Linear Regression Equation_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "868ce1a6",
   "metadata": {},
   "source": [
    "## Practical - 3\n",
    "\n",
    "## Linear Regression Equation\n",
    "\n",
    "## Problem"
   ]
  },
  {
   "attachments": {
    "Prac-3.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0a1afbfb",
   "metadata": {},
   "source": [
    "![Prac-3.png](attachment:Prac-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3d3277d",
   "metadata": {},
   "source": [
    "## Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e610bfc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca5f9ac0",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dd0eea52",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = [1.00,2.00,3.00,4.00,5.00,6.00,7.00,8.00]\n",
    "x2 = [4.00,12.00,16.00,8.00,32.00,24.00,20.00,28.00]\n",
    "y = [9.29,12.67,12.42,0.38,20.77,9.52,2.38,7.46]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "72515efb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'X1':x1,'X2':x2,'Y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5f2fbf8c",
   "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>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>9.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>12.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>20.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>9.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>7.46</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    X1    X2      Y\n",
       "0  1.0   4.0   9.29\n",
       "1  2.0  12.0  12.67\n",
       "2  3.0  16.0  12.42\n",
       "3  4.0   8.0   0.38\n",
       "4  5.0  32.0  20.77\n",
       "5  6.0  24.0   9.52\n",
       "6  7.0  20.0   2.38\n",
       "7  8.0  28.0   7.46"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b2320f83",
   "metadata": {},
   "outputs": [],
   "source": [
    "x= df[['X1','X2']]\n",
    "y = df['Y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3cfd37d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "lm = LinearRegression().fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d6067302",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.032533783783787"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cf2506a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.57336486,  0.96715878])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f3a23be3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated linear regression equation will be :- y = 8.032533783783787 + -3.573364864864868*x1 + 0.9671587837837844*x2\n"
     ]
    }
   ],
   "source": [
    "print(f'The estimated linear regression equation will be :- y = {lm.intercept_} + {lm.coef_[0]}*x1 + {lm.coef_[1]}*x2')"
   ]
  }
 ],
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