Linear Regression From Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "Linear regression is used for finding linear relationship between target and one or more predictors. There are two types of linear regression- Simple and Multiple.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression : real valued output\n",
    "### Classification : Discrete valued (0/1) , Outputs the classes in which the given example belongs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src = 'https://d3c33hcgiwev3.cloudfront.net/imageAssetProxy.v1/bn9SyaDIEeav5QpTGIv-Pg_0d06dca3d225f3de8b5a4a7e92254153_Screenshot-2016-11-01-23.48.26.png?expiry=1530662400000&hmac=ebCW6nOYGNKDJtgnOZpWq5DptJfqVOitgcrbRBtjU3M'/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hours</th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.5</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.2</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.5</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.5</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Hours  Scores\n",
       "0    2.5      21\n",
       "1    5.1      47\n",
       "2    3.2      27\n",
       "3    8.5      75\n",
       "4    3.5      30"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.getcwd() + '/student_scores.csv'  \n",
    "data = pd.read_csv(path)  \n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hours</th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.012000</td>\n",
       "      <td>51.480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.525094</td>\n",
       "      <td>25.286887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.100000</td>\n",
       "      <td>17.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.700000</td>\n",
       "      <td>30.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.800000</td>\n",
       "      <td>47.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.400000</td>\n",
       "      <td>75.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.200000</td>\n",
       "      <td>95.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Hours     Scores\n",
       "count  25.000000  25.000000\n",
       "mean    5.012000  51.480000\n",
       "std     2.525094  25.286887\n",
       "min     1.100000  17.000000\n",
       "25%     2.700000  30.000000\n",
       "50%     4.800000  47.000000\n",
       "75%     7.400000  75.000000\n",
       "max     9.200000  95.000000"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7ff32f646630>"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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I8miS+5M83Fp7YZJHkrx1wHwA9MwOi8BxMEjBrqqTSb6vtfbuJGmtfbm19oUkr07ywPxp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff32f5b2a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind='scatter', x='Hours', y='Scores', figsize=(12,8))  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 0]])"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2)"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data.insert(0, 'Ones', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Hours</th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2.5</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3.2</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Hours  Scores\n",
       "0     1    2.5      21\n",
       "1     1    5.1      47\n",
       "2     1    3.2      27\n",
       "3     1    8.5      75\n",
       "4     1    3.5      30"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Hours</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Hours\n",
       "0     1    2.5\n",
       "1     1    5.1\n",
       "2     1    3.2\n",
       "3     1    8.5\n",
       "4     1    3.5"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data.iloc[:,0:cols-1]  \n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Scores\n",
       "0      21\n",
       "1      47\n",
       "2      27\n",
       "3      75\n",
       "4      30"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data.iloc[:,cols-1:cols]\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.matrix(X.values)  \n",
    "y = np.matrix(y.values) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 2), (1, 2), (25, 1))"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, theta.shape, y.shape  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def computecost(X,y,theta):\n",
    "    inner=np.power(((X*theta.T)-y),2)\n",
    "    suminner=np.sum(inner)\n",
    "    return suminner/(2*len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1632.02"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computecost(X,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradient(X,y,theta,alpha,iters):\n",
    "    temp=np.matrix(np.zeros(theta.shape))\n",
    "    parameter=int(theta.shape[1])\n",
    "    cost=np.zeros(iters)\n",
    "    for i in range(iters):\n",
    "        error=(X*theta.T)-y\n",
    "        for j in range(parameter):\n",
    "            term=np.multiply(error,X[:,j])\n",
    "            temp[0,j]=theta[0,j]-((alpha/len(X))*np.sum(term))\n",
    "        theta = temp\n",
    "        cost[i]=computecost(X,y,theta)\n",
    "    return theta,cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha=0.04\n",
    "iters=2000\n",
    "theta , cost=gradient(X,y,theta,alpha,iters)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 2.48367321,  9.77580342]])"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000,)"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.441365254622738"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computecost(X,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "x = np.linspace(data.Hours.min(), data.Hours.max(), 100) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_pred=theta[0,0]+(theta[0,1]*x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ff32f5440f0>"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ZJ5xwAkceeeTXXufrrvt17z3hhBPo3bs33bt3Z/fdd+fAAw+kffv2X5vtJz/5CWVlZaTT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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff32f5de048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))  \n",
    "ax.plot(x, y_pred, label='Prediction')  \n",
    "ax.scatter(data.Hours, data.Scores ,label='Traning Data')  \n",
    "ax.legend(loc=2)  \n",
    "ax.set_xlabel('Hours')  \n",
    "ax.set_ylabel('Scores')  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 2.48367321,  9.77580342]])"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ff32f4c39e8>"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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53id29+4k6e5bk5w4LX9Ykps3rHfLtAwAAGZvx6oHkKQP5Um7du265/ba2lrW1ta2aDgA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff32f557390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))  \n",
    "ax.plot(np.arange(iters), cost, 'r')  \n",
    "ax.set_xlabel('Iterations')  \n",
    "ax.set_ylabel('Cost')  \n",
    "ax.set_title('Error vs. Training Epoch')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}