Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinay Least Square Method\n",
    "\n",
    "Y=b+mX\n",
    "\n",
    "\n",
    "we will need to min the sum all of all errors\n",
    "\n",
    "D=SUM(d^2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import Libraries\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (20.0, 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(237, 4)\n"
     ]
    },
    {
     "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>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0       1          1             4512                 1530\n",
       "1       1          1             3738                 1297\n",
       "2       1          1             4261                 1335\n",
       "3       1          1             3777                 1282\n",
       "4       1          1             4177                 1590"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reading Data\n",
    "data = pd.read_csv('headbrain.csv')\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=data['Head Size(cm^3)'].values\n",
    "Y=data['Brain Weight(grams)'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.26342933948939945 325.57342104944223\n"
     ]
    }
   ],
   "source": [
    "numerator=0\n",
    "denominator=0\n",
    "\n",
    "mean_X=np.mean(X)\n",
    "mean_y=np.mean(Y)\n",
    "for i in range(len(X)):\n",
    "    numerator+=(X[i]-mean_X)*(Y[i]-mean_y)\n",
    "    denominator+=(X[i]-mean_X)**2\n",
    "b1=numerator/denominator\n",
    "b0=mean_y-(mean_X*b1)\n",
    "print(b1,b0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16c28531cf8>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_x = np.max(X) + 100\n",
    "min_x = np.min(X) - 100\n",
    "\n",
    "# Calculating line values x and y\n",
    "x = np.linspace(min_x, max_x, 1000)\n",
    "y = b0 + b1 * x\n",
    "\n",
    "# Ploting Line\n",
    "plt.plot(x, y, color='#58b970', label='Regression Line')\n",
    "# Ploting Scatter Points\n",
    "plt.scatter(X, Y, c='#ef5423', label='Scatter Plot')\n",
    "\n",
    "plt.xlabel('Head Size in cm3')\n",
    "plt.ylabel('Brain Weight in grams')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "rmse=0\n",
    "for i in range(len(X)):\n",
    "    Y_pred=b0+b1*X[i]\n",
    "    rmse+=(Y[i]-Y_pred)**2\n",
    "rmse=np.sqrt(rmse/len(X))\n",
    "print(rmse)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6393117199570003\n"
     ]
    }
   ],
   "source": [
    "ss_t = 0\n",
    "ss_r = 0\n",
    "for i in range(len(X)):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    ss_t += (Y[i] - mean_y) ** 2\n",
    "    ss_r += (Y[i] - y_pred) ** 2\n",
    "r2 = 1 - (ss_r/ss_t)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using SkLearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=X.reshape((len(X),1))\n",
    "model=LinearRegression()\n",
    "model=model.fit(X,Y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred=model.predict(X)\n",
    "mse=mean_squared_error(Y,Y_pred)\n",
    "root_mse=np.sqrt(mse)\n",
    "r2=model.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.639311719957 72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "print(r2,root_mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Multivariate Linear Regresion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.read_csv('student.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 3)\n"
     ]
    },
    {
     "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>Math</th>\n",
       "      <th>Reading</th>\n",
       "      <th>Writing</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>48</td>\n",
       "      <td>68</td>\n",
       "      <td>63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>62</td>\n",
       "      <td>81</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>76</td>\n",
       "      <td>83</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>59</td>\n",
       "      <td>64</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Math  Reading  Writing\n",
       "0    48       68       63\n",
       "1    62       81       72\n",
       "2    79       80       78\n",
       "3    76       83       79\n",
       "4    59       64       62"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "math = data['Math'].values\n",
    "read = data['Reading'].values\n",
    "write = data['Writing'].values\n",
    "m = len(math)\n",
    "x0 = np.ones(m)\n",
    "X = np.array([x0, math, read]).T\n",
    "# Initial Coefficients\n",
    "B = np.array([0, 0, 0])\n",
    "Y = np.array(write)\n",
    "alpha = 0.0001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(X, Y, B):\n",
    "    m = len(Y)\n",
    "    J = np.sum((X.dot(B) - Y) ** 2)/(2 * m)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2470.11"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_function(X,Y,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, Y, B, alpha, iterations):\n",
    "    cost_history = [0] * iterations\n",
    "    m = len(Y)\n",
    "    \n",
    "    for iteration in range(iterations):\n",
    "        # Hypothesis Values\n",
    "        h = X.dot(B)\n",
    "        # Difference b/w Hypothesis and Actual Y\n",
    "        loss = h - Y\n",
    "        # Gradient Calculation\n",
    "        gradient = X.T.dot(loss) / m\n",
    "        # Changing Values of B using Gradient\n",
    "        B = B - alpha * gradient\n",
    "        # New Cost Value\n",
    "        cost = cost_function(X, Y, B)\n",
    "        cost_history[iteration] = cost      \n",
    "    return B, cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\constantin\\Anaconda3\\envs\\keras\\lib\\site-packages\\numpy\\core\\fromnumeric.py:90: RuntimeWarning: overflow encountered in reduce\n",
      "  return ufunc.reduce(obj, axis, dtype, out, **passkwargs)\n",
      "C:\\Users\\constantin\\Anaconda3\\envs\\keras\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in square\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\Users\\constantin\\Anaconda3\\envs\\keras\\lib\\site-packages\\ipykernel_launcher.py:13: RuntimeWarning: invalid value encountered in subtract\n",
      "  del sys.path[0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[nan nan nan]\n",
      "nan\n"
     ]
    }
   ],
   "source": [
    "# 100000 Iterations\n",
    "newB, cost_history = gradient_descent(X, Y, B, 0.001, 100000)\n",
    "\n",
    "# New Values of B\n",
    "print(newB)\n",
    "\n",
    "# Final Cost of new B\n",
    "print(cost_history[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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