraRFgI7FBCgAAaAbPyjMaqdnlGT/zM3+iuQpr9j71qas0MBDX1FRWPT0RTU1lF8Pp+effq5mZfNH1bmUSS/s2z8zklM/bxTppp+dVK8Eo3C8cDmh2tnU3NmkUSlIAAEAj+VKesVrFYt361V+9SMPD33M8Hw4b/dqvXeQayj7+8Tfp9tufKHlOeZmE00Yk5a9V/LxqJRid1o2ik0tSAABAc1GeUSKdntaXv/wDx3OhkNH997+jYiDbs+eSxTKLAqcyiVr6Npc+r5YSjE7qRtGpJSkAAKD5CM0lUqlJWetcm9Hfv7FquUOtm3Y4Bb5w2FR8HhuCFOPzAQAAmoWa5hLp9LTOOedPXM9/97u/sVjDXCmc1dLRwakGuZbyivHxn+ipp05o27ZN6u09e3kfYBuiewYAAGiESjXNhOYS6fS0Nm78E7l9WkIhae3aiGMP5npfbzmBb+niwUaNAQAAAJVDM+UZJarVGudy0uRktmgHwJVYTg3y0sWDjRwDAAAAKiM0l1jOIrJCp4ZmcQr0zR4DAABAJyI0l4jFurV3r+OsfJlsNt/UTg10iwAAAPAHodnB9u2ba7ruppve2NSFZ3SLaK50elpjYycofwEAAGxu4qSvb+NiR4tKPvShy1zP1bLAr56uD43cwMTp9elEMY8FlwAAYClCs4NYrFuf+MSby3b2WyqZvNi13VstgWsloSwW615xoHV6/fmPi6DotFtjMjmigYF4R/8iAQBAJ6PlnIsnnnhBV1wx7HguFDJ65pmbHENzOj2tePygMpnc4rFoNKSJid1Fs7nVrvGS2+tbazUzk/dlTK1kbOyEduw4rMnJ7OKxdesiGh29Tlu3bvJxZAAAwEu0nFum4eFxvfWtf+V6PpezuvTS+/UHf/B/yupda+lw4XcXDKfXDwSMgkHj25haCQsuAQBAKUJziXR6Wjff/E3l85Vn4LPZOd1++xOKxw9qeHh88XgtgcvvUOb0+nNztuxj7tSgyIJLAABQitBcIpWaVCBgql+4oHSDkVoCV7NDWWkXCLfXP3To6pYJin53rhgc7NXExG6Njl6niYndHVnbDQAAXkVNc4l0elrnnfenZTOxlTjVu3rVPWO5Ki04rLV7RrM7atC5AgAA+KFSTTOh2cGtt35Ln/rUccdzwaCUzxcfW7MmqOPHb3DtpuGXRiw4bHaA9XuRJAAA6FwsBFymt7zlXNdzkUhIt922TdFoSNHofMe+QEC67LIvFtU216PRJQkrXXC4tPXa5GS2rBTFC34vkgQAAHBCaHawYcMa13PhcEDvfe/rdPTo+zU3Nz9Ln8nkVxwoh4fHFY8f1I4dh4sWF64kSK90weFyAmyjAr/fiyQBAACcEJod9PVtVMhl25eZmZx6eiKamsqqqytYdK7eGVG3Gd17733aMUjXaqULDmsNsG6Bvx50rgAAAK2ImmYXv//7/0t/+IdjZcfXrAkoEAjowIErtXfv4w2pvXXaTKOnJ6zZ2TmdPr3yzUZWspCvUNNc2Fa8tKbZqxpktvMGAADNVqmmmW20HQwPj+uuu445njt9ek7SnPbufVwHDmzX3r2PFQXKegKe24xuOBwoCs2FmezlvsZKtt0eHOzVwEDcNcAWSjgK202vZJyNGjMAAECjEZpLFEollm4n7SQcDmjLlnM0MbF7xTOihZKEpTO6v/7rF2lo6Lmi6/yq7a0UYKlB7gzM/AMAOh2huYTTzKmTQjBs1Izo0hndnp6ILrvsi2XXHDiwveUCi1Pgpwa5vdA3GwAAQnMZp5nTpc44I6JcrvZguJwZukIAHxs7URbcu7tDuuCCdQ15nUarVsKB1WvpItXC12MyOaKBgTj/nwEAHYXuGSUKM6fhsPOn5nOf21nztsr1dpVwCu7T0zldc82DjvdoZPeKesVi3dq6dRNBqs3QNxsAgHmEZgcDA3G5dRXJZHI1zzDXuzHI0rZrS83M5Mvu4ccGJOgc1KwDADCP0OwglZrUmjVBx3Pbtm2q+R4rmaEbHOzVgw9eo7Vri4Nz6T2YCYSX6JsNAMA8apodJBLrNedQ1myM9MADP9D73vfzmprKutbvptPTOnVqpuIMXWkNslNNcl/fxrJxlM7yMRMIr1GzDgAAM82OCrNrpTv+WSvdfvsTesMbPq+3vvVLjvXDhfri66//mnK5vCKRQNkMXWkN8gc/OOpYk1zLLB8zgWgGatYBAJ2OHQEreOSRH+m9731Yr7wy63rN0t3vnHbH6+oK6v77364NG9aor2+jJJVdU+meUm2dMbzunkGfXgAA0O7YEbBOmzevUy7n3n5Omi/ZOH78pHbuvMC1x/MNN/yNurqCymbntG/f5VX7QJfuqFdoRZdOT2ts7IRjcPVyBz369AIAgE5HeYaL4eFxXXbZFxUImIrXTU/n9M53fkXDw+OO9cUzM3mdPp1f7Gxxxx3/ULEPtORck7zctnKFgL3SLhp05wAAACA0Oyre0GG+jCIUCmjNmvn/SuVyVjff/E1JKqovXrMmWNY2LhIJat++y4tqkD/wgUsr1iQvN7g2sm8z3TmKNeqXEQDl+P4C0Mooz3DgVGaRy83pIx/ZqosuOlu/9VujZTXJwaBRKjVZdTvs2dk57dlzifbsuaSoRvgTn/hF15php/EsLeFYWm8syXUHt8K9aq1LLnQBOX06X/YxdGJ3DspUAO/w/QWg1RGaHbhtpX3XXcd07NgNjhuf5PN2MUgurS8eGtqlZHJE4XBAs7PF22+XdsFwC7KV2sqV/qBxqpkOhwO6996ntX//UzX/QFp637k5q3DYKBoNl30MnYLtpAHv8P0FYDWgPMNBLNatffsuLzseiQT1wAPfVz5fHGDDYaNDh652fHMfHOzVxMRujY5eV/P2207jcWorJ6msbGP//ifLZoaz2bz273+q5vKO0nKQbHZOoVBQhw+/u+6PYbWjTAXwDt9fAFYDQrOLPXsuKevTXAifs7OvzjRHIgF95zs3lQXJpbV5jehx6xS+3X7QfPzjbyoK2B//+JuW9QPJ7b5nntklSR1Zc8gmMoB3+P4CsBoQml3EYt06dOhqdXUFtXZtSF1dQdfw+eyz6aIg2ciFeKVjWhq+3X7Q7NlzSVHA3rPnEtcfSE4Lb9zue+zYSU8+rtWATWQA7/D9BWA1YHOTCgp1vYGA0dyc1YED2/XBD44WzTQXFLpkHDhwpfbufbxooWDpZiUrUbrJSGGMS2umnconnK6T5LrwpvR6rz+u1YJNXgDv8P0FwG+VNjchNLtw2t0vHDaOgXmpNWuCikSCevnl7OKxdesiGh29Tlu3blrRmNxWlzv9oKl2TCrfmbDSToSp1KR27DisycnGf1wAAACtgB0B6+DU5q1aYJbmyzWy2ca0aKu1lVxp5w23cL30urGxEzW3sSs8h5pDAADQqQjNLtzazlWTz1vdffdV2rv3Mcc2c7WqtZXc0u22pdpbNy2njV2hlCOXe/WXgUgkQM0hAADoGIRmF7FYt5LJi3XPPU8vHgsGpXzxJLJCIaNczi7WNBdmdd/73tfVXZvnFHz373+yrD+000xvtY1Qln58Tj2kJecZbWtt0Ux7IGAWN0zxC/WPAACgWQjNLtLpaQ0NPVd0zBgj6dXg+Ou/fpE+/OHL1NMT0dRUtmHhzS34fvSjW7V//5MVZ7Brad1UCJsDA3FNTOzW8eMnJUl9fRsdXzsQMGVjjESCRUG82QHWy93DCOMAAKAUodlFKjWpUKg4LOZyxTO9X/3qD3XjjW9UIrFevb1nLx5faaCr1EqudPvtUm4zyIVrS8eWTF6soaHnFh8fOHBl2WvPzdmKs9zN3v7Wy93D2MoXAAA4oXuGi3vvfVq33DJa9bq1a0PK560+/vE3ac+eSyRV70pRi1pbyblx655ROrZS0WhIBw5sL6vJluQ4Hqd7et2KbmzshCedPPz4WAAAQOuge8YypdPT2rv38bLjoZCUK8mbr7wyf+D225/Q/v1P1rRgr5Z//h8c7NXAQHzZZQKFe/f0RMrOOZVelAqHA9qy5RxNTOwue22n8TjdMxg0ZTXUjeTV7mG11oMDAIDOQ2h24BSeenrC+tjHtmn//icVCBi98sps2fMymZzuuOMfFmqfX1VvKUNpK7lK0ulp3XvvdxZfP5PJKRoNSjKLr1FLR5DCWJe+9tKQXzqT63TPqalZHTv2omf9m6uVoNSLrXwBAIAbttF24BYEY7GoJiZ26ytfeY+6uoKOz41Egtq373LH7WCX1uJOTmaVyeSUTI4UbWFdj8K23bff/oRmZvKL5QWZTL7oNWKxbu3bd7njPdauDTluXVttS/BYrFsHDlxZdr+9ex9b8cdVyeBgb9FW4Y2oO2YrXwAA4IaaZhf33vsd3XLLo0XHlta33nvv0/rt3x7VXMnEbeEaSUVdKWKxbk9qcWupU176Gun0tM4//17NzLzaOy8aDem++67Whg1rFsfqdm+nGt+xsRN629sOe7ILoh9aqXtGK40FAIB2R01zHbZsOUdnnBHWyy+/WoZRqG8dHZ3Q3r2PlwVmSTpwYLtisW7HMoyBgXjD//m/ljrl2dk59fRENDZ2QonEeh06dHVRaUMyebFuuumbZSUjtdb4JhLrlcu1T1nDcspivEQnDwAAWgflGS7mg2B5m7WenshiiUWpnp6wtmw5x7UMQ1LD//m/Up1yV1dQ0WhIyeTFuuyyLy6WWEhaLG04evT9Ghp6zrFkpNYaX8oaGs+rUh4AAFAfZppduC02m5rKus7s5vNWicT6ijO0tXbFqPWf5Z3GuW/f5Xrf+35eU1NZ9fREdNllXyzraTwxsVtbt27S2NgJx7EeP35SZ57ZpQMHrtTevY9XXXBXb7eP5X68nYJOHgAAtBZCcwVOQTCdnnacZe7qChYFykoztNX++X+5/yxfKbC6heJC+HKaTc5kZnXttQ8t2fBkuy64YJ2k+fpsN/WWNVCGUI5OHgAAtBYWAi5TOj2tc8/9rGZnX/28BYNGzz57k+OugMvdnKTWxXe1zszWcr+lY81m85qbs0WBLRw2CoWCnm1ZzYYizla6wQ0AAFgeFgI2UCo1qe7ucFEHjLVrw5qayhZdV2+5Qi3/LL/cXs/VehovHeupUzO6/vqvKZt99eOZnbWanW38ltW1frydaqUlLwAAoHEIzcu0nH82r6dcodr9ly4QqzXEloYvSYudNArPKYw1nZ6uugFKI0MtZQiVtUonDwAAOh3dM5bJ604R1e5fmJldqhBiq91369ZNGh2dqLpZydLX7+oKlr1eI0MtnTcAAMBqQE1znbzu9uB2/5XUAC/nuYXX7+mJ6IEHfqD9+5/0tLaW7hkAAMBv1DTXqVKQ8/qfzd3uX0uNspvl1A/HYt0aHZ1YrJ221uqjH92qPXsu8eTjXs7ns5UDdiuPDQAA1I+ZZheNbIPmRZCq557LnWmudq0fAbGV29O18tgAAEB1lWaaqWl20Mjd2IaHxyvWENerUKO8nLBaqX44nZ7W2NiJxY+xWu20Vx+XpLKxLD3eqrvktfLYAADAylGe4aBRbdDq6XThNac2Zk4zpAMDcdeuFl5+XJVma1u5PV0rjw0AAKwcM80OGtUGrd5OF14r7ASYSk1qfPwnjjOkklxnpb36uKrN1rZye7pWHhsAAFg5QrODRrVBa9UgtbS0oq/vC2XnCwF4cLBXExO7NTp6nSYmdi/O+Hr1cVUL463cnq6VxwYAAFaOhYAVNGKhW6tthey0wK9UNBrSgw9eo76+ja4ftxcfV6O3EPdDK48NAABUVmkhIKG5CVopSI2NndCOHYeLtgHv6grKWmnNmqBmZnKy1qq7O1y1A4QXH1er/ZIBAAA6B6G5wy0Nt5IcZ3OPHn2/nn/+p7rmmgc1M5MvOlfLxilejdfvXzIAAEDnoOVcByttDTc6OuFYe9vbe7bOPLNLa9YEi57vx8LFetrpSe6t6oB68TUFACig5Vwbc2sNNzGxWxMTu8tmc5u5cLHRs8lsLIJG42sKALAUM81trFI3CqfZ3GZ1gGj0xihsLIJG42sKAFCKmeY2Vs/MsdPmJ43kxcYobCyCRuNrCgBQipnmNlbvzHG9NcW18GJjlFbth+1mpXWy1Nl6b7V9TQEAvEdobnNuG5T4xYswspo2Fllpacpyn0/Ars9q+poCgHbTqj+7aDmHpli68G90dKLmXszLWTBYz+LCZra3q3XzlkY9n4VsK0f7QwBoLr9/dlVqOedZTbMx5pCkd0l60Vp78cKxsyR9SVJCUkrS9dbaU16NAa3B6RvAqXtHLc+r9I0Ti3UvK9g0+xtzpXWyy3m+F7XjnWi5X1MAgPq1+s8uL8sz7pN0dcmx2yR9y1r7OknfWniMNubWhUBSxbppr7sX+NEdYaWlKct5vhe14wAAeKnVf3Z5FpqttX8r6T9KDl8j6f6Fv98v6VqvXh+tod5vAK+/cfz4xlxpnexyns9CNgDAatPqP7ua3XJuo7X2xMLf/03Sxia/Ppqs3m8Ar79x/PrGXGlLv1qfXwjYpbXjrfDPWwAAOGn1n12eLgQ0xiQkfX1JTfNL1toNS86fstae6fLc3ZJ2S9L5559/2cTEhGfjRGOVLp4q1A7XsvBvqXqfVyuv798KWMgGAFht/PzZVWkhYLND8/clXWmtPWGM2STpcWvt66vdh+4ZzVfvF6zb4rp675dOT+v48ZOSpL6+jZ5stkKoBAAAkk/dM1w8LOlGSX+48OdDTX591KDerhLVVr3WE0oL7em86nBBdwQAAFALzxYCGmOGJf0fSa83xvzYGJPUfFjeYYz5J0kDC4/RQlbSVaLRi+v86HABAADgxLOZZmvtoMupt3n1mli5lfQSbvTiupX2NQYAAGgUttFGkZUE30ZvPdzqrWcAAEDnIDSjyEqD7+BgryYmdmt09DpNTOxeUf1xo0M4AABAvTztntEodM9ovlbqKtFKYwEAAO2rlbpnYJVopa4SrTSWUgR6AFg9eM/GSlCegVUpnZ7W2NgJXztpDA+PKx4/qB07DiseP6jh4XHfxgIAqIz3bKwUobmDtELQbIRWeOOjHR4aqV2+N4FWxXs2GoHQ3CH8CJr1BIFqz2mVN75G96RG52qFXwKBdsd7NhqB0NwB/Aia9QSBWp5T6Y2vmbN1rdIOjxnK1a1VfgkE2l2rvGdjdSM0d4Bm/4ZdTxCo9Tlub3zHjp1s6mxdK7TDY4Zy9WP2C2iOVnjPxupH94wq2mGlbbN/w65nJ79an1N440smRxQOBzQ7O6cDB7Zr797HlMnkFp+fTI5oYCDu6f+zwcFeDQzEffn6WPpLRjM/ZjQWs19A8/j5no32wExzBe0yk9fs37DrCQLLeU7pBipbtpzj22xdLNatrVs3Nf3NlxnK9sDsF9Bcfr1noz0w0+yi3WbymvkbttNscLUgsNznlPZu7rTZOmYo2wezXwCwOhCaXdRTYtDqmrlJSD1BoN7wUE9IX+068WNuZ628gQ8AYB7baLtIp6cVjx9UJpNbPBaNhjQxsZsfbi2qHerPl6sTP2YAALzCNtp1YCavNq0U2jpxtq4TP2YAAPxAaK6AWsPKhofHlUyOKBIJKJud/6VicLDX72GtOq30iwcAAHBGeQbqQvlKY/CLBwAAraNSeQYt51CXZrU8a8SOd7Xcw4+d9dgNDgCA1YPQXAFbFLtrRsuzRvTJruUefvXjptcy/MT7GwAsD6HZRbtsbOIVrzdlaMQsbC338HO2l17L8AvvbwCwfIRmB/yzeW1Kd+ZrZC1uI2Zha7mHn7O97AYHP/D+BgD1oXuGg3bc2MQrXrU8a8QsbC338Hu2lw4taDbe3wCgPsw0O/A7SKExs7C13KMVZntjsW5t3bqJwIKm4P0NAOpDyzkXhVZgSzc2oRVY8zWih3Et96BXMjoJ728A4KxSyzlCcwUEKQDtivc3ACjHNtp1YoviV/EDFmgvvL8BwPJQ04yqaE8FAAA6HaEZFdGeCgAAgNCMKti1DgAAgNCMKmhPBQAAQGhGFa3QxxgAAMBvdM9AVexa1/robgIAgLcIzagJ7alaV2GjikgkoGyWjSoAAPAC5RnAKkZ3EwAAmoPQDKxidDcBAKA5CM3AKkZ3EwAAmoPQDKxidDdpvnR6WmNjJyiBASrg+wTtiIWAwCpHd5PmYdElUB3fJ2hXxlrr9xiq6u/vt0eOHPF7GAA6WDo9rXj8oDKZ3OKxaDSkiYnd/KICLOD7BKudMeaotbbf6RzlGQBQAxZdAtXxfYJ2RmgGgBqw6BKoju8TtDNCMwDUgEWXQHV8n6CdUdMMAMvAluVAdXyfYLWqVNNM9wwAWAa2lAeq4/sE7YjyDAAAAKAKQjMAAABQBaEZAAAAqILQDAAAAFRBaAYAAACqIDQDAAAAVRCaAQAAgCoIzQAAAEAVhGYAAACgCkIzAAAAUAWhGQAAAKiC0AwAAABUQWgGAAAAqiA0AwAAAFUQmgEAAIAqjLXW7zFUZYxJS5rw4aVfI+nffXhdrB58jaAavkZQDV8jqIavkeaJW2tjTidWRWj2izHmiLW23+9xoHXxNYJq+BpBNXyNoBq+RloD5RkAAABAFYRmAAAAoApCc2UHkx/R7QAABN5JREFU/R4AWh5fI6iGrxFUw9cIquFrpAVQ0wwAAABUwUwzAAAAUAWh2YUx5mpjzPeNMT80xtzm93jgL2PMZmPMY8aY7xpj/tEYc+vC8bOMMY8aY/5p4c8z/R4r/GWMCRpjjhtjvr7w+AJjzJML7yVfMsZE/B4j/GOM2WCM+bIx5nvGmHFjzJt5H8FSxpi9Cz9nnjPGDBtjungfaQ2EZgfGmKCkz0h6u6Q3SBo0xrzB31HBZzlJ/81a+wZJb5L0OwtfE7dJ+pa19nWSvrXwGJ3tVknjSx7/kaQD1toLJZ2SlPRlVGgVd0v6prX2IkmXaP5rhfcRSJKMMedK+pCkfmvtxZKCkn5NvI+0BEKzs22Sfmit/RdrbVbSX0m6xucxwUfW2hPW2mMLf39Z8z/oztX818X9C5fdL+laf0aIVmCMOU/SOyV9buGxkXSVpC8vXMLXSAczxqyX9EuShiTJWpu11r4k3kdQLCQpaowJSeqWdEK8j7QEQrOzcyU9v+TxjxeOATLGJCT1SXpS0kZr7YmFU/8maaNPw0JruEvS70maW3h8tqSXrLW5hce8l3S2CySlJX1+oYTnc8aYteJ9BAustS9I+qSkf9V8WJ6UdFS8j7QEQjOwDMaYHkkPSPqwtfanS8/Z+VY0tKPpUMaYd0l60Vp71O+xoGWFJG2R9FlrbZ+kV1RSisH7SGdbqGe/RvO/YP2spLWSrvZ1UFhEaHb2gqTNSx6ft3AMHcwYE9Z8YP4La+1XFg6fNMZsWji/SdKLfo0PvnuLpPcYY1KaL+m6SvP1qxsW/plV4r2k0/1Y0o+ttU8uPP6y5kM07yMoGJD0I2tt2lo7K+krmn9v4X2kBRCanY1Jet3CatWI5ovwH/Z5TPDRQm3qkKRxa+2dS049LOnGhb/fKOmhZo8NrcFa+/vW2vOstQnNv2d821r7XyQ9JulXFi7ja6SDWWv/TdLzxpjXLxx6m6TvivcRvOpfJb3JGNO98HOn8DXC+0gLYHMTF8aYd2i+PjEo6ZC19g6fhwQfGWOukPS/JT2rV+tV92m+rvmvJZ0vaULS9dba//BlkGgZxpgrJX3EWvsuY8xrNT/zfJak45L+H2vtaT/HB/8YYy7V/ELRiKR/kfQbmp/A4n0EkiRjzP8r6Vc137XpuKTf1HwNM+8jPiM0AwAAAFVQngEAAABUQWgGAAAAqiA0AwAAAFUQmgEAAIAqCM0AAABAFYRmAGgzxpj3GGNuq34lAKBWtJwDgDZijAlZa3N+jwMA2g2hGQBWGWPMDZI+IslKekZSXtKMpD5JTywc67fWfsAYc5+kzMK5cyTdLOkGSW+W9KS19qZmjx8AViPKMwBgFTHGvFHSf5d0lbX2Ekm3Lpw6T9IvWmt/1+FpZ2o+JO/V/JbNByS9UdIvLOxQBwCogtAMAKvLVZIOW2v/XZKWbLd82Fqbd3nO1+z8Pys+K+mktfZZa+2cpH+UlPB6wADQDgjNANAeXqlw7vTCn3NL/l54HPJsRADQRgjNALC6fFvSdcaYsyXJGHOWz+MBgI7ADAMArCLW2n80xtwh6X8ZY/KSjvs9JgDoBHTPAAAAAKqgPAMAAACogtAMAAAAVEFoBgAAAKogNAMAAABVEJoBAACAKgjNAAAAQBWEZgAAAKAKQjMAAABQxf8FKP9ubZvc6VUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 444
},
"id": "OL7XDbwE18Nt",
"outputId": "19f60228-a116-426c-a60b-e80258f17c7a"
},
"source": [
"lm = sm.OLS.from_formula('medv ~ crim', df)\n",
"result = lm.fit()\n",
"result.summary()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>medv</td> <th> R-squared: </th> <td> 0.151</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.149</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 89.49</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 10 Nov 2021</td> <th> Prob (F-statistic):</th> <td>1.17e-19</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>07:55:01</td> <th> Log-Likelihood: </th> <td> -1798.9</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 506</td> <th> AIC: </th> <td> 3602.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 504</td> <th> BIC: </th> <td> 3610.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</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> 24.0331</td> <td> 0.409</td> <td> 58.740</td> <td> 0.000</td> <td> 23.229</td> <td> 24.837</td>\n",
"</tr>\n",
"<tr>\n",
" <th>crim</th> <td> -0.4152</td> <td> 0.044</td> <td> -9.460</td> <td> 0.000</td> <td> -0.501</td> <td> -0.329</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>139.832</td> <th> Durbin-Watson: </th> <td> 0.713</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 295.404</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 1.490</td> <th> Prob(JB): </th> <td>7.14e-65</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 5.264</td> <th> Cond. No. </th> <td> 10.1</td>\n",
"</tr>\n",
"</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: medv R-squared: 0.151\n",
"Model: OLS Adj. R-squared: 0.149\n",
"Method: Least Squares F-statistic: 89.49\n",
"Date: Wed, 10 Nov 2021 Prob (F-statistic): 1.17e-19\n",
"Time: 07:55:01 Log-Likelihood: -1798.9\n",
"No. Observations: 506 AIC: 3602.\n",
"Df Residuals: 504 BIC: 3610.\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 24.0331 0.409 58.740 0.000 23.229 24.837\n",
"crim -0.4152 0.044 -9.460 0.000 -0.501 -0.329\n",
"==============================================================================\n",
"Omnibus: 139.832 Durbin-Watson: 0.713\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 295.404\n",
"Skew: 1.490 Prob(JB): 7.14e-65\n",
"Kurtosis: 5.264 Cond. No. 10.1\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"metadata": {},
"execution_count": 28
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OwQQWlh_7iGO"
},
"source": [
"$$R^2 = 1 - \\frac{\\Sigma_{i=1}^n (Y_i - \\hat{Y}_i)^2}{\\Sigma_{i=1}^n (Y_i - \\bar{Y}_i)^2}=1 - \\frac{RSS}{TSS}$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6X0L3z4JArbh"
},
"source": [
"$$\\hat{\\beta_1}=\\frac{\\Sigma_{i=1}^n (X_i-\\bar{X_n})(Y_i-\\bar{Y_i})}{\\Sigma_{i=1}^n(X_i-\\bar{X_n})^2}=\\frac{Cov(X,Y)}{Var(X)}=\\rho_{X,Y} \\frac{\\sigma_Y}{\\sigma_X}$$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "D6eeDYBYyCAK",
"outputId": "7173dfd0-8321-49e3-8b7a-06b1763a2e9b"
},
"source": [
"df[['crim','medv']].corr().iloc[0,1]*(df['medv'].std()/df['crim'].std())"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.4151902779150908"
]
},
"metadata": {},
"execution_count": 29
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 514
},
"id": "2ZpHD3rRAVK3",
"outputId": "9861c129-6244-425e-88d5-3f67e7564e12"
},
"source": [
"sns.regplot(x='crim',y='medv',data=df)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf1ec1c2d0>"
]
},
"metadata": {},
"execution_count": 30
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 514
},
"id": "SjlxFxXQBO3Y",
"outputId": "68b98776-cd31-47e3-99e9-69d0e00ec1f3"
},
"source": [
"df[['lstat','medv']].plot.scatter(x='lstat',\n",
"... y='medv',\n",
"... c='DarkBlue')"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf1ec0dd90>"
]
},
"metadata": {},
"execution_count": 31
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 444
},
"id": "7lVRNzPYBdsl",
"outputId": "9bb2907f-df6d-43ff-de2c-32bbe00252b4"
},
"source": [
"lm = sm.OLS.from_formula('medv ~ lstat', df)\n",
"result = lm.fit()\n",
"result.summary()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>medv</td> <th> R-squared: </th> <td> 0.544</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.543</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 601.6</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 10 Nov 2021</td> <th> Prob (F-statistic):</th> <td>5.08e-88</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>08:01:42</td> <th> Log-Likelihood: </th> <td> -1641.5</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 506</td> <th> AIC: </th> <td> 3287.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 504</td> <th> BIC: </th> <td> 3295.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</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> 34.5538</td> <td> 0.563</td> <td> 61.415</td> <td> 0.000</td> <td> 33.448</td> <td> 35.659</td>\n",
"</tr>\n",
"<tr>\n",
" <th>lstat</th> <td> -0.9500</td> <td> 0.039</td> <td> -24.528</td> <td> 0.000</td> <td> -1.026</td> <td> -0.874</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>137.043</td> <th> Durbin-Watson: </th> <td> 0.892</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 291.373</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 1.453</td> <th> Prob(JB): </th> <td>5.36e-64</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 5.319</td> <th> Cond. No. </th> <td> 29.7</td>\n",
"</tr>\n",
"</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: medv R-squared: 0.544\n",
"Model: OLS Adj. R-squared: 0.543\n",
"Method: Least Squares F-statistic: 601.6\n",
"Date: Wed, 10 Nov 2021 Prob (F-statistic): 5.08e-88\n",
"Time: 08:01:42 Log-Likelihood: -1641.5\n",
"No. Observations: 506 AIC: 3287.\n",
"Df Residuals: 504 BIC: 3295.\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 34.5538 0.563 61.415 0.000 33.448 35.659\n",
"lstat -0.9500 0.039 -24.528 0.000 -1.026 -0.874\n",
"==============================================================================\n",
"Omnibus: 137.043 Durbin-Watson: 0.892\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 291.373\n",
"Skew: 1.453 Prob(JB): 5.36e-64\n",
"Kurtosis: 5.319 Cond. No. 29.7\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"metadata": {},
"execution_count": 32
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 514
},
"id": "F9LaexLjBpyP",
"outputId": "2f16e276-e5fb-4a73-a4f3-9cddd8c718dc"
},
"source": [
"sns.regplot(x='lstat',y='medv',data=df)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf1ed1fb50>"
]
},
"metadata": {},
"execution_count": 33
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "73v0MnoPCwwo"
},
"source": [
"## Линейная регрессия в общем виде (Multiple linear regression)\n",
"\n",
"Предположем, что одно наблюдение это не одномерное значение, а вектор $X_i \\in R^k$. \n",
"\n",
"Выразим все наши наши данные наблюдений в матричной форме:\n",
"\n",
"$$\\bf{X}=\\left[ \\begin{matrix} 1 & X_{11} & X_{12} & ... & X_{1k}\\\\ 1& X_{21} & X_{22} & ... & X_{2k} \\\\ ... & ... & ... & ... & ... \\\\ 1 & X_{n1} & X_{n2} & ... & X_{nk} \\end{matrix} \\right]$$\n",
"\n",
"Запишем зависимую переменную, коэффициенты регрессии и остаточной ошибки в виде векторов: \n",
"\n",
"$$\\bf{Y}=\\left[ \\begin{matrix} Y_1 \\\\ Y_2 \\\\ ... \\\\ Y_n \\end{matrix} \\right], \\bf{\\beta}=\\left[ \\begin{matrix} \\beta_0 \\\\ \\beta_1 \\\\ ... \\\\ \\beta_k \\end{matrix} \\right], \\bf{\\epsilon}=\\left[ \\begin{matrix} \\epsilon_1 \\\\ \\epsilon_2 \\\\ ... \\\\ \\epsilon_n \\end{matrix} \\right]$$\n",
"\n",
"Тогда модель линейной регрессии для многомерного случая будет иметь вид: \n",
"\n",
"$$Y = \\bf{X \\beta + \\epsilon}$$\n",
"\n",
"где $E[\\bf{\\epsilon}]=\\bf{0}$, $Var(\\epsilon_i|X_i)=\\sigma^2$, $Cov(\\epsilon_i,\\epsilon_j)=0$ для всех $i$,$j$ таких что $i\\neq j$\n",
"\n",
"Если матрица $\\bf{X^TX}$ размерностью $kxk$ имеет обратную матрицу, то оценка коэффициентов регрессии методом наименьших квадратов имеет вид:\n",
"\n",
"$$\\bf{\\hat{\\beta}=(X^TX)^{-1}X^TY}$$\n",
"\n",
"\n",
"$$\\bf{\\hat{\\beta}} \\approx N(\\bf{\\beta,\\sigma^2(X^TX)^{-1}})$$\n",
"\n",
"$$\\hat{\\sigma}^2=\\frac{1}{n-k} \\Sigma_{i=1}^n \\hat{\\epsilon_i}^2$$\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 419
},
"id": "rD-qDCETKnpv",
"outputId": "19fe9d0d-665d-41e8-b536-fe9a58e865e3"
},
"source": [
"X = df.drop(columns='medv')\n",
"X"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>crim</th>\n",
" <th>zn</th>\n",
" <th>indus</th>\n",
" <th>chas</th>\n",
" <th>nox</th>\n",
" <th>rm</th>\n",
" <th>age</th>\n",
" <th>dis</th>\n",
" <th>rad</th>\n",
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" <th>1</th>\n",
" <td>0.00632</td>\n",
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" <td>15.3</td>\n",
" <td>396.90</td>\n",
" <td>4.98</td>\n",
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" <td>0.02731</td>\n",
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" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
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" <td>9.14</td>\n",
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" <td>242</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
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" <td>0.03237</td>\n",
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" <td>2.18</td>\n",
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" <td>0.458</td>\n",
" <td>6.998</td>\n",
" <td>45.8</td>\n",
" <td>6.0622</td>\n",
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" <td>222</td>\n",
" <td>18.7</td>\n",
" <td>394.63</td>\n",
" <td>2.94</td>\n",
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" <td>0.06905</td>\n",
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" <td>7.147</td>\n",
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" <td>...</td>\n",
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" <tr>\n",
" <th>502</th>\n",
" <td>0.06263</td>\n",
" <td>0.0</td>\n",
" <td>11.93</td>\n",
" <td>0</td>\n",
" <td>0.573</td>\n",
" <td>6.593</td>\n",
" <td>69.1</td>\n",
" <td>2.4786</td>\n",
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" <td>273</td>\n",
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" <td>9.67</td>\n",
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" <td>6.120</td>\n",
" <td>76.7</td>\n",
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" <td>273</td>\n",
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" <td>9.08</td>\n",
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" <td>0</td>\n",
" <td>0.573</td>\n",
" <td>6.976</td>\n",
" <td>91.0</td>\n",
" <td>2.1675</td>\n",
" <td>1</td>\n",
" <td>273</td>\n",
" <td>21.0</td>\n",
" <td>396.90</td>\n",
" <td>5.64</td>\n",
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" <tr>\n",
" <th>505</th>\n",
" <td>0.10959</td>\n",
" <td>0.0</td>\n",
" <td>11.93</td>\n",
" <td>0</td>\n",
" <td>0.573</td>\n",
" <td>6.794</td>\n",
" <td>89.3</td>\n",
" <td>2.3889</td>\n",
" <td>1</td>\n",
" <td>273</td>\n",
" <td>21.0</td>\n",
" <td>393.45</td>\n",
" <td>6.48</td>\n",
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" <td>273</td>\n",
" <td>21.0</td>\n",
" <td>396.90</td>\n",
" <td>7.88</td>\n",
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],
"text/plain": [
" crim zn indus chas nox ... rad tax ptratio black lstat\n",
"1 0.00632 18.0 2.31 0 0.538 ... 1 296 15.3 396.90 4.98\n",
"2 0.02731 0.0 7.07 0 0.469 ... 2 242 17.8 396.90 9.14\n",
"3 0.02729 0.0 7.07 0 0.469 ... 2 242 17.8 392.83 4.03\n",
"4 0.03237 0.0 2.18 0 0.458 ... 3 222 18.7 394.63 2.94\n",
"5 0.06905 0.0 2.18 0 0.458 ... 3 222 18.7 396.90 5.33\n",
".. ... ... ... ... ... ... ... ... ... ... ...\n",
"502 0.06263 0.0 11.93 0 0.573 ... 1 273 21.0 391.99 9.67\n",
"503 0.04527 0.0 11.93 0 0.573 ... 1 273 21.0 396.90 9.08\n",
"504 0.06076 0.0 11.93 0 0.573 ... 1 273 21.0 396.90 5.64\n",
"505 0.10959 0.0 11.93 0 0.573 ... 1 273 21.0 393.45 6.48\n",
"506 0.04741 0.0 11.93 0 0.573 ... 1 273 21.0 396.90 7.88\n",
"\n",
"[506 rows x 13 columns]"
]
},
"metadata": {},
"execution_count": 34
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "17aMKZNOLCuo",
"outputId": "ab2082db-2358-4977-a632-65b357b6e53e"
},
"source": [
"X = X.to_numpy()\n",
"X = np.c_[np.ones(506), X]\n",
"X"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[1.0000e+00, 6.3200e-03, 1.8000e+01, ..., 1.5300e+01, 3.9690e+02,\n",
" 4.9800e+00],\n",
" [1.0000e+00, 2.7310e-02, 0.0000e+00, ..., 1.7800e+01, 3.9690e+02,\n",
" 9.1400e+00],\n",
" [1.0000e+00, 2.7290e-02, 0.0000e+00, ..., 1.7800e+01, 3.9283e+02,\n",
" 4.0300e+00],\n",
" ...,\n",
" [1.0000e+00, 6.0760e-02, 0.0000e+00, ..., 2.1000e+01, 3.9690e+02,\n",
" 5.6400e+00],\n",
" [1.0000e+00, 1.0959e-01, 0.0000e+00, ..., 2.1000e+01, 3.9345e+02,\n",
" 6.4800e+00],\n",
" [1.0000e+00, 4.7410e-02, 0.0000e+00, ..., 2.1000e+01, 3.9690e+02,\n",
" 7.8800e+00]])"
]
},
"metadata": {},
"execution_count": 35
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "yK7PtvMmLMxs"
},
"source": [
"Y = df['medv'].to_numpy()"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "vC_AG2odLS6f",
"outputId": "9db0872f-2049-44fe-d933-d7ad5409eeda"
},
"source": [
"Betta = np.linalg.inv(X.T@X)@X.T@Y\n",
"Betta"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([ 3.64594884e+01, -1.08011358e-01, 4.64204584e-02, 2.05586264e-02,\n",
" 2.68673382e+00, -1.77666112e+01, 3.80986521e+00, 6.92224640e-04,\n",
" -1.47556685e+00, 3.06049479e-01, -1.23345939e-02, -9.52747232e-01,\n",
" 9.31168327e-03, -5.24758378e-01])"
]
},
"metadata": {},
"execution_count": 37
}
]
},
{
"cell_type": "code",
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"height": 730
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"id": "biPTraBxB0WU",
"outputId": "780b9a3d-07be-46a4-a727-2ef4bb84a760"
},
"source": [
"lm = sm.OLS.from_formula('medv ~ crim + zn + indus + chas + nox + rm + age + dis + rad + tax + ptratio + black + lstat', df)\n",
"result = lm.fit()\n",
"result.summary()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>medv</td> <th> R-squared: </th> <td> 0.741</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.734</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 108.1</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 10 Nov 2021</td> <th> Prob (F-statistic):</th> <td>6.72e-135</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>08:15:01</td> <th> Log-Likelihood: </th> <td> -1498.8</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 506</td> <th> AIC: </th> <td> 3026.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 492</td> <th> BIC: </th> <td> 3085.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 13</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> 36.4595</td> <td> 5.103</td> <td> 7.144</td> <td> 0.000</td> <td> 26.432</td> <td> 46.487</td>\n",
"</tr>\n",
"<tr>\n",
" <th>crim</th> <td> -0.1080</td> <td> 0.033</td> <td> -3.287</td> <td> 0.001</td> <td> -0.173</td> <td> -0.043</td>\n",
"</tr>\n",
"<tr>\n",
" <th>zn</th> <td> 0.0464</td> <td> 0.014</td> <td> 3.382</td> <td> 0.001</td> <td> 0.019</td> <td> 0.073</td>\n",
"</tr>\n",
"<tr>\n",
" <th>indus</th> <td> 0.0206</td> <td> 0.061</td> <td> 0.334</td> <td> 0.738</td> <td> -0.100</td> <td> 0.141</td>\n",
"</tr>\n",
"<tr>\n",
" <th>chas</th> <td> 2.6867</td> <td> 0.862</td> <td> 3.118</td> <td> 0.002</td> <td> 0.994</td> <td> 4.380</td>\n",
"</tr>\n",
"<tr>\n",
" <th>nox</th> <td> -17.7666</td> <td> 3.820</td> <td> -4.651</td> <td> 0.000</td> <td> -25.272</td> <td> -10.262</td>\n",
"</tr>\n",
"<tr>\n",
" <th>rm</th> <td> 3.8099</td> <td> 0.418</td> <td> 9.116</td> <td> 0.000</td> <td> 2.989</td> <td> 4.631</td>\n",
"</tr>\n",
"<tr>\n",
" <th>age</th> <td> 0.0007</td> <td> 0.013</td> <td> 0.052</td> <td> 0.958</td> <td> -0.025</td> <td> 0.027</td>\n",
"</tr>\n",
"<tr>\n",
" <th>dis</th> <td> -1.4756</td> <td> 0.199</td> <td> -7.398</td> <td> 0.000</td> <td> -1.867</td> <td> -1.084</td>\n",
"</tr>\n",
"<tr>\n",
" <th>rad</th> <td> 0.3060</td> <td> 0.066</td> <td> 4.613</td> <td> 0.000</td> <td> 0.176</td> <td> 0.436</td>\n",
"</tr>\n",
"<tr>\n",
" <th>tax</th> <td> -0.0123</td> <td> 0.004</td> <td> -3.280</td> <td> 0.001</td> <td> -0.020</td> <td> -0.005</td>\n",
"</tr>\n",
"<tr>\n",
" <th>ptratio</th> <td> -0.9527</td> <td> 0.131</td> <td> -7.283</td> <td> 0.000</td> <td> -1.210</td> <td> -0.696</td>\n",
"</tr>\n",
"<tr>\n",
" <th>black</th> <td> 0.0093</td> <td> 0.003</td> <td> 3.467</td> <td> 0.001</td> <td> 0.004</td> <td> 0.015</td>\n",
"</tr>\n",
"<tr>\n",
" <th>lstat</th> <td> -0.5248</td> <td> 0.051</td> <td> -10.347</td> <td> 0.000</td> <td> -0.624</td> <td> -0.425</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>178.041</td> <th> Durbin-Watson: </th> <td> 1.078</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 783.126</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 1.521</td> <th> Prob(JB): </th> <td>8.84e-171</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 8.281</td> <th> Cond. No. </th> <td>1.51e+04</td> \n",
"</tr>\n",
"</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.51e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: medv R-squared: 0.741\n",
"Model: OLS Adj. R-squared: 0.734\n",
"Method: Least Squares F-statistic: 108.1\n",
"Date: Wed, 10 Nov 2021 Prob (F-statistic): 6.72e-135\n",
"Time: 08:15:01 Log-Likelihood: -1498.8\n",
"No. Observations: 506 AIC: 3026.\n",
"Df Residuals: 492 BIC: 3085.\n",
"Df Model: 13 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 36.4595 5.103 7.144 0.000 26.432 46.487\n",
"crim -0.1080 0.033 -3.287 0.001 -0.173 -0.043\n",
"zn 0.0464 0.014 3.382 0.001 0.019 0.073\n",
"indus 0.0206 0.061 0.334 0.738 -0.100 0.141\n",
"chas 2.6867 0.862 3.118 0.002 0.994 4.380\n",
"nox -17.7666 3.820 -4.651 0.000 -25.272 -10.262\n",
"rm 3.8099 0.418 9.116 0.000 2.989 4.631\n",
"age 0.0007 0.013 0.052 0.958 -0.025 0.027\n",
"dis -1.4756 0.199 -7.398 0.000 -1.867 -1.084\n",
"rad 0.3060 0.066 4.613 0.000 0.176 0.436\n",
"tax -0.0123 0.004 -3.280 0.001 -0.020 -0.005\n",
"ptratio -0.9527 0.131 -7.283 0.000 -1.210 -0.696\n",
"black 0.0093 0.003 3.467 0.001 0.004 0.015\n",
"lstat -0.5248 0.051 -10.347 0.000 -0.624 -0.425\n",
"==============================================================================\n",
"Omnibus: 178.041 Durbin-Watson: 1.078\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 783.126\n",
"Skew: 1.521 Prob(JB): 8.84e-171\n",
"Kurtosis: 8.281 Cond. No. 1.51e+04\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n",
"\"\"\""
]
},
"metadata": {},
"execution_count": 38
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 80
},
"id": "oeeP-FvjKJC3",
"outputId": "83bffc56-bdf3-43e0-d54b-381ddba7c6f9"
},
"source": [
"df_new_data = pd.DataFrame(np.array([[0, 0, 0 , 1, 0.4, 10, 0, 2, 20, 400, 15, 0, 0]]), \n",
" columns=['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax', 'ptratio', 'black', 'lstat'])\n",
"df_new_data"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <th></th>\n",
" <th>crim</th>\n",
" <th>zn</th>\n",
" <th>indus</th>\n",
" <th>chas</th>\n",
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" <th>lstat</th>\n",
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" <td>1.0</td>\n",
" <td>0.4</td>\n",
" <td>10.0</td>\n",
" <td>0.0</td>\n",
" <td>2.0</td>\n",
" <td>20.0</td>\n",
" <td>400.0</td>\n",
" <td>15.0</td>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" crim zn indus chas nox rm ... dis rad tax ptratio black lstat\n",
"0 0.0 0.0 0.0 1.0 0.4 10.0 ... 2.0 20.0 400.0 15.0 0.0 0.0\n",
"\n",
"[1 rows x 13 columns]"
]
},
"metadata": {},
"execution_count": 39
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "P8Z98W3UX_Oa",
"outputId": "c13d4795-766c-48e3-8991-d509430caae6"
},
"source": [
"result.predict(df_new_data)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0 54.08304\n",
"dtype: float64"
]
},
"metadata": {},
"execution_count": 40
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 500
},
"id": "E6xriKXXWqJp",
"outputId": "1fe7787e-a78b-42c3-87f5-6feea87b6e2b"
},
"source": [
"df['medv'].hist(bins=40)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7faf116d2510>"
]
},
"metadata": {},
"execution_count": 44
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "moUPnO2n70dW"
},
"source": [
""
],
"execution_count": null,
"outputs": []
}
]
}
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