Linear_Regression_simple.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b2b4ee18",
   "metadata": {},
   "source": [
    "# Linear Regression Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cd98ec1",
   "metadata": {},
   "source": [
    "data_source = \"https://www.kaggle.com/datasets/erolmasimov/price-prediction-multiple-linear-regression\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c7167d8",
   "metadata": {},
   "source": [
    "### Let's load the data and understand it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "96c55e82",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import all necessary packages\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "a0c9d056",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load data to a new dataframe\n",
    "df = pd.read_csv(\"car_dataset.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7cc1121f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(205, 26)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the shape\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "9de983cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>symboling</th>\n",
       "      <th>name</th>\n",
       "      <th>fueltypes</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>doornumbers</th>\n",
       "      <th>carbody</th>\n",
       "      <th>drivewheels</th>\n",
       "      <th>enginelocation</th>\n",
       "      <th>wheelbase</th>\n",
       "      <th>...</th>\n",
       "      <th>enginesize</th>\n",
       "      <th>fuelsystem</th>\n",
       "      <th>boreratio</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compressionratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peakrpm</th>\n",
       "      <th>citympg</th>\n",
       "      <th>highwaympg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>alfa-romero giulia</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>alfa-romero stelvio</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>alfa-romero Quadrifoglio</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>...</td>\n",
       "      <td>152</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154</td>\n",
       "      <td>5000</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>audi 100 ls</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>...</td>\n",
       "      <td>109</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102</td>\n",
       "      <td>5500</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>audi 100ls</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>...</td>\n",
       "      <td>136</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115</td>\n",
       "      <td>5500</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   ID  symboling                      name fueltypes aspiration doornumbers  \\\n",
       "0   1          3        alfa-romero giulia       gas        std         two   \n",
       "1   2          3       alfa-romero stelvio       gas        std         two   \n",
       "2   3          1  alfa-romero Quadrifoglio       gas        std         two   \n",
       "3   4          2               audi 100 ls       gas        std        four   \n",
       "4   5          2                audi 100ls       gas        std        four   \n",
       "\n",
       "       carbody drivewheels enginelocation  wheelbase  ...  enginesize  \\\n",
       "0  convertible         rwd          front       88.6  ...         130   \n",
       "1  convertible         rwd          front       88.6  ...         130   \n",
       "2    hatchback         rwd          front       94.5  ...         152   \n",
       "3        sedan         fwd          front       99.8  ...         109   \n",
       "4        sedan         4wd          front       99.4  ...         136   \n",
       "\n",
       "   fuelsystem  boreratio  stroke compressionratio horsepower  peakrpm citympg  \\\n",
       "0        mpfi       3.47    2.68              9.0        111     5000      21   \n",
       "1        mpfi       3.47    2.68              9.0        111     5000      21   \n",
       "2        mpfi       2.68    3.47              9.0        154     5000      19   \n",
       "3        mpfi       3.19    3.40             10.0        102     5500      24   \n",
       "4        mpfi       3.19    3.40              8.0        115     5500      18   \n",
       "\n",
       "   highwaympg    price  \n",
       "0          27  13495.0  \n",
       "1          27  16500.0  \n",
       "2          26  16500.0  \n",
       "3          30  13950.0  \n",
       "4          22  17450.0  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first five rows of the dataframe\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9dc87d6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>symboling</th>\n",
       "      <th>wheelbase</th>\n",
       "      <th>carlength</th>\n",
       "      <th>carwidth</th>\n",
       "      <th>carheight</th>\n",
       "      <th>curbweight</th>\n",
       "      <th>enginesize</th>\n",
       "      <th>boreratio</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compressionratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peakrpm</th>\n",
       "      <th>citympg</th>\n",
       "      <th>highwaympg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "      <td>205.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>103.000000</td>\n",
       "      <td>0.834146</td>\n",
       "      <td>98.756585</td>\n",
       "      <td>174.049268</td>\n",
       "      <td>65.907805</td>\n",
       "      <td>53.724878</td>\n",
       "      <td>2555.565854</td>\n",
       "      <td>126.907317</td>\n",
       "      <td>3.329756</td>\n",
       "      <td>3.255415</td>\n",
       "      <td>10.142537</td>\n",
       "      <td>104.117073</td>\n",
       "      <td>5125.121951</td>\n",
       "      <td>25.219512</td>\n",
       "      <td>30.751220</td>\n",
       "      <td>13276.710571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>59.322565</td>\n",
       "      <td>1.245307</td>\n",
       "      <td>6.021776</td>\n",
       "      <td>12.337289</td>\n",
       "      <td>2.145204</td>\n",
       "      <td>2.443522</td>\n",
       "      <td>520.680204</td>\n",
       "      <td>41.642693</td>\n",
       "      <td>0.270844</td>\n",
       "      <td>0.313597</td>\n",
       "      <td>3.972040</td>\n",
       "      <td>39.544167</td>\n",
       "      <td>476.985643</td>\n",
       "      <td>6.542142</td>\n",
       "      <td>6.886443</td>\n",
       "      <td>7988.852332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-2.000000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>141.100000</td>\n",
       "      <td>60.300000</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>52.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>166.300000</td>\n",
       "      <td>64.100000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2145.000000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7788.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>103.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>173.200000</td>\n",
       "      <td>65.500000</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5200.000000</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>154.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>183.100000</td>\n",
       "      <td>66.900000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2935.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16503.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>205.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>208.100000</td>\n",
       "      <td>72.300000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>288.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               ID   symboling   wheelbase   carlength    carwidth   carheight  \\\n",
       "count  205.000000  205.000000  205.000000  205.000000  205.000000  205.000000   \n",
       "mean   103.000000    0.834146   98.756585  174.049268   65.907805   53.724878   \n",
       "std     59.322565    1.245307    6.021776   12.337289    2.145204    2.443522   \n",
       "min      1.000000   -2.000000   86.600000  141.100000   60.300000   47.800000   \n",
       "25%     52.000000    0.000000   94.500000  166.300000   64.100000   52.000000   \n",
       "50%    103.000000    1.000000   97.000000  173.200000   65.500000   54.100000   \n",
       "75%    154.000000    2.000000  102.400000  183.100000   66.900000   55.500000   \n",
       "max    205.000000    3.000000  120.900000  208.100000   72.300000   59.800000   \n",
       "\n",
       "        curbweight  enginesize   boreratio      stroke  compressionratio  \\\n",
       "count   205.000000  205.000000  205.000000  205.000000        205.000000   \n",
       "mean   2555.565854  126.907317    3.329756    3.255415         10.142537   \n",
       "std     520.680204   41.642693    0.270844    0.313597          3.972040   \n",
       "min    1488.000000   61.000000    2.540000    2.070000          7.000000   \n",
       "25%    2145.000000   97.000000    3.150000    3.110000          8.600000   \n",
       "50%    2414.000000  120.000000    3.310000    3.290000          9.000000   \n",
       "75%    2935.000000  141.000000    3.580000    3.410000          9.400000   \n",
       "max    4066.000000  326.000000    3.940000    4.170000         23.000000   \n",
       "\n",
       "       horsepower      peakrpm     citympg  highwaympg         price  \n",
       "count  205.000000   205.000000  205.000000  205.000000    205.000000  \n",
       "mean   104.117073  5125.121951   25.219512   30.751220  13276.710571  \n",
       "std     39.544167   476.985643    6.542142    6.886443   7988.852332  \n",
       "min     48.000000  4150.000000   13.000000   16.000000   5118.000000  \n",
       "25%     70.000000  4800.000000   19.000000   25.000000   7788.000000  \n",
       "50%     95.000000  5200.000000   24.000000   30.000000  10295.000000  \n",
       "75%    116.000000  5500.000000   30.000000   34.000000  16503.000000  \n",
       "max    288.000000  6600.000000   49.000000   54.000000  45400.000000  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# describe the dataframe with some statistical info\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f941fd0f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 205 entries, 0 to 204\n",
      "Data columns (total 26 columns):\n",
      " #   Column            Non-Null Count  Dtype  \n",
      "---  ------            --------------  -----  \n",
      " 0   ID                205 non-null    int64  \n",
      " 1   symboling         205 non-null    int64  \n",
      " 2   name              205 non-null    object \n",
      " 3   fueltypes         205 non-null    object \n",
      " 4   aspiration        205 non-null    object \n",
      " 5   doornumbers       205 non-null    object \n",
      " 6   carbody           205 non-null    object \n",
      " 7   drivewheels       205 non-null    object \n",
      " 8   enginelocation    205 non-null    object \n",
      " 9   wheelbase         205 non-null    float64\n",
      " 10  carlength         205 non-null    float64\n",
      " 11  carwidth          205 non-null    float64\n",
      " 12  carheight         205 non-null    float64\n",
      " 13  curbweight        205 non-null    int64  \n",
      " 14  enginetype        205 non-null    object \n",
      " 15  cylindernumber    205 non-null    object \n",
      " 16  enginesize        205 non-null    int64  \n",
      " 17  fuelsystem        205 non-null    object \n",
      " 18  boreratio         205 non-null    float64\n",
      " 19  stroke            205 non-null    float64\n",
      " 20  compressionratio  205 non-null    float64\n",
      " 21  horsepower        205 non-null    int64  \n",
      " 22  peakrpm           205 non-null    int64  \n",
      " 23  citympg           205 non-null    int64  \n",
      " 24  highwaympg        205 non-null    int64  \n",
      " 25  price             205 non-null    float64\n",
      "dtypes: float64(8), int64(8), object(10)\n",
      "memory usage: 41.8+ KB\n"
     ]
    }
   ],
   "source": [
    "# check data types in the dataframe\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "010c1226",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ID                  205\n",
       "symboling             6\n",
       "name                147\n",
       "fueltypes             2\n",
       "aspiration            2\n",
       "doornumbers           2\n",
       "carbody               5\n",
       "drivewheels           3\n",
       "enginelocation        2\n",
       "wheelbase            53\n",
       "carlength            75\n",
       "carwidth             44\n",
       "carheight            49\n",
       "curbweight          171\n",
       "enginetype            7\n",
       "cylindernumber        7\n",
       "enginesize           44\n",
       "fuelsystem            8\n",
       "boreratio            38\n",
       "stroke               37\n",
       "compressionratio     32\n",
       "horsepower           59\n",
       "peakrpm              23\n",
       "citympg              29\n",
       "highwaympg           30\n",
       "price               189\n",
       "dtype: int64"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check unique data for each feature in the dataframe\n",
    "df.nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "869f7f4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['ID', 'symboling', 'name', 'fueltypes', 'aspiration', 'doornumbers',\n",
       "       'carbody', 'drivewheels', 'enginelocation', 'wheelbase', 'carlength',\n",
       "       'carwidth', 'carheight', 'curbweight', 'enginetype', 'cylindernumber',\n",
       "       'enginesize', 'fuelsystem', 'boreratio', 'stroke', 'compressionratio',\n",
       "       'horsepower', 'peakrpm', 'citympg', 'highwaympg', 'price'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# column names of the dataframe\n",
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07cc977c",
   "metadata": {},
   "source": [
    "### Now, we can prepare the data for the linear regression model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3d1d6165",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>enginesize</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>130</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>130</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>152</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>109</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>136</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>141</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>201</th>\n",
       "      <td>141</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>173</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>203</th>\n",
       "      <td>145</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>204</th>\n",
       "      <td>141</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>205 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     enginesize    price\n",
       "0           130  13495.0\n",
       "1           130  16500.0\n",
       "2           152  16500.0\n",
       "3           109  13950.0\n",
       "4           136  17450.0\n",
       "..          ...      ...\n",
       "200         141  16845.0\n",
       "201         141  19045.0\n",
       "202         173  21485.0\n",
       "203         145  22470.0\n",
       "204         141  22625.0\n",
       "\n",
       "[205 rows x 2 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a new simple dataframe using the existing one\n",
    "new_df = df[['enginesize', 'price']]\n",
    "new_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "af2f1d41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='enginesize', ylabel='price'>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check the distribution of data by plotting as scatter\n",
    "new_df.plot(x='enginesize', y='price', kind='scatter')\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "c68fd951",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='fueltypes', ylabel='price'>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare below plot with the previous one\n",
    "df.plot(x='fueltypes', y='price', kind='scatter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f938d9cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define x and y by using the new dataframe\n",
    "x = new_df['enginesize']\n",
    "y = new_df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37f818fe",
   "metadata": {},
   "source": [
    "### Now Machine Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "6ace0f92",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import ML related packages of sklearn\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5f3cf1bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# split the data as train and test\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "31076407",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train: (164,)\n",
      "X_test: (41,)\n",
      "Y_train: (164,)\n",
      "Y_test: (41,)\n"
     ]
    }
   ],
   "source": [
    "#shapes of splitted data - sizes of the X_train and Y_train should be same. Also, tests.\n",
    "print(\"X_train:\",x_train.shape)\n",
    "print(\"X_test:\",x_test.shape)\n",
    "print(\"Y_train:\",y_train.shape)\n",
    "print(\"Y_test:\",y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "936bbd2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a linear regression model\n",
    "model = LinearRegression()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "a891f7aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train the model using training data\n",
    "# since we have only one independent variable, you should use 'values.reshape(-1,1)'. Otherwise, x_train is enough.\n",
    "model.fit(x_train.values.reshape(-1,1), y_train)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "b36084ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([164.31545172])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print coefficient\n",
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "90c2193b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7613.3709394898"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print y_intercept | bias\n",
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "ecb4f3df",
   "metadata": {},
   "outputs": [],
   "source": [
    "# make predictions using test data\n",
    "y_pred = model.predict(x_test.values.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "65bae947",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE -->  16835544.03813768\n"
     ]
    }
   ],
   "source": [
    "# let's calculate the metrics\n",
    "# MSE\n",
    "mse = mean_squared_error(y_test, y_pred)\n",
    "print(\"MSE --> \", mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "de22d4e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE -->  4103.113944084137\n"
     ]
    }
   ],
   "source": [
    "# RMSE\n",
    "import math\n",
    "rmse = math.sqrt(mse)\n",
    "print(\"RMSE --> \", rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "bc37d239",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE -->  3195.031239500043\n"
     ]
    }
   ],
   "source": [
    "# MAE\n",
    "mae = mean_absolute_error(y_test, y_pred)\n",
    "print(\"MAE --> \", mae)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "dd7185be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 -->  0.7825324721447274\n"
     ]
    }
   ],
   "source": [
    "# R2\n",
    "r2 = r2_score(y_test, y_pred)\n",
    "print(\"R2 --> \", r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "b12348f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE -->  16835544.03813768\n",
      "RMSE -->  4103.113944084137\n",
      "MAE -->  3195.031239500043\n",
      "R2 -->  0.7825324721447274\n"
     ]
    }
   ],
   "source": [
    "# print them all\n",
    "print(\"MSE --> \", mse)\n",
    "print(\"RMSE --> \", rmse)\n",
    "print(\"MAE --> \", mae)\n",
    "print(\"R2 --> \", r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "a6b85cb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import plotting packages\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "48b8b0c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Predicted')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot actual and predicted values\n",
    "plt.scatter(y_test, y_pred)\n",
    "plt.xlabel('Actual')\n",
    "plt.ylabel('Predicted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "a0558916",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='enginesize', ylabel='price'>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot regression model line\n",
    "sns.regplot(x=x, y=y, ci=None, color ='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36de38d3",
   "metadata": {},
   "source": [
    "### What about other independent variables?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "2bc7d147",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='horsepower', ylabel='price'>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot horsepower - price distribution\n",
    "df.plot(x='horsepower', y='price', kind='scatter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "614ef7d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>enginesize</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>130</td>\n",
       "      <td>111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>130</td>\n",
       "      <td>111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>152</td>\n",
       "      <td>154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>109</td>\n",
       "      <td>102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>136</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>141</td>\n",
       "      <td>114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>201</th>\n",
       "      <td>141</td>\n",
       "      <td>160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>173</td>\n",
       "      <td>134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>203</th>\n",
       "      <td>145</td>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>204</th>\n",
       "      <td>141</td>\n",
       "      <td>114</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>205 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     enginesize  horsepower\n",
       "0           130         111\n",
       "1           130         111\n",
       "2           152         154\n",
       "3           109         102\n",
       "4           136         115\n",
       "..          ...         ...\n",
       "200         141         114\n",
       "201         141         160\n",
       "202         173         134\n",
       "203         145         106\n",
       "204         141         114\n",
       "\n",
       "[205 rows x 2 columns]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# new x will be X1 and X2\n",
    "x = df[['enginesize', 'horsepower']]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "e6b04561",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      13495.0\n",
       "1      16500.0\n",
       "2      16500.0\n",
       "3      13950.0\n",
       "4      17450.0\n",
       "        ...   \n",
       "200    16845.0\n",
       "201    19045.0\n",
       "202    21485.0\n",
       "203    22470.0\n",
       "204    22625.0\n",
       "Name: price, Length: 205, dtype: float64"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y will be same\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "4e7df432",
   "metadata": {},
   "outputs": [],
   "source": [
    "# split the data as train and test\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "25ae0b9a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train: (164, 2)\n",
      "X_test: (41, 2)\n",
      "Y_train: (164,)\n",
      "Y_test: (41,)\n"
     ]
    }
   ],
   "source": [
    "#shapes of splitted data - sizes of the X_train and Y_train should be same. Also, tests.\n",
    "print(\"X_train:\",x_train.shape)\n",
    "print(\"X_test:\",x_test.shape)\n",
    "print(\"Y_train:\",y_train.shape)\n",
    "print(\"Y_test:\",y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "2b2f8b2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a linear regression model\n",
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "db601be3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train the model using training data\n",
    "model.fit(x_train, y_train)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "196386fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([115.9909421,  64.2026329])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print coefficients\n",
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "0a9554d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8148.677422999757"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print y_intercept | bias\n",
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "6323fef9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# make predictions using test data\n",
    "y_pred = model.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "38d048cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's calculate the metrics\n",
    "mse_2 = mean_squared_error(y_test, y_pred)\n",
    "rmse_2 = math.sqrt(mse_2)\n",
    "mae_2 = mean_absolute_error(y_test, y_pred)\n",
    "r2_2 = r2_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "3e2ab342",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE -->  15514797.066791015\n",
      "RMSE -->  3938.882718080219\n",
      "MAE -->  3061.6172627779792\n",
      "R2 -->  0.7995927808659935\n"
     ]
    }
   ],
   "source": [
    "# print them all\n",
    "print(\"MSE --> \", mse_2)\n",
    "print(\"RMSE --> \", rmse_2)\n",
    "print(\"MAE --> \", mae_2)\n",
    "print(\"R2 --> \", r2_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "330a0459",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Predicted')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot actual and predicted values\n",
    "plt.scatter(y_test, y_pred)\n",
    "plt.xlabel('Actual')\n",
    "plt.ylabel('Predicted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "2b2507c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='price'>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LFBbC1Kkx4Oykk/I3GUC0G2zatGts0ybo2zcrxWl0Sggiws6dcN99UQv46U+jhtC5c3QpXbo0pqpWN9KYf2nr1ljj2T3ut26NeGughCCS5/72Nxg6FL73PXjzzTjxn3VW9By6+OK4Ti6huBimTIla07p1cT9lSsRbA+V8kTz14otwwQUwa1Zl7LTTYnrqAQOyV65cV1zcehJAVUoIInlm2TK49FL43e8q5xz60peizeDII7NaNMkyJQSRPPH++/Hrf8qUuO4NMHgw3HBD/OLN58ZiCUoIIq3c5s2xWtm118ZEdAC9esWaBKNHx2hjEVBCEGm1duyInkOXXgrLk1XOu3SBSZPgJz+J/vMi6ZQQRFoZ9xhVfMEFMXYAoF07GD8+eg11757d8knuUkIQaUXmz49ZR2fProyVlETbwQEHZK9c0jIoIYi0AhUV8ev//vsrY8OHR4Px0KHZK5e0LLUOTDOzPmb2lJktNrOFZnZ2Er/CzN42s5eS2wlpx0wys3IzW2JmX0uLDzWzV5LnbjWLfg1m1t7MHkzic82sbxN8VpFW59134dxzY4WyVDI49NCYffOJJ5QMpG4yqSFsB/7X3V8ws87AfDNLDWW52d1vTN/ZzAYBJcBgYH/gCTM70N13ALcDY4HngL8CI4BSYAywzt0HmFkJcD1wesM/nkjrtGkT/PKXcN11sH59xPr0gZ/9DL77XfUckvqptYbg7qvc/YVkewOwGOhVwyEnAw+4+xZ3rwDKgWFmVgh0cfc57u7APcDItGOmJdszgGNTtQcRqbRjB9x1V0w7fdFFkQz23jtmIV2yRN1IpWHqNJdRcinncGBuEppgZgvM7C4z65rEegHL0w5bkcR6JdtV47sc4+7bgQ+Bfat5/7FmVmZmZWvXrq1L0UVaNHf4y19iXYIxY+Dtt2Me/vPOizmHzj8fOnTIdimlpcs4IZjZXsBDwDnuvp64/NMfGAKsAm5K7VrN4V5DvKZjdg24T3X3Incv6tGjR6ZFF2nRnn8+GohPPBFefTVi3/lO1Ahuugn2/cRPJ5H6ySghmFk7Ihn8zt3/CODuq919h7vvBH4LDEt2XwH0STu8N7AyifeuJr7LMWbWFtgbeL8+H0iktXjjDTj9dBg2DJ5+OmLHHx9LWN53X+uZg19yRya9jAy4E1js7r9Iixem7XYKkPx2YSZQkvQc6gcMBOa5+ypgg5kdlbzmGcAjaceMTrZHAbOTdgaRvLN2bYwkPvhgmD49YkOGwOOPx1TVhx+e1eJJK5ZJL6MvAN8DXjGzl5LYRcC3zGwIcWlnGfAjAHdfaGbTgUVED6XxSQ8jgHHA3UAHondRamnqO4F7zaycqBmUNORDibREGzfCzTfH2IENGyL26U/HIjXf/ja00eol0sSspf4QLyoq8rKysmwXQ6TBtm+H//s/uPxyWLUqYl27xkCz8eNhzz2zWz5pXcxsvrsXVfecRiqLZIk7/PnPcOGFsHhxxNq3j8tFkyZFUhBpTqqESpMpLY3eMf36xX1pae3H5IvnnotFaU4+OZKBWYwheP31uGSkZCDZoIQgTaK0FCZMiEsg3brF/YQJSgqvvw6jRsHnPw/PPBOxESPgpZfg7rvhU5/KZukk3ykhSJOYPDkGTnXqFL9+O3WKx5MnZ7tk2bF6dbQHDBoEDz0UsSOOiPmGSktj/iGRbFMbgjSJioqoGaTr2DHW880nH30Ev/hFJMKPPopY375wzTUxxkA9hySXKCFIk+jXLy4TdepUGdu0KX8GU23bBnfeCVdcEbUDiAR56aUwblw0HovkGv0+kSYxcWIs5L5xY/Sm2bgxHk+cmO2SNS13ePhhOOSQOPGvXh3dRi+8MEYen3OOkoHkLiUEqZfaehAVF8OUKVBYCOvWxf2UKRFvrf75Tzj6aPiv/4rG4zZt4Ac/gKVLY4H7ffbJdglFaqaBaVJnqR5Ee+wR7QKbNsWv/9Z+wt+d116LcQN/+lNl7Otfj7UKDjkka8USqVZNA9NUQ5A6Uw+isGoVnHlmnPRTyaCoCJ56Ch59VMlAWh41Kkud5XsPog0b4MYb47ZpU8QOOCAuC516aiRJkZZICUHqLF97EG3bBlOnwlVXwZo1EevePXoOnXlm1JJEWjJdMpI6y7ceRO4wYwYMHhxtJ2vWxOpkF18cPYd+8hMlA2kdlBCkzvKpB9Hf/x7TTJx6avQWatMG/ud/YvvnP4cuXbJdQpHGo0tGUi/Fxa0zAaQsWhQ9h2bOrIx94xvRc2jQoOyVS6QpqYYgddLaZzBduRJ++EP47Gcrk8HnPhc1hZkzlQykdVNCkIy15hlM16+HSy6BAQPgjjtg587Y/sMfYM4c+OIXs11CkaaXyZrKfczsKTNbbGYLzezsJN7NzGaZ2dLkvmvaMZPMrNzMlpjZ19LiQ83sleS5W5O1lUnWX34wic81s75N8FmlgVrj+IOtW+FXv4L+/eHqq2HzZujRA37967hsNGqUupFK/sikhrAd+F93Pxg4ChhvZoOAC4En3X0g8GTymOS5EmAwMAK4zcwKkte6HRgLDExuI5L4GGCduw8Abgaub4TPJo2soiLGG6RrqeMP3GMB+0GDopfQu+/GZ7nssug59OMfQ7t22S6lSPOqNSG4+yp3fyHZ3gAsBnoBJwPTkt2mASOT7ZOBB9x9i7tXAOXAMDMrBLq4+xyP+TLuqXJM6rVmAMemag+SO/r1qxyIldISxx88/XS0C5x+epz8Cwpg7FgoL4crr4TOnbNdQpHsqFMbQnIp53BgLrCfu6+CSBpAz2S3XsDytMNWJLFeyXbV+C7HuPt24ENg37qUTZpeSx9/sHAhnHgifOUr8PzzERs5El59FX7zm+g+K5LPMk4IZrYX8BBwjruvr2nXamJeQ7ymY6qWYayZlZlZ2dq1a2srsjSyljr+YMUKGDMmViX7y18i9vnPwz/+EVNVf+Yz2S2fSK7IaByCmbUjksHv3P2PSXi1mRW6+6rkclAymJ8VQJ+0w3sDK5N472ri6cesMLO2wN7A+1XL4e5TgakQs51mUnZpXC1p/MEHH8D118Mtt8DHH0fswANjLMHIkWosFqkqk15GBtwJLHb3X6Q9NRMYnWyPBh5Ji5ckPYf6EY3H85LLShvM7KjkNc+ockzqtUYBs72lzsstWbdlSySB/v3j5P/xx7DffnD77XF56JRTlAxEqpNJDeELwPeAV8zspSR2EXAdMN3MxgBvAacCuPtCM5sOLCJ6KI139x3JceOAu4EOQGlyg0g495pZOVEzKGnYx5J8tHMnPPggXHRRZc+nvfaKNo7zzottEdk9LZAjrcKTT8aMo+Xl8dgsFqm5446oHUAMoJs8ObrP9usXiaKlXP4SaSxaIEdarQUL4qR+3HGVyWCffeKEv2gRvPBCxFrzKGuRxqKEIC3S8uXw/e/DkCHw2GMR69ABDjoo2g66dt11FHVrHGUt0tg026m0KOvWxcpkt94ajccABx8M770HvXrF9NQp6aOo832VN5FMqIYgLcLHH8NNN8Wv/8mTIxkUFsYKZgsWxOI1mzfvekz6KOrWMspapCkpIUhO27kT7r03LgX99KdRQ+jcORanWbo0pqpu27b2UdQtfZS1SHNQQpCcNWsWDB0KZ5wBb70VJ/6zzor5hy6+eNc1nWsbRd1SR1mLNCd1O5Wc8+KLcP758MQTlbHTTovpqQcMyF65RFoDdTuVFmHZMvje9+CIIyqTwZe/DPPmxYAzJQORpqVeRpJ1778P11wTC9Vs3RqxwYNjHqITTtA0EyLNRQlBsmbz5kgC114bE9FBdB392c+i3aCgoMbDRaSRKSFIs9uxA+67Dy69NAaYAXTpAhdeCGef/clV2USkeSghSLNxh8cfhwsuiLEDEMtUjh8fvYa6d89u+UTynRqVs6y0FIYPj4FTw4dXP7dO+j6HHRa3mvbPRfPnx3xDxcWVyaBnz7i9/HLlCmYikj1KCFmUyYRr6fsUFMDixTFpW0FBy5igraICvv1tKCqC2bMjduih0VbQrVvMRNoSPodIPlBCyKJMJlxL32fNmpirp23b2M7lCdrefRfOPTdGGN9/f8QOPTRO+t26xWhjTTQnkluUELKoouKTDahVJ1xL32fLlkgIbdpUTuyWaxO0bd4cq5T17x+rlm3bBn36wN13x1TUI0ZEeWv73CLS/JQQsiiTCdfS92nfPub22bkztqvbP1t27IC77oKBA2HSJFi/HvbeG264AZYsgdGjK7uRaqI5kdykhJBFmUy4lr5Pz56RDLZvj+1cmKDNHf7yl2joHjMG3n47Lv+cd17MOTRxYqxTkE4TzYnkploTgpndZWZrzOzVtNgVZva2mb2U3E5Ie26SmZWb2RIz+1pafKiZvZI8d6tZjD81s/Zm9mASn2tmfRv5M+asTCZcS99n586Y+3/QoNjO9gRtzz8PX/kKnHgiLFwYse9+N2oEN90E++5b/XGaaE4kN9U6uZ2ZHQN8BNzj7ocksSuAj9z9xir7DgLuB4YB+wNPAAe6+w4zmwecDTwH/BW41d1LzezHwKHufqaZlQCnuPvptRVck9tlT3l5jBuYPr0ydvzxMdXE4Ydnr1wiUrsGTW7n7n8H3s/wvU4GHnD3Le5eAZQDw8ysEOji7nM8MtA9wMi0Y6Yl2zOAY1O1B8m+9DEQRx8NJ50UtZRUMjjssBhs9re/NU4yyGRchog0jYa0IUwwswXJJaWuSawXsDxtnxVJrFeyXTW+yzHuvh34EKj2YoOZjTWzMjMrW7t2bQOKLplIjYF4++3o1TRnDvz5z9GG8elPx8I1L7wAX/1q475fTeMyRKTp1Dch3A70B4YAq4Cbknh1v+y9hnhNx3wy6D7V3YvcvahHjx51KrDU3fXXR++fioo4Oe/cGV1e+/eH116L9oI2jdgtIZNxGSLSdOo1l5G7r05tm9lvgUeThyuAPmm79gZWJvHe1cTTj1lhZm2Bvcn8EpU0AXeYOROefTbGEUCcoHv2jJHFGzbAnns2/vtWVETNIJ3GJ4g0n3r9vkvaBFJOAVI9kGYCJUnPoX7AQGCeu68CNpjZUUn7wBnAI2nHjE62RwGzvaUu49YKPPccHHMMjBxZmQz23RcOOQR6947uoU01XkDjE0Syq9YagpndD3wZ6G5mK4DLgS+b2RDi0s4y4EcA7r7QzKYDi4DtwHh335G81DjgbqADUJrcAO4E7jWzcqJmUNIIn0vq6PXX4aKL4KGHKmNDh8I778Q0E+3aNf14gYkTo80AomawaZPGJ4g0J62pnOdWr4arroLf/CZGG0MsYXnDDXDssdGgO3lyXLbp2zdOzk05XqC5308k39TU7VQJIU999FEMHrvxxtiGOAFffTWUlDRuY7GI5I6aEoIWyMkz27bBnXfCFVdE7QCiIffSS2HcuMo5kkQk/yghNKPU5ZCKimhA/fKX4emnKx835eURd/jTn2KZytdfj9iee8I558QKZvvs0zTvKyIthxJCM0kNutpjj/hFvnQpPPMM/Md/RHfO1CCsppjT55//hPPPj26kEF1Iv//9aDvo3bvGQ0Ukj+hKcTOpOujqww/jOv2HHzbdIKzXXoNTTokpJ1LJ4OtfjyUs77pLyUBEdqWE0EyqLoazZUusD5Ba6AYabxDWO+/AmWfG2IE//SliRx4JTz0Fjz4acRGRqpQQmknVQVft20c3z/RG3IYOwtqwAS6/HAYMqOxGesAB8MADMHdutFmIiOyOEkIzqboozN57V658tmQJvPxy1A7qc9Letg1uuy0SwVVXxXt07w633gqLF8Ppp8dlqVyjmU1FcosSQhNLnfR+/GPYa69oJ1i3LpaaPP30GAOwZUv0+OneHaZNy/zE6A4zZsDgwTB+PKxZE6uTXXxxrFZ21lnxfo35OWo6edflBK+ZTUVyjwamNaH0nkXpUzGkehINHx4nwk6dKo/ZuDFWEJs9u+bXfuaZ6Dn03HPxuE2bWMLyiitg//2b93Nkuk+6hnx2Eam/Bi2QI/VX23TOVRuaofaG5UWLYpGaY46pTAYnnQSvvAJTpzZ+Msjkc2S6T7r6fHYRaVpKCE2otpNeXWb3XLkSfvhD+OxnY5EagM99Dv7+d3jkkVhnualkcvKu6wleM5uK5B4lhCZU20mvakNzdbOJrl8Pl1wSDcZ33BEN0QMHRtvBnDnwxS9m/3Nkuk+6TD67iDQvJYQmVNtJr7gYRo+OcQMvvxz3o0dHfOtW+NWvYnWyq6+GzZuhR4+4Jr9wIXzzm83XcyiTk3ddT/DFxfFZCgujkb2wsGlGaYtI5tSo3MRqms65uobYLVvgtNPgD3+Af/0r9uvYEX7607h17px7n6Mu+4hIdmn66xxVtafNhg3w1lvw8cfxuKAg2g0uvzzmPBIRaShNf52jUmsIb94MK1ZEe0HKyJFw3XVw0EFZK56I5Bm1ITRQQ0bbFhbGALJFiyqTQYcOcPjh8PDD1SeD6t5PI35FpDHUmhDM7C4zW2Nmr6bFupnZLDNbmtx3TXtukpmVm9kSM/taWnyomb2SPHerWTSJmll7M3swic81s76N/BmbTKoNYOlSePdd+Mc/4L/+K6aPqMmHH8KkSTB/fmxDTGHRq1dcGrr66prfL31073//N/zgBxrxKyINl0kN4W5gRJXYhcCT7j4QeDJ5jJkNAkqAwckxt5lZQXLM7cBYYGByS73mGGCduw8Abgaur++HaW6TJ0dPmjVrYj6htm2jW+i111Z/Qt6yBW65JXoOXXddHNu1Kxx4YNQWDjwQfv3r3TfEVjf4a/36aHvIdECYiMju1JoQ3P3vwPtVwicD05LtacDItPgD7r7F3SuAcmCYmRUCXdx9jkcr9j1Vjkm91gzg2FTtIddVVMAHH8SJuKAg7tu2he3bdz0h79wJv/89HHwwnHsuvPdezGt05ZXRiLxkSbzW7Nk198qpbvDXtm3xfuk04ldE6qO+bQj7ufsqgOS+ZxLvBSxP229FEuuVbFeN73KMu28HPgT2re5NzWysmZWZWdnatWvrWfTG069f/OpPX5B+586YqC51Qp49O9Yi+M534oTetm1MRFdeDpddFomhLu9XdfBXu3bxmuk04ldE6qOxG5Wr+2XvNcRrOuaTQfep7l7k7kU9evSoZxEbz8SJUTPYsSMe79wZt332iZlLi4vh2GPhhRfi+W9+MwaVTZkC++1Xv/erOvirS5cYm6ARvyLSUPVNCKuTy0Ak92uS+AqgT9p+vYGVSbx3NfFdjjGztsDefPISVU4qLo7G4TZt4iTctm007H7wAZSVwWOPxX6pJSxnzIh2goa8X9XRvXfdBf/3fxrxKyINV99xCDOB0cB1yf0jafHfm9kvgP2JxuN57r7DzDaY2VHAXOAM4FdVXmsOMAqY7S1otNxll8UloWuuiRlH16yJWgLAZz4D118P3/hG400zUVxc/cleCUBEGqrWhGBm9wNfBrqb2QrgciIRTDezMcBbwKkA7r7QzKYDi4DtwHh3Ty6oMI7osdQBKE1uAHcC95pZOVEzKGmUT9ZMtmyJVckWLqzsQlpYGA3GP/jBJ6/vi4jkKk1dUU+pnkOXXAJvvhmxzp1j0Zpzz9114RcRkVyhqSsa2axZceJ/6aV43LYtjBsHl14aM5KKiLRESgh18OKLcMEFkRBSTj012g8GDMheuUREGoMSQgbefDMuDd13X2XsS1+CG26AYcOyVy4Rkcakye1q8P77sQbBgAGVyaBTp5iO+qmnqk8GmmhORFqqvEoI6Sfrww6LW3Un7s2b49d///5w002VU0O0bx+Dzu69t3KMQdXXrzr5nCaaE5GWIm96GaWvTrZtW8wh5A6f/nRM/7B1K/zylzHP0KWXwvLlux7frl0MQHOHnj1jXePZs3fdp+qCNxAjhwsLP7mviEg2qJcRu84U+vrrcXI3i4FkAwfCRx9BSUmcwFNSE9WZxf0ee8T2Bx9UP3lcasGbdJpoTkRairy5ZJQ+U2hqQro2beLy0NKlsWJZKhn07AkHHFCZNFK2bYvYli3VTx5X3eRzmmhORFqKvEkI6SfrgoJIBJs2xS//DRsivs8+8PzzkTj22SfaDFKXidxjMNrWrXF8dZPHVTf53DvvwLx5Udvo2rX2xXNERLIlbxJC6mS9cmUkg6q6doXf/Q6KimIG0ddei4SRmsk0ZceOmLV0d/MJpU8+9/HHkWy2bYvLTZs2wc9+pqQgIrkpbxJCcXGsZPbOO5Wx1MI2HTpAnz5wwgnR+LxmTVwWqpoMOnSA3r0jqaRU7WYK0YD8r39FW0NBQdQOUovntGkDN9+cWZnVhVVEmlPeJASA006Ly0EFBbF+8ZAhcTv44MrLRpMnV57A05nFMT17VjYS19bNdMOGeK90BQXRgF0bdWEVkeaWVwkBIgEccEAsZp9a6Sy94Te1LGbq17xZ3Nxh9epd961ujeP09Yw7d67+klMmq6TV9toiIo0t7xLCxRfHSXl3K4z16xfX/tu0ibEHEPu1aRPx9H2rW+M4vZvpuedGQ/T27fEa27fH43PPrb2ctb22iEhjy7uEUN2qY+krjE2cWDn+oE2bXS8fdeq06761dTO97LIY5NaxYzQsd+wYjy+7rPZyqguriDS3vBmpXBdXXRUN0Dt2VE5Xsccen1yaMn30c8eOccLeurVxlrBsytcWkfxV00jlvKshZOKyy+CPf4y1kHv0iJHM1Z2Ia6ttNERTvraISHVUQxARySNNVkMws2Vm9oqZvWRmZUmsm5nNMrOlyX3XtP0nmVm5mS0xs6+lxYcmr1NuZreaNdaS9CIikqnGuGT0FXcfkpZxLgSedPeBwJPJY8xsEFACDAZGALeZWaqX/u3AWGBgchvRCOUSEZE6aIo2hJOBacn2NGBkWvwBd9/i7hVAOTDMzAqBLu4+x+P61T1px4iISDNpaEJw4G9mNt/Mxiax/dx9FUBy3zOJ9wLSVxlYkcR6JdtV459gZmPNrMzMytauXdvAoouISLqGrofwBXdfaWY9gVlm9loN+1bXLuA1xD8ZdJ8KTIVoVK5rYUVEZPcaVENw95XJ/RrgYWAYsDq5DERyvybZfQXQJ+3w3sDKJN67mriIiDSjeicEM+tkZp1T28BXgVeBmcDoZLfRwCPJ9kygxMzam1k/ovF4XnJZaYOZHZX0Ljoj7RgREWkmDblktB/wcNJDtC3we3d/zMyeB6ab2RjgLeBUAHdfaGbTgUXAdmC8u6emfhsH3A10AEqTm4iINCMNTBMRySOaukJERGqlhCAiIoASgoiIJJQQREQEUEIQEZGEEoKIiABKCCIiksi7hFBaCsOHx5rFw4fHYxERybOEkFqneNUq6NYt7idMUFIQEYE8SwiTJ8ei9Z06gVnc77FHxEVE8l1eJYSKCujYcddYx46wbFlWiiMiklPyKiH06webNu0a27QJ+vbNSnFERHJKXiWEiRNh61bYuBHc437r1oiLiOS7vEoIxcUwZQoUFsK6dXE/ZUrERUTyXUOX0GxxiouVAEREqpNXNQQREdk9JQQREQGUEEREJKGEICIigBKCiIgkzN2zXYZ6MbO1wJv1OLQ78G4jF6cxqFx1o3JlLhfLBCpXXTVWuT7t7j2qe6LFJoT6MrMydy/KdjmqUrnqRuXKXC6WCVSuumqOcumSkYiIAEoIIiKSyMeEMDXbBdgNlatuVK7M5WKZQOWqqyYvV961IYiISPXysYYgIiLVUEIQEZHg7i3+BiwDXgFeAsqSWDdgFrA0ue+atv8koBxYAnwtLT40eZ1y4FaSS2p1KMddwBrg1bRYo5UDaA88mMTnAn0bUK4rgLeT7+wl4IQslKsP8BSwGFgInJ3t76yGMmX1+wL2BOYBLyflujLb31Ut5cqFv68C4EXg0Vz4rmooV9a/q3+/bl12ztUbkRC6V4ndAFyYbF8IXJ9sD0r+eNsD/YA3gILkuXnA5wEDSoHiOpbjGOAIdj3xNlo5gB8D/y/ZLgEebEC5rgB+Ws2+zVmuQuCIZLsz8Hry/ln7zmooU1a/r+Q19kq22xH/2Y/K9t9XDeXKhb+v84DfU3nizfr/xd2UK+vf1b/fsy475+qN6hPCEqAw2S4EliTbk4BJafs9nnyxhcBrafFvAb+pR1n6suuJt9HKkdon2W5LjFrMqBZTTbl290fYrOWq8t6PAMfnyndWpUw5830BHYEXgM/l2HeVXq6sfl9Ab+BJYDiVJ96sf1e7KVfO/G21ljYEB/5mZvPNbGwS28/dVwEk9z2TeC9gedqxK5JYr2S7aryhGrMc/z7G3bcDHwL7NqBsE8xsgZndZWZds1kuM+sLHE78wsyJ76xKmSDL35eZFZjZS8Tlv1nunhPf1W7KBdn9vm4Bzgd2psWy/l3tplyQI/8XW0tC+IK7HwEUA+PN7Jga9rVqYl5DvKnUpxyNWcbbgf7AEGAVcFO2ymVmewEPAee4+/qadm2uslVTpqx/X+6+w92HEL8yh5nZITV9hCyXK2vfl5mdCKxx9/m1lb25ylRLubL+t5XSKhKCu69M7tcADwPDgNVmVgiQ3K9Jdl9BNBym9AZWJvHe1cQbqjHL8e9jzKwtsDfwfn0K5e6rk//IO4HfEt9Zs5fLzNoRJ97fufsfk3BWv7PqypQr31dSlg+Ap4ER5NDfV3q5svx9fQE4ycyWAQ8Aw83sPrL/XVVbrlz622rxCcHMOplZ59Q28FXgVWAmMDrZbTRxLZgkXmJm7c2sHzAQmJdUITeY2VFmZsAZacc0RGOWI/21RgGzPblYWFep/xiJU4jvrFnLlbzOncBid/9F2lNZ+852V6Zsf19m1sPM9km2OwDHAa9l87uqqVzZ/L7cfZK793b3vkTD6mx3/262v6vdlSvbf1tVC9mib8ABREt8qtvbxUl8X6LxZmly3y3tmIuJFvslpPUkAoqSf4w3gCnUvdvp/USVbxuRqcc0ZjmILn5/ILqUzQMOaEC57iW6rS1I/ogKs1Cuo4nq7ALSutxl8zuroUxZ/b6AQ4muiguS17yssf/OG7lcWf/7So79MpWNt1n/v7ibcuXEd+XumrpCRERCi79kJCIijUMJQUREACUEERFJKCGIiAighCAiIgklBJFGZGZXmdlx2S6HSH2o26lIIzGzAnffke1yiNSXaggiGTCzvmb2mplNSyYhm2FmHc1smZldZmb/AE41s7vNbFRyzJFm9qyZvWxm88ysczIR3GQzez55nR9l+aOJ/JsSgkjmDgKmuvuhwHpi7nmAj939aHd/ILWjme1BLFRytrsfRkzpsJkYJf6hux8JHAn8MJmWQCTrlBBEMrfc3f+ZbN9HTHMBceKv6iBglbs/D+Du6z2mI/4qcEYyXfRcYjqFgU1aapEMtc12AURakKoNbqnHG6vZ16rZPxU/y90fb8yCiTQG1RBEMvcpM/t8sv0t4B817PsasL+ZHQmQtB+0JVa0GpdMsY2ZHZjM0iuSdUoIIplbDIw2swXEgu23725Hd98KnA78ysxeJhZ13xO4A1gEvGBmrwK/QTV1yRHqdiqSAYvlNB9195pWKRNp0VRDEBERQDUEERFJqIYgIiKAEoKIiCSUEEREBFBCEBGRhBKCiIgA8P8B/EFivWYPnHUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot regression model line\n",
    "sns.regplot(x=y_test, y=y_pred, ci=None, color ='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "418622cb",
   "metadata": {},
   "source": [
    "### Let's compare the metrics of two models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "98cc53b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a metrics dataframe using metric values\n",
    "metrics = {\n",
    "    'Model': ['First', 'Second'],\n",
    "    'MSE' : [mse, mse_2],\n",
    "    'RMSE' : [rmse, rmse_2],\n",
    "    'MAE' : [mae, mae_2],\n",
    "    'R2' : [r2, r2_2]\n",
    "    }\n",
    "\n",
    "metrics_df = pd.DataFrame(data=metrics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "6b1cb32f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model</th>\n",
       "      <th>MSE</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>MAE</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>First</td>\n",
       "      <td>1.683554e+07</td>\n",
       "      <td>4103.113944</td>\n",
       "      <td>3195.031240</td>\n",
       "      <td>0.782532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Second</td>\n",
       "      <td>1.551480e+07</td>\n",
       "      <td>3938.882718</td>\n",
       "      <td>3061.617263</td>\n",
       "      <td>0.799593</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Model           MSE         RMSE          MAE        R2\n",
       "0   First  1.683554e+07  4103.113944  3195.031240  0.782532\n",
       "1  Second  1.551480e+07  3938.882718  3061.617263  0.799593"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare the values\n",
    "metrics_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a941e81a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
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