Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "Implementing Linear Regression for predicting profit of a food truck given the population and profits of different cities\n",
    "- Reference: Coursera Machine Learning Andrew Ng's course "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('data\\ex1data1.txt', header = None, names = ['Population', 'Profit'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population     Profit\n",
       "count   97.000000  97.000000\n",
       "mean     8.159800   5.839135\n",
       "std      3.869884   5.510262\n",
       "min      5.026900  -2.680700\n",
       "25%      5.707700   1.986900\n",
       "50%      6.589400   4.562300\n",
       "75%      8.578100   7.046700\n",
       "max     22.203000  24.147000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>87</th>\n",
       "      <th>88</th>\n",
       "      <th>89</th>\n",
       "      <th>90</th>\n",
       "      <th>91</th>\n",
       "      <th>92</th>\n",
       "      <th>93</th>\n",
       "      <th>94</th>\n",
       "      <th>95</th>\n",
       "      <th>96</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Population</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>8.3829</td>\n",
       "      <td>7.4764</td>\n",
       "      <td>8.5781</td>\n",
       "      <td>6.4862</td>\n",
       "      <td>5.0546</td>\n",
       "      <td>...</td>\n",
       "      <td>6.00200</td>\n",
       "      <td>5.5204</td>\n",
       "      <td>5.0594</td>\n",
       "      <td>5.7077</td>\n",
       "      <td>7.6366</td>\n",
       "      <td>5.8707</td>\n",
       "      <td>5.3054</td>\n",
       "      <td>8.29340</td>\n",
       "      <td>13.3940</td>\n",
       "      <td>5.43690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Profit</th>\n",
       "      <td>17.5920</td>\n",
       "      <td>9.1302</td>\n",
       "      <td>13.6620</td>\n",
       "      <td>11.8540</td>\n",
       "      <td>6.8233</td>\n",
       "      <td>11.8860</td>\n",
       "      <td>4.3483</td>\n",
       "      <td>12.0000</td>\n",
       "      <td>6.5987</td>\n",
       "      <td>3.8166</td>\n",
       "      <td>...</td>\n",
       "      <td>0.92695</td>\n",
       "      <td>0.1520</td>\n",
       "      <td>2.8214</td>\n",
       "      <td>1.8451</td>\n",
       "      <td>4.2959</td>\n",
       "      <td>7.2029</td>\n",
       "      <td>1.9869</td>\n",
       "      <td>0.14454</td>\n",
       "      <td>9.0551</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 97 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0       1        2        3       4        5       6   \\\n",
       "Population   6.1101  5.5277   8.5186   7.0032  5.8598   8.3829  7.4764   \n",
       "Profit      17.5920  9.1302  13.6620  11.8540  6.8233  11.8860  4.3483   \n",
       "\n",
       "                 7       8       9    ...          87      88      89      90  \\\n",
       "Population   8.5781  6.4862  5.0546   ...     6.00200  5.5204  5.0594  5.7077   \n",
       "Profit      12.0000  6.5987  3.8166   ...     0.92695  0.1520  2.8214  1.8451   \n",
       "\n",
       "                91      92      93       94       95       96  \n",
       "Population  7.6366  5.8707  5.3054  8.29340  13.3940  5.43690  \n",
       "Profit      4.2959  7.2029  1.9869  0.14454   9.0551  0.61705  \n",
       "\n",
       "[2 rows x 97 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2b24645e278>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b24643eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind = 'scatter', x = 'Population', y = 'Profit', figsize = (10,7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function to compute the cost function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(X, y, theta):\n",
    "    inner_product = np.power(((X * theta.T) - y) , 2)\n",
    "    return np.sum(inner_product) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Appending 1s to the front of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.insert(0, 'Ones', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Ones</th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population   Profit\n",
       "0     1      6.1101  17.5920\n",
       "1     1      5.5277   9.1302\n",
       "2     1      8.5186  13.6620\n",
       "3     1      7.0032  11.8540\n",
       "4     1      5.8598   6.8233"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set training data (X) and target variable (y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = df.shape[1]\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.iloc[:, 0:cols-1]\n",
    "y = df.iloc[:, cols-1:cols]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Converting dataframe to numpy matrices and creating a parameter (theta) matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.matrix(X.values)\n",
    "y = np.matrix(y.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 0]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((97, 2), (97, 1), (1, 2))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, y.shape, theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, y, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function to perform gradient descent on parameters theta by repeatedly updating the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, theta, alpha, iters):\n",
    "    temp = np.matrix(np.zeros(theta.shape))\n",
    "    parameters = int(theta.ravel().shape[1])\n",
    "    cost = np.zeros(iters)\n",
    "    \n",
    "    # With each iteration, we are calculating the changes to be made to the\n",
    "    # parameter (theta) value to reduce the error (cost)\n",
    "    for i in range(iters):\n",
    "        error = (X * theta.T) - y\n",
    "        \n",
    "        # number of parameters to be calculated,here we have 2 parameters theta [0,0] and theta [0,1]\n",
    "        for j in range(parameters):\n",
    "            term  = np.multiply(error, X[:, j])\n",
    "            temp[0,j] = theta[0,j] -((alpha / len(X)) * np.sum(term))\n",
    "          \n",
    "        theta = temp\n",
    "        cost[i] = computeCost(X, y, theta)\n",
    "        \n",
    "    return theta, cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set values for learning rate and number of iterations\n",
    "- alpha here denotes the learning rate that helps to determine how quickly the algorithm\n",
    "    will converge to the optimal solution\n",
    "- iters denotes the number of iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.24140214  1.1272942 ]]\n",
      "[ 6.73719046  5.93159357  5.90115471  5.89522859  5.89009494  5.88500416\n",
      "  5.87993248  5.87487909  5.86984391  5.86482687  5.85982789  5.85484692\n",
      "  5.84988389  5.84493874  5.8400114   5.83510181  5.8302099   5.82533562\n",
      "  5.82047889  5.81563965  5.81081784  5.8060134   5.80122627  5.79645638\n",
      "  5.79170367  5.78696808  5.78224955  5.77754801  5.77286341  5.76819568\n",
      "  5.76354477  5.75891061  5.75429313  5.7496923   5.74510803  5.74054027\n",
      "  5.73598897  5.73145406  5.72693549  5.72243319  5.71794711  5.71347718\n",
      "  5.70902336  5.70458558  5.70016379  5.69575792  5.69136792  5.68699373\n",
      "  5.6826353   5.67829257  5.67396548  5.66965398  5.665358    5.6610775\n",
      "  5.65681242  5.6525627   5.64832829  5.64410913  5.63990517  5.63571635\n",
      "  5.63154261  5.62738391  5.6232402   5.6191114   5.61499748  5.61089837\n",
      "  5.60681403  5.60274441  5.59868944  5.59464907  5.59062326  5.58661195\n",
      "  5.58261509  5.57863263  5.57466451  5.57071068  5.56677109  5.5628457\n",
      "  5.55893444  5.55503727  5.55115414  5.547285    5.54342979  5.53958847\n",
      "  5.53576098  5.53194728  5.52814732  5.52436105  5.52058841  5.51682936\n",
      "  5.51308385  5.50935183  5.50563326  5.50192808  5.49823624  5.49455771\n",
      "  5.49089242  5.48724033  5.4836014   5.47997558  5.47636282  5.47276307\n",
      "  5.46917628  5.46560242  5.46204143  5.45849326  5.45495788  5.45143522\n",
      "  5.44792526  5.44442794  5.44094322  5.43747105  5.43401138  5.43056418\n",
      "  5.42712939  5.42370698  5.42029689  5.41689909  5.41351352  5.41014015\n",
      "  5.40677893  5.40342982  5.40009277  5.39676774  5.39345469  5.39015357\n",
      "  5.38686434  5.38358696  5.38032138  5.37706756  5.37382547  5.37059505\n",
      "  5.36737627  5.36416908  5.36097345  5.35778933  5.35461667  5.35145544\n",
      "  5.3483056   5.34516711  5.34203991  5.33892399  5.33581928  5.33272576\n",
      "  5.32964339  5.32657211  5.3235119   5.32046271  5.3174245   5.31439724\n",
      "  5.31138088  5.30837538  5.30538071  5.30239683  5.2994237   5.29646127\n",
      "  5.29350951  5.29056839  5.28763786  5.28471789  5.28180843  5.27890945\n",
      "  5.27602092  5.27314279  5.27027503  5.26741759  5.26457045  5.26173356\n",
      "  5.2589069   5.25609041  5.25328407  5.25048783  5.24770167  5.24492555\n",
      "  5.24215942  5.23940326  5.23665702  5.23392068  5.23119419  5.22847752\n",
      "  5.22577064  5.22307351  5.22038609  5.21770835  5.21504026  5.21238178\n",
      "  5.20973288  5.20709351  5.20446365  5.20184327  5.19923232  5.19663078\n",
      "  5.19403861  5.19145577  5.18888224  5.18631798  5.18376295  5.18121713\n",
      "  5.17868048  5.17615296  5.17363455  5.17112521  5.16862491  5.16613361\n",
      "  5.16365129  5.16117791  5.15871344  5.15625784  5.15381109  5.15137315\n",
      "  5.148944    5.14652359  5.1441119   5.1417089   5.13931455  5.13692883\n",
      "  5.1345517   5.13218314  5.1298231   5.12747157  5.1251285   5.12279388\n",
      "  5.12046766  5.11814983  5.11584034  5.11353917  5.11124629  5.10896167\n",
      "  5.10668527  5.10441708  5.10215706  5.09990518  5.0976614   5.09542571\n",
      "  5.09319808  5.09097846  5.08876685  5.08656319  5.08436748  5.08217967\n",
      "  5.07999975  5.07782768  5.07566343  5.07350697  5.07135828  5.06921734\n",
      "  5.0670841   5.06495855  5.06284065  5.06073039  5.05862772  5.05653263\n",
      "  5.05444508  5.05236505  5.05029252  5.04822745  5.04616982  5.0441196\n",
      "  5.04207676  5.04004129  5.03801314  5.0359923   5.03397874  5.03197243\n",
      "  5.02997335  5.02798147  5.02599676  5.0240192   5.02204877  5.02008543\n",
      "  5.01812917  5.01617995  5.01423775  5.01230255  5.01037431  5.00845303\n",
      "  5.00653866  5.00463119  5.00273059  5.00083684  4.9989499   4.99706977\n",
      "  4.9951964   4.99332979  4.99146989  4.9896167   4.98777018  4.98593031\n",
      "  4.98409707  4.98227043  4.98045038  4.97863687  4.9768299   4.97502944\n",
      "  4.97323547  4.97144795  4.96966687  4.96789221  4.96612395  4.96436205\n",
      "  4.96260649  4.96085726  4.95911433  4.95737768  4.95564729  4.95392312\n",
      "  4.95220517  4.95049341  4.94878781  4.94708835  4.94539502  4.94370778\n",
      "  4.94202663  4.94035152  4.93868246  4.9370194   4.93536233  4.93371123\n",
      "  4.93206608  4.93042686  4.92879354  4.9271661   4.92554453  4.92392879\n",
      "  4.92231888  4.92071476  4.91911642  4.91752384  4.915937    4.91435587\n",
      "  4.91278043  4.91121067  4.90964657  4.9080881   4.90653524  4.90498798\n",
      "  4.90344629  4.90191015  4.90037954  4.89885445  4.89733485  4.89582073\n",
      "  4.89431206  4.89280882  4.891311    4.88981857  4.88833152  4.88684982\n",
      "  4.88537346  4.88390242  4.88243668  4.88097622  4.87952102  4.87807106\n",
      "  4.87662632  4.87518678  4.87375243  4.87232325  4.87089922  4.86948031\n",
      "  4.86806652  4.86665782  4.86525419  4.86385562  4.86246208  4.86107357\n",
      "  4.85969005  4.85831152  4.85693796  4.85556934  4.85420565  4.85284687\n",
      "  4.85149299  4.85014399  4.84879984  4.84746054  4.84612606  4.84479638\n",
      "  4.8434715   4.84215138  4.84083603  4.83952541  4.83821951  4.83691831\n",
      "  4.83562181  4.83432997  4.83304278  4.83176023  4.83048231  4.82920898\n",
      "  4.82794024  4.82667607  4.82541645  4.82416138  4.82291082  4.82166476\n",
      "  4.8204232   4.8191861   4.81795347  4.81672527  4.81550149  4.81428213\n",
      "  4.81306715  4.81185656  4.81065032  4.80944843  4.80825086  4.80705761\n",
      "  4.80586866  4.80468399  4.80350359  4.80232744  4.80115553  4.79998784\n",
      "  4.79882435  4.79766505  4.79650993  4.79535897  4.79421216  4.79306948\n",
      "  4.79193091  4.79079644  4.78966606  4.78853976  4.7874175   4.7862993\n",
      "  4.78518511  4.78407495  4.78296878  4.78186659  4.78076838  4.77967412\n",
      "  4.7785838   4.77749741  4.77641493  4.77533635  4.77426166  4.77319084\n",
      "  4.77212387  4.77106075  4.77000146  4.76894598  4.7678943   4.76684642\n",
      "  4.7658023   4.76476195  4.76372535  4.76269247  4.76166332  4.76063788\n",
      "  4.75961613  4.75859806  4.75758366  4.75657291  4.7555658   4.75456232\n",
      "  4.75356245  4.75256619  4.75157351  4.75058441  4.74959887  4.74861688\n",
      "  4.74763843  4.7466635   4.74569209  4.74472417  4.74375974  4.74279878\n",
      "  4.74184129  4.74088724  4.73993663  4.73898945  4.73804567  4.7371053\n",
      "  4.73616831  4.7352347   4.73430445  4.73337755  4.73245399  4.73153376\n",
      "  4.73061684  4.72970322  4.7287929   4.72788585  4.72698207  4.72608155\n",
      "  4.72518427  4.72429022  4.72339939  4.72251177  4.72162735  4.72074611\n",
      "  4.71986805  4.71899315  4.7181214   4.71725279  4.71638731  4.71552495\n",
      "  4.71466569  4.71380953  4.71295645  4.71210645  4.71125951  4.71041561\n",
      "  4.70957476  4.70873694  4.70790213  4.70707033  4.70624153  4.70541571\n",
      "  4.70459287  4.70377299  4.70295606  4.70214208  4.70133103  4.7005229\n",
      "  4.69971768  4.69891536  4.69811593  4.69731938  4.6965257   4.69573487\n",
      "  4.6949469   4.69416177  4.69337946  4.69259997  4.69182329  4.6910494\n",
      "  4.69027831  4.68950999  4.68874444  4.68798164  4.68722159  4.68646428\n",
      "  4.6857097   4.68495784  4.68420868  4.68346223  4.68271846  4.68197737\n",
      "  4.68123895  4.68050319  4.67977008  4.67903961  4.67831177  4.67758656\n",
      "  4.67686395  4.67614395  4.67542654  4.67471172  4.67399947  4.67328979\n",
      "  4.67258266  4.67187808  4.67117604  4.67047652  4.66977953  4.66908504\n",
      "  4.66839306  4.66770357  4.66701656  4.66633203  4.66564997  4.66497036\n",
      "  4.6642932   4.66361847  4.66294618  4.66227631  4.66160885  4.6609438\n",
      "  4.66028114  4.65962087  4.65896298  4.65830745  4.65765429  4.65700348\n",
      "  4.65635502  4.65570889  4.65506509  4.6544236   4.65378443  4.65314756\n",
      "  4.65251298  4.65188069  4.65125068  4.65062293  4.64999745  4.64937422\n",
      "  4.64875324  4.64813449  4.64751797  4.64690367  4.64629158  4.6456817\n",
      "  4.64507402  4.64446852  4.64386521  4.64326406  4.64266509  4.64206827\n",
      "  4.6414736   4.64088107  4.64029068  4.63970241  4.63911626  4.63853223\n",
      "  4.63795029  4.63737046  4.63679271  4.63621704  4.63564345  4.63507192\n",
      "  4.63450245  4.63393503  4.63336966  4.63280632  4.63224501  4.63168573\n",
      "  4.63112845  4.63057319  4.63001992  4.62946865  4.62891937  4.62837206\n",
      "  4.62782672  4.62728335  4.62674193  4.62620247  4.62566495  4.62512936\n",
      "  4.62459571  4.62406397  4.62353415  4.62300624  4.62248023  4.62195612\n",
      "  4.62143389  4.62091355  4.62039507  4.61987847  4.61936373  4.61885084\n",
      "  4.6183398   4.6178306   4.61732323  4.61681769  4.61631397  4.61581207\n",
      "  4.61531197  4.61481368  4.61431718  4.61382246  4.61332954  4.61283838\n",
      "  4.612349    4.61186137  4.61137551  4.61089139  4.61040902  4.60992838\n",
      "  4.60944948  4.6089723   4.60849684  4.6080231   4.60755106  4.60708071\n",
      "  4.60661207  4.60614511  4.60567983  4.60521623  4.6047543   4.60429404\n",
      "  4.60383543  4.60337847  4.60292316  4.60246949  4.60201745  4.60156704\n",
      "  4.60111826  4.60067109  4.60022553  4.59978157  4.59933922  4.59889846\n",
      "  4.59845928  4.59802169  4.59758567  4.59715123  4.59671835  4.59628702\n",
      "  4.59585726  4.59542904  4.59500236  4.59457722  4.59415361  4.59373152\n",
      "  4.59331096  4.59289191  4.59247437  4.59205834  4.5916438   4.59123076\n",
      "  4.5908192   4.59040913  4.59000053  4.58959341  4.58918775  4.58878355\n",
      "  4.58838081  4.58797952  4.58757968  4.58718127  4.5867843   4.58638876\n",
      "  4.58599465  4.58560195  4.58521067  4.5848208   4.58443233  4.58404526\n",
      "  4.58365959  4.58327531  4.5828924   4.58251088  4.58213074  4.58175196\n",
      "  4.58137454  4.58099849  4.58062379  4.58025044  4.57987844  4.57950777\n",
      "  4.57913844  4.57877044  4.57840377  4.57803841  4.57767437  4.57731165\n",
      "  4.57695023  4.57659011  4.57623129  4.57587376  4.57551752  4.57516256\n",
      "  4.57480888  4.57445648  4.57410534  4.57375547  4.57340686  4.57305951\n",
      "  4.5727134   4.57236854  4.57202493  4.57168255  4.57134141  4.57100149\n",
      "  4.5706628   4.57032533  4.56998908  4.56965403  4.56932019  4.56898756\n",
      "  4.56865612  4.56832588  4.56799682  4.56766896  4.56734227  4.56701676\n",
      "  4.56669242  4.56636925  4.56604724  4.5657264   4.56540671  4.56508817\n",
      "  4.56477078  4.56445453  4.56413942  4.56382544  4.5635126   4.56320088\n",
      "  4.56289029  4.56258082  4.56227246  4.56196521  4.56165906  4.56135402\n",
      "  4.56105008  4.56074723  4.56044548  4.56014481  4.55984522  4.55954672\n",
      "  4.55924929  4.55895293  4.55865763  4.5583634   4.55807023  4.55777812\n",
      "  4.55748706  4.55719705  4.55690808  4.55662015  4.55633326  4.5560474\n",
      "  4.55576258  4.55547878  4.555196    4.55491424  4.55463349  4.55435376\n",
      "  4.55407503  4.55379731  4.55352058  4.55324486  4.55297012  4.55269638\n",
      "  4.55242362  4.55215185  4.55188105  4.55161123  4.55134239  4.55107451\n",
      "  4.55080759  4.55054164  4.55027664  4.5500126   4.54974951  4.54948737\n",
      "  4.54922617  4.54896591  4.54870659  4.5484482   4.54819075  4.54793422\n",
      "  4.54767862  4.54742393  4.54717017  4.54691731  4.54666537  4.54641434\n",
      "  4.54616421  4.54591498  4.54566665  4.54541921  4.54517267  4.54492701\n",
      "  4.54468224  4.54443835  4.54419534  4.5439532   4.54371194  4.54347154\n",
      "  4.54323201  4.54299334  4.54275554  4.54251859  4.54228249  4.54204724\n",
      "  4.54181284  4.54157929  4.54134657  4.5411147   4.54088366  4.54065345\n",
      "  4.54042407  4.54019552  4.53996779  4.53974088  4.53951478  4.53928951\n",
      "  4.53906504  4.53884138  4.53861853  4.53839648  4.53817523  4.53795478\n",
      "  4.53773512  4.53751625  4.53729817  4.53708088  4.53686437  4.53664864\n",
      "  4.53643368  4.5362195   4.5360061   4.53579346  4.53558158  4.53537047\n",
      "  4.53516012  4.53495053  4.53474169  4.53453361  4.53432627  4.53411968\n",
      "  4.53391384  4.53370873  4.53350437  4.53330074  4.53309784  4.53289568\n",
      "  4.53269424  4.53249353  4.53229355  4.53209428  4.53189573  4.53169789\n",
      "  4.53150077  4.53130436  4.53110866  4.53091366  4.53071936  4.53052576\n",
      "  4.53033286  4.53014066  4.52994915  4.52975832  4.52956819  4.52937874\n",
      "  4.52918997  4.52900188  4.52881447  4.52862773  4.52844167  4.52825628\n",
      "  4.52807155  4.52788749  4.52770409  4.52752136  4.52733928  4.52715786\n",
      "  4.52697709  4.52679697  4.5266175   4.52643868  4.5262605   4.52608297\n",
      "  4.52590607  4.52572981  4.52555418  4.52537919  4.52520483  4.52503109\n",
      "  4.52485799  4.5246855   4.52451364  4.52434239  4.52417177  4.52400175\n",
      "  4.52383235  4.52366356  4.52349538  4.5233278   4.52316083  4.52299446\n",
      "  4.52282868  4.52266351  4.52249893  4.52233494  4.52217154  4.52200874\n",
      "  4.52184651  4.52168488  4.52152382  4.52136335  4.52120345  4.52104413\n",
      "  4.52088538  4.5207272   4.5205696   4.52041256  4.52025609  4.52010018\n",
      "  4.51994483  4.51979004  4.51963581  4.51948214  4.51932902  4.51917645\n",
      "  4.51902443  4.51887295  4.51872203  4.51857164  4.5184218   4.5182725\n",
      "  4.51812373  4.51797551  4.51782781  4.51768065  4.51753402  4.51738791\n",
      "  4.51724233  4.51709728  4.51695275  4.51680874  4.51666525  4.51652227\n",
      "  4.51637981  4.51623786  4.51609643  4.5159555 ]\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.01\n",
    "iters = 1000\n",
    "# perform gradient descent to fit the model parameters and compute the cost\n",
    "g, cost = gradientDescent(X, y, theta, alpha, iters)\n",
    "print(g)\n",
    "print(cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5159555030789118"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, y, g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "### Using Matplotlib library to visualize our solution using scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Predicted Profit vs. Population Size')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b2465fba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# linspace function will create an evenly-spaced series of points within the range of our data\n",
    "x = np.linspace(df.Population.min(), df.Population.max(), 100)  \n",
    "f = g[0, 0] + (g[0, 1] * x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 7))  \n",
    "ax.plot(x, f, 'r', label='Prediction')  \n",
    "ax.scatter(df.Population, df.Profit, label='Traning Data')  \n",
    "ax.legend(loc=2)  \n",
    "ax.set_xlabel('Population')  \n",
    "ax.set_ylabel('Profit')  \n",
    "ax.set_title('Predicted Profit vs. Population Size')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Plotting the graph of the gradient descent function which outputs a vector with the cost at each training iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Error vs Training epoch')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b247988d30>"
      ]
     },
     "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')"
   ]
  }
 ],
 "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": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}