Simple Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7192fb30",
   "metadata": {},
   "source": [
    "# Simple Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "86b9a294",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7edfabc4",
   "metadata": {},
   "source": [
    "# scikit-learn is a machine learning library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ffd0a59",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn #importing scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5328a773",
   "metadata": {},
   "source": [
    "## Steps of machine learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f5553aa0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# collect and prepare data\n",
    "# choose alogrithm\n",
    "# train algo using training data\n",
    "# evaluate madel performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "062f7417",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('Salary_Data.csv') #importing data and make a dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d4cbffe2",
   "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>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.1</td>\n",
       "      <td>39343.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.3</td>\n",
       "      <td>46205.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>37731.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>43525.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.2</td>\n",
       "      <td>39891.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.9</td>\n",
       "      <td>56642.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.0</td>\n",
       "      <td>60150.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.2</td>\n",
       "      <td>54445.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.2</td>\n",
       "      <td>64445.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.7</td>\n",
       "      <td>57189.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.9</td>\n",
       "      <td>63218.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.0</td>\n",
       "      <td>55794.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.0</td>\n",
       "      <td>56957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.1</td>\n",
       "      <td>57081.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.5</td>\n",
       "      <td>61111.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.9</td>\n",
       "      <td>67938.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5.1</td>\n",
       "      <td>66029.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5.3</td>\n",
       "      <td>83088.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5.9</td>\n",
       "      <td>81363.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>6.0</td>\n",
       "      <td>93940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>6.8</td>\n",
       "      <td>91738.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>7.1</td>\n",
       "      <td>98273.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>7.9</td>\n",
       "      <td>101302.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.2</td>\n",
       "      <td>113812.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>8.7</td>\n",
       "      <td>109431.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.0</td>\n",
       "      <td>105582.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>9.5</td>\n",
       "      <td>116969.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>9.6</td>\n",
       "      <td>112635.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>10.3</td>\n",
       "      <td>122391.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>10.5</td>\n",
       "      <td>121872.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    YearsExperience    Salary\n",
       "0               1.1   39343.0\n",
       "1               1.3   46205.0\n",
       "2               1.5   37731.0\n",
       "3               2.0   43525.0\n",
       "4               2.2   39891.0\n",
       "5               2.9   56642.0\n",
       "6               3.0   60150.0\n",
       "7               3.2   54445.0\n",
       "8               3.2   64445.0\n",
       "9               3.7   57189.0\n",
       "10              3.9   63218.0\n",
       "11              4.0   55794.0\n",
       "12              4.0   56957.0\n",
       "13              4.1   57081.0\n",
       "14              4.5   61111.0\n",
       "15              4.9   67938.0\n",
       "16              5.1   66029.0\n",
       "17              5.3   83088.0\n",
       "18              5.9   81363.0\n",
       "19              6.0   93940.0\n",
       "20              6.8   91738.0\n",
       "21              7.1   98273.0\n",
       "22              7.9  101302.0\n",
       "23              8.2  113812.0\n",
       "24              8.7  109431.0\n",
       "25              9.0  105582.0\n",
       "26              9.5  116969.0\n",
       "27              9.6  112635.0\n",
       "28             10.3  122391.0\n",
       "29             10.5  121872.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "662c58ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "# checking missing data in the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5346d94d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "YearsExperience    0\n",
       "Salary             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "63ec136d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Split data into training and test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f8005843",
   "metadata": {},
   "outputs": [],
   "source": [
    "#train data : 80 or 70%\n",
    "#test data : 20 or 30%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1a59ff4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# x = df.iloc[starting row index:ending row index,starting column index:ending column index].values\n",
    "'''\n",
    "x = df.iloc[:,:-1].values will give you all the columns except the last column from the data frame\n",
    "x = df.iloc[:,:1].values will give you only the first column ignoring all the columns in the data frame\n",
    "'''\n",
    "x = df.iloc[:,:-1].values # 2 dimensional we've used iloc here beacause we want iloc to be 2D\n",
    "#x = input data should be 2D\n",
    "y = df.Salary.values\n",
    "#y = output data should be 1D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "11db49df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 39343.,  46205.,  37731.,  43525.,  39891.,  56642.,  60150.,\n",
       "        54445.,  64445.,  57189.,  63218.,  55794.,  56957.,  57081.,\n",
       "        61111.,  67938.,  66029.,  83088.,  81363.,  93940.,  91738.,\n",
       "        98273., 101302., 113812., 109431., 105582., 116969., 112635.,\n",
       "       122391., 121872.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y #output data Salary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "87f3d02a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "89bd3e3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.1],\n",
       "       [ 1.3],\n",
       "       [ 1.5],\n",
       "       [ 2. ],\n",
       "       [ 2.2],\n",
       "       [ 2.9],\n",
       "       [ 3. ],\n",
       "       [ 3.2],\n",
       "       [ 3.2],\n",
       "       [ 3.7],\n",
       "       [ 3.9],\n",
       "       [ 4. ],\n",
       "       [ 4. ],\n",
       "       [ 4.1],\n",
       "       [ 4.5],\n",
       "       [ 4.9],\n",
       "       [ 5.1],\n",
       "       [ 5.3],\n",
       "       [ 5.9],\n",
       "       [ 6. ],\n",
       "       [ 6.8],\n",
       "       [ 7.1],\n",
       "       [ 7.9],\n",
       "       [ 8.2],\n",
       "       [ 8.7],\n",
       "       [ 9. ],\n",
       "       [ 9.5],\n",
       "       [ 9.6],\n",
       "       [10.3],\n",
       "       [10.5]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x #input data Years of experience"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "37a0bb37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "320b8738",
   "metadata": {},
   "source": [
    "# Splitting data into training and test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9ecc8838",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bd35dbb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Spliting data into training and testing data\n",
    "#Spliting happens randomly so the accuracy changes everytime you run this line\n",
    "train_input,test_input,train_output,test_output = train_test_split(x,y,test_size=.20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "67b1d3f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 1)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_input.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "06239883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 1)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_input.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "963de4e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24,)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_output.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "88ecbd40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_output.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e94a5211",
   "metadata": {},
   "source": [
    "# Choose ML algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d491de45",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Linear regression when all the values are continues not as a label\n",
    "# for example predicting salary, sales,student marks, stock market prediciton etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cddc9111",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ba19671f",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2560b093",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train set:training a model (60%)\n",
    "# valid set:evaluation       (20%)\n",
    "# test set: once we get our final model (20%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "25a5a42e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(train_input,train_output)\n",
    "# lr.fit(train_input data,train_output data)\n",
    "# y=mx+b fit will find m and b values incase of regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1f020e27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9437.295717371964"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = lr.coef_[0] # y = mx+b finding m coefficient may be one or more hence it returns values in array\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c9e0d04e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25567.63928072182"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = lr.intercept_ # y = mx+b finding b always returns only one value\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63a2d7fb",
   "metadata": {},
   "source": [
    "# Evaluate model performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "23391afb",
   "metadata": {},
   "outputs": [],
   "source": [
    "test = 7.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b3e3db12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([93516.1684458])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([[test]])# it finds m and b in formula y=mx+b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "319dce72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.2],\n",
       "       [3.9],\n",
       "       [5.1],\n",
       "       [8.7],\n",
       "       [1.1],\n",
       "       [6. ]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "51aa2d27",
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = lr.predict(test_input) #testing Linear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2788b4b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 55766.98557631,  62373.09257847,  73697.84743932, 107672.11202186,\n",
       "        35948.66456983,  82191.41358495])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "16724f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 54445.,  63218.,  66029., 109431.,  39343.,  93940.])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "760aaa36",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score,mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "40110354",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9364223738472344"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(test_output,pred)  #test accuracy score of the model its only used in case of regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "66c9531a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35652869.691073775"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(test_output,pred) # "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1148c778",
   "metadata": {},
   "source": [
    "# Pratice regression on generated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "aea3017f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "5c684145",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x1,y1 = make_regression(n_samples=500,n_features=1,noise=12,random_state=2)\n",
    "#arguments:\n",
    "#n_samples = no of samples\n",
    "#n_features no of features\n",
    "#noise to add noise in data (complexity of data)\n",
    "# random_state ; pass any integer no to get same random values\n",
    "plt.scatter(x1,y1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "597cc6dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 1)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1.shape #x1 is 2D which is going to be our input data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "b8b924d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500,)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1.shape #y1 is 1D which is going to be our output data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "72e3075a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "#Spliting data into training and testing data\n",
    "#Spliting happens randomly so the accuracy changes everytime you run this line\n",
    "train_input,test_input,train_output,test_output = train_test_split(x1,y1,test_size=.20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "af200bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(400, 1)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_input.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4d0a2355",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_input.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "efc8acb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(400,)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_output.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a7463c4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_output.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "d9651d9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Linear regression when all the values are continues not as a label\n",
    "# for example predicting salary, sales,student marks, stock market prediciton etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "6bf7e8f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9105509d",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression() #initializing Regression class and creating an object of it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a5144577",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train set:training a model (60%)\n",
    "# valid set:evaluation       (20%)\n",
    "# test set: once we get our final model (20%)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd834a76",
   "metadata": {},
   "source": [
    "## Training Linear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5be98ab4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(train_input,train_output)\n",
    "# lr.fit(train_input data,train_output data)\n",
    "# y=mx+b fit will find m and b values incase of regression \n",
    "# fit method call means training model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "0f083b8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.618447821258602"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = lr.coef_[0] # y = mx+b finding m coefficient may be one or more hence it returns values in array\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2baceafe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.1917406740743022"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = lr.intercept_ # y = mx+b finding b always returns only one value\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "21f3a2ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "test = 0.52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "1136869d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.52985219])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([[test]]) # it finds m and b in formula y=mx+b and solves it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "57310606",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.67736049],\n",
       "       [-0.44817482],\n",
       "       [-0.16396283],\n",
       "       [ 0.42560621],\n",
       "       [-0.37566942],\n",
       "       [ 3.2797454 ],\n",
       "       [-0.63467931],\n",
       "       [ 1.24821292],\n",
       "       [-0.51688389],\n",
       "       [-1.15100294],\n",
       "       [-1.28089518],\n",
       "       [ 0.18652152],\n",
       "       [ 0.79918   ],\n",
       "       [ 0.75650214],\n",
       "       [-0.44750088],\n",
       "       [ 0.18040981],\n",
       "       [-0.63765501],\n",
       "       [ 0.04797059],\n",
       "       [ 1.54627765],\n",
       "       [ 1.2484503 ],\n",
       "       [ 0.52429643],\n",
       "       [ 0.05725095],\n",
       "       [ 2.28253964],\n",
       "       [-0.82913529],\n",
       "       [-0.15842922],\n",
       "       [ 0.63062197],\n",
       "       [ 1.01985473],\n",
       "       [ 1.14950057],\n",
       "       [-1.45535944],\n",
       "       [-2.08265194],\n",
       "       [-0.56449343],\n",
       "       [-1.12590378],\n",
       "       [-0.01766068],\n",
       "       [-0.07087636],\n",
       "       [-0.40389227],\n",
       "       [ 0.50288142],\n",
       "       [ 1.53176032],\n",
       "       [-0.18337674],\n",
       "       [ 0.30752553],\n",
       "       [ 0.41759273],\n",
       "       [-0.45422785],\n",
       "       [-0.61209475],\n",
       "       [ 0.33048806],\n",
       "       [ 1.79259285],\n",
       "       [ 0.48849667],\n",
       "       [-1.02141473],\n",
       "       [-0.33484413],\n",
       "       [-1.1598069 ],\n",
       "       [ 0.77101174],\n",
       "       [ 0.51437072],\n",
       "       [ 0.51325144],\n",
       "       [-0.49299491],\n",
       "       [-1.24572655],\n",
       "       [ 0.54235257],\n",
       "       [ 1.0281849 ],\n",
       "       [-2.02336394],\n",
       "       [ 0.29952681],\n",
       "       [-1.02351498],\n",
       "       [ 1.11788673],\n",
       "       [ 0.1941687 ],\n",
       "       [ 2.14467809],\n",
       "       [ 0.61134078],\n",
       "       [-0.18904405],\n",
       "       [ 0.1127265 ],\n",
       "       [ 0.42475367],\n",
       "       [-1.90382114],\n",
       "       [ 0.15908849],\n",
       "       [ 0.06046245],\n",
       "       [-1.41881055],\n",
       "       [-0.65771845],\n",
       "       [-0.79487244],\n",
       "       [-0.4493286 ],\n",
       "       [-0.26905696],\n",
       "       [ 4.10869262],\n",
       "       [-1.38451867],\n",
       "       [-0.06163508],\n",
       "       [-0.2424406 ],\n",
       "       [-1.40084545],\n",
       "       [ 0.44068987],\n",
       "       [-0.98656966],\n",
       "       [-0.72187973],\n",
       "       [ 0.34321273],\n",
       "       [-2.50545813],\n",
       "       [ 2.23136679],\n",
       "       [-0.57138161],\n",
       "       [-0.5961597 ],\n",
       "       [ 1.33556617],\n",
       "       [ 0.38186623],\n",
       "       [ 0.71268327],\n",
       "       [-1.33858888],\n",
       "       [-2.43476758],\n",
       "       [-1.98584577],\n",
       "       [-1.91352322],\n",
       "       [ 1.1735315 ],\n",
       "       [-1.07502856],\n",
       "       [-1.11526396],\n",
       "       [ 0.82470301],\n",
       "       [ 0.73527958],\n",
       "       [ 0.5862041 ],\n",
       "       [-0.14959135]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "454d7618",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.51578626e+01, -1.04324099e+01, -4.57239978e+00,  7.58359878e+00,\n",
       "       -8.93746107e+00,  6.64315187e+01, -1.42778428e+01,  2.45444723e+01,\n",
       "       -1.18490843e+01, -2.49236348e+01, -2.76018111e+01,  2.65404355e+00,\n",
       "        1.52861104e+01,  1.44061593e+01, -1.04185141e+01,  2.52802952e+00,\n",
       "       -1.43391973e+01, -2.02661529e-01,  3.06901043e+01,  2.45493667e+01,\n",
       "        9.61843791e+00, -1.13150205e-02,  4.58706838e+01, -1.82872234e+01,\n",
       "       -4.45830537e+00,  1.18107055e+01,  1.98360808e+01,  2.25091768e+01,\n",
       "       -3.11989935e+01, -4.41327909e+01, -1.28307190e+01, -2.44061290e+01,\n",
       "       -1.55587648e+00, -2.65310112e+00, -9.51937235e+00,  9.17689359e+00,\n",
       "        3.03907795e+01, -4.97268432e+00,  5.14895835e+00,  7.41837325e+00,\n",
       "       -1.05572140e+01, -1.38121843e+01,  5.62241023e+00,  3.57687415e+01,\n",
       "        8.88030234e+00, -2.22517270e+01, -8.09570680e+00, -2.51051586e+01,\n",
       "        1.47053246e+01,  9.41378512e+00,  9.39070745e+00, -1.13565305e+01,\n",
       "       -2.68766886e+01,  9.99072754e+00,  2.00078360e+01, -4.29103645e+01,\n",
       "        4.98403729e+00, -2.22950310e+01,  2.18573486e+01,  2.81171645e+00,\n",
       "        4.30281926e+01,  1.14131573e+01, -5.08953559e+00,  1.13250488e+00,\n",
       "        7.56602075e+00, -4.04455776e+01,  2.08841699e+00,  5.49011758e-02,\n",
       "       -3.04454120e+01, -1.47528742e+01, -1.75807767e+01, -1.04561990e+01,\n",
       "       -6.73927757e+00,  8.35231238e+01, -2.97383666e+01, -2.46256045e+00,\n",
       "       -6.19048954e+00, -3.00749996e+01,  7.89460047e+00, -2.15332758e+01,\n",
       "       -1.60757801e+01,  5.88477314e+00, -5.28503984e+01,  4.48155790e+01,\n",
       "       -1.29727425e+01, -1.34836283e+01,  2.63455607e+01,  6.68174835e+00,\n",
       "        1.35026822e+01, -2.87913656e+01, -5.13928689e+01, -4.21367981e+01,\n",
       "       -4.06456193e+01,  2.30046573e+01, -2.33571610e+01, -2.41867525e+01,\n",
       "        1.58123552e+01,  1.39685829e+01,  1.08948779e+01, -4.27608217e+00])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = lr.predict(test_input) #testing Linear regression model actual predictions\n",
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "378f6176",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d07ef096",
   "metadata": {},
   "source": [
    "## How to draw a best fit line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "23a25b5c",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(test_input,test_output,label='test data') # x_test = test_input and y_test = test_output\n",
    "plt.plot(test_input,pred,color='red',marker='*') ##doubt what is pred and marker role in this plot function\n",
    "#  The line is coming from test_input and pred  (Prediction hai is line me)\n",
    "#  Blue points are plotted using test_input and test_output\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6de96d3c",
   "metadata": {},
   "source": [
    "### In the above graph all the blue points represents the test data (test_input,test_output)\n",
    "### Here pred is responsible to plot the best fit line with respect to the test input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "99501489",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score,mean_squared_error #testing model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "91246fe5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8118883408651347"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(test_output,pred)  #test accuracy score of the model its only used in case of regression\n",
    "# r2_score is actually r squared value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88a999de",
   "metadata": {},
   "source": [
    "# When will Linear Regression be used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "acd24cae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Tock price predictions\n",
    "# student marks prediction etc\n",
    "# We will implement regression when there are no column which contains categories but only contains numbers\n",
    "# in regression we have to find best fit line by finding linear relation \n",
    "# equation used to find best fit line y=mx+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "507bf7e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# If the value of sse(sum of squared error) is close to zero then Linear regression model have high accuracy\n",
    "# Mean of Squared error MSE it have the same function as SSE\n",
    "\n",
    "# $$ Mostly used is R squared value if R squared value is closer to 1 then Regression model performance is good \n",
    "# (if R^2 value is closer to 1 then actual value and predicted vale have smaller gap between them)\n",
    "# If R squared value is closer to 0 then performance of regression model is not good \n",
    "# (if R^2 value is closer to 0 then actual value and predicted vale have Larger gap between them)$$\n",
    "# Syntax to use R squared in Ml is r2_score(test_output,pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "939a4c28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' \\n1. when we have only 1 feature and we have to find output data in Linear regression\\n   then we will use y=mx+b\\n2. when we have multiple features and we have to find output data in Linear regression\\n   then the number of coefficient will increase y=( m1x1 +m2x2 ....)+b\\n'"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''' \n",
    "1. when we have only 1 feature and we have to find output data in Linear regression\n",
    "   then we will use y=mx+b\n",
    "2. when we have multiple features and we have to find output data in Linear regression\n",
    "   then the number of coefficient will increase y=( m1x1 +m2x2 ....)+b\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ca09374",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c50df51f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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