Linear_reg.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implement linear regression and perform the following operations:\n",
    "# 1. Generate a proper 2D dataset of n points, split it into training and testing data and perform linear regression using R2 method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(84, 2)\n",
      "Index(['SAT', 'GPA'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('slr.csv')\n",
    "print(data.shape)\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "msk = np.random.rand(len(data)) < 0.8\n",
    "train = data[msk]\n",
    "test = data[~msk]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA\n",
       "0  1714  2.40\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "6  1764  3.00"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63 21\n"
     ]
    }
   ],
   "source": [
    "print(len(train), len(test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = train['SAT']\n",
    "Y_train = train['GPA']\n",
    "X_test = test['SAT']\n",
    "Y_test = test['GPA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1843.936507936508 3.314603174603175\n"
     ]
    }
   ],
   "source": [
    "x_mean = sum(X_train)/len(X_train)\n",
    "y_mean = sum(Y_train)/len(Y_train)\n",
    "print(x_mean, y_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1 = sum((X_train - x_mean)*(Y_train - y_mean)) / sum((X_train - x_mean)**2)\n",
    "b0 = y_mean - b1*x_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.16705420536473436 0.0018881655441944278\n"
     ]
    }
   ],
   "source": [
    "print(b0,b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe4c0243fd0>"
      ]
     },
     "execution_count": 12,
     "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": [
    "plt.scatter(X_train, Y_train, color = \"b\", marker = \"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = b0 + b1*X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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.plot(X_test, Y_pred, color=\"g\")\n",
    "plt.plot()\n",
    "plt.plot(X_test, Y_test, color=\"r\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8829116848754562\n"
     ]
    }
   ],
   "source": [
    "R_2 = sum((Y_pred - y_mean)**2) / sum((Y_test - y_mean)**2)\n",
    "print(R_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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