{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "e16ccbe1-4aa6-4eb8-82ed-cfeb6b99bd90",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "import statsmodels.api as sm\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.linear_model import LinearRegression\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1bf12f2f-20bb-4104-9cd1-f963cd83feec",
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>17.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>14.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>18.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        TV  Radio  Newspaper  Sales\n",
       "0    230.1   37.8       69.2   22.1\n",
       "1     44.5   39.3       45.1   10.4\n",
       "2     17.2   45.9       69.3   12.0\n",
       "3    151.5   41.3       58.5   16.5\n",
       "4    180.8   10.8       58.4   17.9\n",
       "..     ...    ...        ...    ...\n",
       "195   38.2    3.7       13.8    7.6\n",
       "196   94.2    4.9        8.1   14.0\n",
       "197  177.0    9.3        6.4   14.8\n",
       "198  283.6   42.0       66.2   25.5\n",
       "199  232.1    8.6        8.7   18.4\n",
       "\n",
       "[200 rows x 4 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advertising = pd.read_csv(\"Company_data.csv\")\n",
    "advertising"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "42cd520e-68f5-43dc-aad2-bcb48429b10a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advertising.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "65d21e47-f13a-4895-97b7-c07d0d0cf47f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 200 entries, 0 to 199\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   TV         200 non-null    float64\n",
      " 1   Radio      200 non-null    float64\n",
      " 2   Newspaper  200 non-null    float64\n",
      " 3   Sales      200 non-null    float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 6.4 KB\n"
     ]
    }
   ],
   "source": [
    "advertising.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "56248bd0-25fb-4511-aa37-05ca2285466a",
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>147.042500</td>\n",
       "      <td>23.264000</td>\n",
       "      <td>30.554000</td>\n",
       "      <td>15.130500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>85.854236</td>\n",
       "      <td>14.846809</td>\n",
       "      <td>21.778621</td>\n",
       "      <td>5.283892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>1.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>74.375000</td>\n",
       "      <td>9.975000</td>\n",
       "      <td>12.750000</td>\n",
       "      <td>11.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>149.750000</td>\n",
       "      <td>22.900000</td>\n",
       "      <td>25.750000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>218.825000</td>\n",
       "      <td>36.525000</td>\n",
       "      <td>45.100000</td>\n",
       "      <td>19.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>296.400000</td>\n",
       "      <td>49.600000</td>\n",
       "      <td>114.000000</td>\n",
       "      <td>27.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TV       Radio   Newspaper       Sales\n",
       "count  200.000000  200.000000  200.000000  200.000000\n",
       "mean   147.042500   23.264000   30.554000   15.130500\n",
       "std     85.854236   14.846809   21.778621    5.283892\n",
       "min      0.700000    0.000000    0.300000    1.600000\n",
       "25%     74.375000    9.975000   12.750000   11.000000\n",
       "50%    149.750000   22.900000   25.750000   16.000000\n",
       "75%    218.825000   36.525000   45.100000   19.050000\n",
       "max    296.400000   49.600000  114.000000   27.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advertising.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2b449417-06e5-422c-b227-8b15a2d970d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(advertising, x_vars=['TV', 'Radio', 'Newspaper'], y_vars='Sales', height=4, aspect=1, kind='scatter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f8fe9849-b8ae-4da0-8774-dadb1f5c949a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(advertising.corr(), cmap='YlGnBu', annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9732dc55-8874-4bfe-a1c2-7120158e707d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = advertising['TV']\n",
    "y = advertising['Sales']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "07d5b573-5577-4f1d-8ab4-6aaab7fadfba",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, train_size=0.7, test_size=0.3, random_state=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4d18a989-ccb5-454f-928b-4aa7935b5331",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    6.948683\n",
       "TV       0.054546\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train_sm = sm.add_constant(x_train)\n",
    "lr = sm.OLS(y_train, x_train_sm).fit()\n",
    "lr.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ffc75ce3-8f2a-4749-b05a-ce7edc1753a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>Sales</td>      <th>  R-squared:         </th> <td>   0.816</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.814</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   611.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 30 Aug 2021</td> <th>  Prob (F-statistic):</th> <td>1.52e-52</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:45:42</td>     <th>  Log-Likelihood:    </th> <td> -321.12</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   140</td>      <th>  AIC:               </th> <td>   646.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   138</td>      <th>  BIC:               </th> <td>   652.1</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>const</th> <td>    6.9487</td> <td>    0.385</td> <td>   18.068</td> <td> 0.000</td> <td>    6.188</td> <td>    7.709</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TV</th>    <td>    0.0545</td> <td>    0.002</td> <td>   24.722</td> <td> 0.000</td> <td>    0.050</td> <td>    0.059</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.027</td> <th>  Durbin-Watson:     </th> <td>   2.196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.987</td> <th>  Jarque-Bera (JB):  </th> <td>   0.150</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.006</td> <th>  Prob(JB):          </th> <td>   0.928</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.840</td> <th>  Cond. No.          </th> <td>    328.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  Sales   R-squared:                       0.816\n",
       "Model:                            OLS   Adj. R-squared:                  0.814\n",
       "Method:                 Least Squares   F-statistic:                     611.2\n",
       "Date:                Mon, 30 Aug 2021   Prob (F-statistic):           1.52e-52\n",
       "Time:                        18:45:42   Log-Likelihood:                -321.12\n",
       "No. Observations:                 140   AIC:                             646.2\n",
       "Df Residuals:                     138   BIC:                             652.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          6.9487      0.385     18.068      0.000       6.188       7.709\n",
       "TV             0.0545      0.002     24.722      0.000       0.050       0.059\n",
       "==============================================================================\n",
       "Omnibus:                        0.027   Durbin-Watson:                   2.196\n",
       "Prob(Omnibus):                  0.987   Jarque-Bera (JB):                0.150\n",
       "Skew:                          -0.006   Prob(JB):                        0.928\n",
       "Kurtosis:                       2.840   Cond. No.                         328.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f0c0bdb8-7880-49c2-9763-2e02e15e16ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train)\n",
    "plt.plot(x_train, 6.948 + 0.054 * x_train, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8cfba9e5-a4dc-4785-873d-318d43b32cb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = lr.predict(x_train_sm)\n",
    "res = y_train - y_train_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "cb61864d-6abc-42d2-947d-ce29358ce0aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "sns.displot(res, bins=15)\n",
    "plt.title(\"Error Terms\", fontsize=15)\n",
    "plt.xlabel('y_train - y_train_pred', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "e1556302-227c-4a75-9062-d01cffe3b38b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9f73474640>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ab3c0ec4-8090-420b-a915-d49f45e339d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/vincent/anaconda3/envs/jupyterLab/lib/python3.9/site-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "126     7.374140\n",
       "104    19.941482\n",
       "99     14.323269\n",
       "92     18.823294\n",
       "111    20.132392\n",
       "167    18.228745\n",
       "116    14.541452\n",
       "96     17.726924\n",
       "52     18.752384\n",
       "69     18.774202\n",
       "164    13.341445\n",
       "124    19.466933\n",
       "182    10.014155\n",
       "154    17.192376\n",
       "125    11.705073\n",
       "196    12.086893\n",
       "194    15.114182\n",
       "177    16.232370\n",
       "163    15.866914\n",
       "31     13.106899\n",
       "11     18.659656\n",
       "73     14.006904\n",
       "15     17.606923\n",
       "41     16.603281\n",
       "97     17.034193\n",
       "128    18.965113\n",
       "133    18.937840\n",
       "82     11.055978\n",
       "139    17.034193\n",
       "123    13.663265\n",
       "83     10.679613\n",
       "65     10.712340\n",
       "151    13.548719\n",
       "162    17.225103\n",
       "170     9.675971\n",
       "77     13.521446\n",
       "32     12.250530\n",
       "173    16.134188\n",
       "174    19.079659\n",
       "85     17.486923\n",
       "168    18.697838\n",
       "112    16.532372\n",
       "171    15.921460\n",
       "181    18.866930\n",
       "7      13.505083\n",
       "46     11.841437\n",
       "75      7.870506\n",
       "28     20.519667\n",
       "29     10.799613\n",
       "195     9.032331\n",
       "40     17.994198\n",
       "153    16.292371\n",
       "115    11.045069\n",
       "64     14.099631\n",
       "59     18.441473\n",
       "1       9.375969\n",
       "192     7.886870\n",
       "136     8.345054\n",
       "152    17.726924\n",
       "161    11.623254\n",
       "dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test_sm = sm.add_constant(x_test)\n",
    "y_test_pred = lr.predict(x_test_sm)\n",
    "y_test_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a4c90bfd-deaf-4d4d-a297-6bfd4d7b65b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7921031601245659"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_squ = r2_score(y_test, y_test_pred)\n",
    "r_squ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "df1c7041-bc0c-440b-961c-cb3f184a3f14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_test, y_test)\n",
    "plt.plot(x_test, y_test_pred, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "45bfa3b2-12f8-4ed5-95bb-2e9da30ac8e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140,)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "x_train_lm, x_test_lm, y_train_lm, y_test_lm = train_test_split(x, y, train_size=0.7, test_size=0.3, random_state=100)\n",
    "x_train_lm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "07005d97-16d8-4b67-92d8-9a5f32e6229a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(140, 1)\n",
      "(60, 1)\n"
     ]
    }
   ],
   "source": [
    "x_train_lm = x_train_lm.values.reshape(-1,1)\n",
    "x_test_lm = x_test_lm.values.reshape(-1,1)\n",
    "print(x_train_lm.shape)\n",
    "print(x_test_lm.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "e7a04fa1-4439-4d5a-8193-3279cfc2a9cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 6.948683200001357\n",
      "Slope: [0.05454575]\n"
     ]
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "\n",
    "lm.fit(x_train_lm, y_train_lm)\n",
    "\n",
    "print(\"Intercept:\",lm.intercept_)\n",
    "print(\"Slope:\", lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "516c7966-595b-47cb-ae0e-988e9c48adec",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9 (XPython)",
   "language": "python",
   "name": "xpython"
  },
  "language_info": {
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}