LinearRegressionCode.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "76cf3be5",
   "metadata": {},
   "source": [
    "# Code for Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "affda783",
   "metadata": {},
   "source": [
    "Firstly loading the data and spliting it into input and output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eefd9406",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "data=np.loadtxt(\"data.csv\",delimiter=\",\")\n",
    "input=data[:,0]\n",
    "output=data[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eace4817",
   "metadata": {},
   "source": [
    "Now we will divide this data into training and testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e7e9622d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "x_train,x_test,y_train,y_test=train_test_split(input,output,random_state=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da76cb73",
   "metadata": {},
   "source": [
    "Firstly we will define some functions like one for finding optimal coefficient,one for calculating cost,one for predicting output given an input using optimal coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e1d3dc06",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimal_coefficients(x_train,y_train):\n",
    "    '''\n",
    "    Takes training data as input and returns the optimal coefficient ie. m and c values for minimum cost in form of tuple (m,c)\n",
    "    '''\n",
    "    m=((x_train*y_train).mean()-(x_train.mean()*y_train.mean()))/((x_train**2).mean()-(x_train.mean()**2))\n",
    "    c=y_train.mean()-(m*x_train.mean())\n",
    "    return (m,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8bc6a125",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(x_test,m,c):\n",
    "    '''\n",
    "    Takes testing input,m,c as input and returns the y predicted following linear model\n",
    "    '''\n",
    "    return (m*x_test)+c #as x_test is array so this function returns y_predicted array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "78c2135a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def coefficient_of_determination(y_predicted,y_actual):\n",
    "    '''\n",
    "    Calculates the score of the algorithm\n",
    "    '''\n",
    "    u=((y_predicted-y_actual)**2).sum()\n",
    "    v=((y_actual-y_actual.mean())**2).sum()\n",
    "    return 1-(u/v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "572a1d20",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(x,y,m,c):\n",
    "    '''\n",
    "    Returns cost wrt m,c and given input and output\n",
    "    '''\n",
    "    return ((y-(m*x+c))**2).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbeb056b",
   "metadata": {},
   "source": [
    "Now we will use above for our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d4b233b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope :  1.3564840226402484\n",
      "Intercept :  6.566992797895509\n"
     ]
    }
   ],
   "source": [
    "m,c=get_optimal_coefficients(x_train,y_train)\n",
    "print(\"Slope : \",m)\n",
    "print(\"Intercept : \",c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "504383b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.845011865897476\n",
      "11.158986823977074\n",
      "2.2505122455839626\n",
      "17.694182701904566\n",
      "-1.2481152942803533\n",
      "-9.032840784954544\n",
      "-5.656549187904034\n",
      "8.41556667363659\n",
      "-12.337000234805046\n",
      "-12.251271011284096\n",
      "-1.4303907869317172\n",
      "-6.549367892127876\n",
      "-15.714791275177888\n",
      "10.787129282294998\n",
      "-10.486727102257248\n",
      "19.72117939691273\n",
      "2.5841613540640793\n",
      "-11.571943659685338\n",
      "-2.9632782935224\n",
      "-5.31143987459771\n",
      "-7.229549199774858\n",
      "-4.4658970696358296\n",
      "3.5105290358408894\n",
      "-0.4717284820615504\n",
      "-14.56139040910437\n"
     ]
    }
   ],
   "source": [
    "y_predicted=predict(x_test,m,c)\n",
    "for i in range(len(y_predicted)):\n",
    "    print(y_test[i]-y_predicted[i]) #so got an idea kitna far away hai y_predicted from actual y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "07c92eb7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score :  0.41773449983247557\n"
     ]
    }
   ],
   "source": [
    "print(\"Score : \",coefficient_of_determination(y_predicted,y_test)) #to get an actual score value instead of above se better idea lag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c28a7e46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost :  2746.974600484099\n"
     ]
    }
   ],
   "source": [
    "print(\"Cost : \",cost(x_test,y_test,m,c))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73025e7f",
   "metadata": {},
   "source": [
    "See variation of cost with different m values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8c59f70d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "slope_values=np.arange(-5,+5,0.01)\n",
    "cost_value=np.zeros(len(slope_values),int)\n",
    "for i in range(len(slope_values)):\n",
    "    cost_value[i]=cost(x_test,y_test,slope_values[i],c)\n",
    "plt.plot(slope_values,cost_value)\n",
    "plt.axis\n",
    "plt.xlabel(\"m--->\")\n",
    "plt.ylabel(\"cost--->\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f02cee8",
   "metadata": {},
   "source": [
    "So it is clear that m=1.35 ke liye min aa rha cost so whi kiya"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "57e58341",
   "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": [
    "#similar work wrt c->\n",
    "import matplotlib.pyplot as plt\n",
    "intercept_values=np.arange(4,10,0.01)\n",
    "cost_value=np.zeros(len(intercept_values),int)\n",
    "for i in range(len(intercept_values)):\n",
    "    cost_value[i]=cost(x_test,y_test,m,intercept_values[i])\n",
    "plt.plot(intercept_values,cost_value)\n",
    "plt.axis\n",
    "plt.xlabel(\"c--->\")\n",
    "plt.ylabel(\"cost--->\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5ce0217",
   "metadata": {},
   "source": [
    "Again clear that ek c value ke liye min hai"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d54e68e",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}