Chapter-3-Regression-With-Many-Inputs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Like a Machine - Chapter 3\n",
    "Linear Regression with Multiple Variables\n",
    "=================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ACKNOWLEDGEMENT**\n",
    "\n",
    "**The contents of this notebook are adapted from John D. Wittenauer's notebooks that cover the exercises in Andrew Ng's course on Machine Learning on Coursera. This is mostly Wittenauer's and Ng's work and acknowledged as such.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Use the functions from another notebook in this notebook\n",
    "%run SharedFunctions.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import our usual libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Business Problem: Predicting Housing Prices\n",
    "\n",
    "What's the market value of a house? One way to determine the market price is to collect up the prices of houses based on a few characteristics such as size in square feet and number of bedrooms. Then think like a machine and \"learn\" what the price should be based on this data.\n",
    "\n",
    "The data we have is housing prices in Portland, Oregon. Let's see what it looks like."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>Size</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Size  Bedrooms   Price\n",
       "0  2104         3  399900\n",
       "1  1600         3  329900\n",
       "2  2400         3  369000\n",
       "3  1416         2  232000\n",
       "4  3000         4  539900"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "path = os.getcwd() + '/Data/ex1data2.txt'\n",
    "data2 = pd.read_csv(path, header=None, names=['Size', 'Bedrooms', 'Price'])\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>Size</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>47.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2000.680851</td>\n",
       "      <td>3.170213</td>\n",
       "      <td>340412.659574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>794.702354</td>\n",
       "      <td>0.760982</td>\n",
       "      <td>125039.899586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>852.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>169900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1432.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>249900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1888.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>299900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2269.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>384450.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4478.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>699900.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Size   Bedrooms          Price\n",
       "count    47.000000  47.000000      47.000000\n",
       "mean   2000.680851   3.170213  340412.659574\n",
       "std     794.702354   0.760982  125039.899586\n",
       "min     852.000000   1.000000  169900.000000\n",
       "25%    1432.000000   3.000000  249900.000000\n",
       "50%    1888.000000   3.000000  299900.000000\n",
       "75%    2269.000000   4.000000  384450.000000\n",
       "max    4478.000000   5.000000  699900.000000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "852"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.Size.min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have information about 47 homes in this dataset. Each house is described by two characteristics or \"features\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11026ded0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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dQJmmvj3Ar2bme4GngGuoaX2Z+XJmjpX/Ud5Fkb4bc/xmqK8xxw8gM1+LiNuA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110217490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2.plot.scatter(x='Size', y='Price', figsize=(8,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x110351590>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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z49Fkolqgt8bkbcCCiFgbEf8nIk5t2te2cTEMHILM/Aqw8wC7FgOvNLVHgcPa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\nkiTVnGFAkqSaMwxIklRzhgFJkmru/wM+lWrm21X3rgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103acd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2.plot.scatter(x='Bedrooms', y='Price', figsize=(8,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1105191d0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DXwO2ZOZnGw51XZ8cLZZu7JfMvBBYA2yOiKVFddf1CRw5li7rk4uAN0bEvcBJ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\nwUuSVEH/H/IIgPxc4LukAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11053aa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2.plot.scatter(x='Bedrooms', y='Size', figsize=(8,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VKiRJ6plyaPp8FyP2BAovFE8Wm6QGwzrTYcCooETLd21Ok7ZNHh5iUkjwxMC4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\nJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11027ad10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3D scatter plot -- just because...\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "threedee = plt.figure(figsize=(10,8)).gca(projection='3d')\n",
    "threedee.scatter(data2['Bedrooms'], data2['Size'], data2['Price'])\n",
    "threedee.set_xlabel('Bedrooms')\n",
    "threedee.set_ylabel('Size')\n",
    "threedee.set_zlabel('Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rescale/Normalize the Data\n",
    "Notice that the size of a house in square feet is about 1,000 times the number of bedrooms it has. Similarly, the price of a house is about 100 times the size of the house. This is quite common in many datasets, but when it happens, the iterative method of gradient descent (which we'll use again) becomes inefficient. This is simply a matter of making the computations efficient. To do so, we'll do something called *feature normalization*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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>Size</th>\n",
       "      <th>Bedrooms</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.130010</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>0.475747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.504190</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>-0.084074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.502476</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>0.228626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.735723</td>\n",
       "      <td>-1.537767</td>\n",
       "      <td>-0.867025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.257476</td>\n",
       "      <td>1.090417</td>\n",
       "      <td>1.595389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Size  Bedrooms     Price\n",
       "0  0.130010 -0.223675  0.475747\n",
       "1 -0.504190 -0.223675 -0.084074\n",
       "2  0.502476 -0.223675  0.228626\n",
       "3 -0.735723 -1.537767 -0.867025\n",
       "4  1.257476  1.090417  1.595389"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Normalize the dataset\n",
    "data2Norm = (data2 - data2.mean()) / data2.std()\n",
    "data2Norm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000.6808510638298,\n",
       " 3.1702127659574466,\n",
       " 340412.6595744681,\n",
       " 794.70235353388966,\n",
       " 0.76098188678009993,\n",
       " 125039.89958640098)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's keep track of the mean and standard deviation of the house sizes, number of bedrooms, and prices in the dataset.\n",
    "# We'll need these values when we make predictions\n",
    "\n",
    "# We can get them easily for size, bedrooms and price by using data2.mean()[0], ..., [2]\n",
    "data2.mean()[0], data2.mean()[1], data2.mean()[2], data2.std()[0], data2.std()[1], data2.std()[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Define the Inputs\n",
    "In this case we have 2 inputs -- the size and number of bedrooms of the house. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Number of columns in the dataset\n",
    "cols = data2Norm.shape[1]\n",
    "# Inputs are our first two columns\n",
    "X = data2Norm.iloc[:, 0:cols-1]\n",
    "# Add an initial column of 1s to X to keep the notation simple\n",
    "X.insert(0,'x0',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>x0</th>\n",
       "      <th>Size</th>\n",
       "      <th>Bedrooms</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.130010</td>\n",
       "      <td>-0.223675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>-0.504190</td>\n",
       "      <td>-0.223675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0.502476</td>\n",
       "      <td>-0.223675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>-0.735723</td>\n",
       "      <td>-1.537767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1.257476</td>\n",
       "      <td>1.090417</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x0      Size  Bedrooms\n",
       "0   1  0.130010 -0.223675\n",
       "1   1 -0.504190 -0.223675\n",
       "2   1  0.502476 -0.223675\n",
       "3   1 -0.735723 -1.537767\n",
       "4   1  1.257476  1.090417"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Define the Output\n",
    "The output is the house price. Let's set it up as a variable y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The output\n",
    "y = data2Norm.iloc[:, cols-1:cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.475747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.084074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.228626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.867025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.595389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Price\n",
       "0  0.475747\n",
       "1 -0.084074\n",
       "2  0.228626\n",
       "3 -0.867025\n",
       "4  1.595389"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Define the Model\n",
    "We're going to stick to a simple model -- exactly the same one as before but now with an additional input:\n",
    "\n",
    "$$y = h_{\\theta}(X) = \\theta_{0} * x_{0}\\ +\\ \\theta_{1} * x_{1} +\\ \\theta_{2} * x_{2}$$\n",
    "\n",
    "It's still linear but now has more than 1 variable, hence the $x_{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Define the Parameters of the Model\n",
    "$\\theta_{0}$, $\\theta_{1}$, and $\\theta_{2}$ are the *parameters* of the model. Unlike our example of the boiling water in Chapter 1, these parameters can each take on an infinite number of values. $\\theta_{0}$ is called the *bias value*.\n",
    "\n",
    "With this model, we know exactly how to transform an input into an output -- that is, once the values of the parameters are given.\n",
    "\n",
    "Let's pick a value of X from the dataset, fix a specific value for $\\theta_{0}$ and $\\theta_{1}$, and see what we get for the value of y.\n",
    "\n",
    "Specifically, let\n",
    "$\\begin{bmatrix}\n",
    "\\theta_{0} \\\\\n",
    "\\theta_{1} \\\\\n",
    "\\theta_{2}\n",
    "\\end{bmatrix} = \n",
    "\\begin{bmatrix}\n",
    "-10 \\\\\n",
    "1 \\\\\n",
    "0\n",
    "\\end{bmatrix}$\n",
    "\n",
    "This means $\\theta_{0}$ is -10, $\\theta_{1}$ is 1, and $\\theta_{2}$ is 0.\n",
    "\n",
    "Let's try out X * theta for the first few rows of X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ -9.61836088],\n",
       "        [-12.78935942],\n",
       "        [ -7.75602841],\n",
       "        [-15.52393562],\n",
       "        [ -2.40412008]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outputs generated by our model for the first 5 inputs with the specific theta values below\n",
    "theta_test = np.matrix('-10;5;1.2')\n",
    "outputs = np.matrix(X.iloc[0:5, :]) * theta_test\n",
    "outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.475747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.084074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.228626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.867025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.595389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Price\n",
       "0  0.475747\n",
       "1 -0.084074\n",
       "2  0.228626\n",
       "3 -0.867025\n",
       "4  1.595389"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compare these outputs to the actual values of y in the dataset\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's quite a bit off from the actual values; so we know that the values for $\\theta$ in theta_test must be quite far from the optimal values for $\\theta$ -- the values that will minimize the cost of getting it wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5: Define the Cost of Getting it Wrong\n",
    "Our cost function is exactly the same as it was before for the single variable case. \n",
    "\n",
    "The cost of getting it wrong is defined as a function $J(\\theta)$:\n",
    "\n",
    "$$J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^{m} (h_{\\theta}x^{(i)}) - y^{(i)})^2$$\n",
    "\n",
    "The only difference from what we had before is in $h_{\\theta}(x)$ which as a $\\theta_{2}$ and $x_{2}$ now added as we saw above\n",
    "\n",
    "$$h_{\\theta}(X) = \\theta_{0} * x_{0}\\ +\\ \\theta_{1} * x_{1} +\\ \\theta_{2} * x_{2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "62.012999752641328"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the cost for a given set of theta values over the entire dataset\n",
    "# Get X and y in to matrix form\n",
    "computeCost(np.matrix(X.values), np.matrix(y.values), theta_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We don't know yet if this is high or low -- we'll have to try out a whole bunch of $\\theta$ values. Or better yet, we can use pick an iterative method and implement it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 6: Pick an Iterative Method to Minimize the Cost of Getting it Wrong"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, the method that will \"learn\" the optimal values for $\\theta$ is gradient descent. We don't have to do a thing to the function we wrote before for gradient descent. Let's use it to find the minimum cost and the values of $\\theta$ that result in that minimum cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "theta_init = np.matrix('10;10;10')\n",
    "# Run gradient descent for a number of different learning rates\n",
    "alpha = [0.001, 0.003, 0.01, 0.03, 0.1]\n",
    "iters = 500\n",
    "theta_ag = np.matrix(np.zeros((3,5)))\n",
    "cost_ag = np.zeros((5, iters))\n",
    "for i in range(5):\n",
    "    theta_opt, cost_min = gradientDescent(np.matrix(X.values), np.matrix(y.values), theta_init, alpha[i], iters)\n",
    "    theta_ag[:,i] = theta_opt\n",
    "    cost_ag[i,:] = cost_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ -1.05548614e-16],\n",
       "        [  8.84765988e-01],\n",
       "        [ -5.31788195e-02]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_ag[:, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#cost_ag[4,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ -1.05548614e-16],\n",
       "        [  8.84765988e-01],\n",
       "        [ -5.31788195e-02]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the value of theta for the last iteration above -- hence for alpha = 0.1\n",
    "theta_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13068648053904194"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The last cost of the last iteration is the minimum that gradient descent was able to find\n",
    "# See cost_ag[:,4] above to check the structure of this output\n",
    "cost_min[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11099a1d0>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1JXzAK5m2Vp7Ay+rFm7XeYm2HTTyYpyxzjs6m4ZLaUjsXQogsxmWJXCk1BPgM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\nxdMjE8aNJXLAENxDhuI+aTBGbOsndRIiHEmJnCNfNb1RXMi9eTk8n9G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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107aff90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,5))\n",
    "ax.plot(np.arange(iters), cost_ag[0,:], 'g', label=\"alpha = 0.001\")\n",
    "ax.plot(np.arange(iters), cost_ag[1,:], 'r', label=\"alpha = 0.003\")\n",
    "ax.plot(np.arange(iters), cost_ag[2,:], 'y', label=\"alpha = 0.01\")\n",
    "ax.plot(np.arange(iters), cost_ag[3,:], 'b', label=\"alpha = 0.03\")\n",
    "ax.plot(np.arange(iters), cost_ag[4,:], 'c', label=\"alpha = 0.1\")\n",
    "ax.set_xlabel('Iterations')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.legend()\n",
    "ax.set_title('How Costs Fall as Alpha is Changed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Results\n",
    "\n",
    "It looks like a learning rate ($\\alpha$ value) greater than 0.003 is good enough to get our iterative gradient descent to plunge down to arrive at the lowest cost value and stay there. \n",
    "\n",
    "Let's make some predictions...What is our prediction for a house that is 5,000 square feet in size with 4 bedrooms? Let's plug these in to our model and use the optimal $\\theta$ values we've calculated above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Price:               750,700\n"
     ]
    }
   ],
   "source": [
    "# Change size and num_bedrooms to make distinct predictions\n",
    "size = 5000\n",
    "num_bedrooms = 4\n",
    "\n",
    "# Remember we've run the model using rescaled house sizes and number of bedrooms\n",
    "# So we should scale the inputs down and then scale the prediction up when we're done\n",
    "size_scaled = (size - data2.mean()[0])/data2.std()[0]\n",
    "beds_scaled = (num_bedrooms - data2.mean()[1])/data2.std()[1]\n",
    "\n",
    "# This is our model -- we're just using it here to make a calculation\n",
    "pred_price = (theta_opt.item(0,0) * 1) + (theta_opt.item(1,0) * size_scaled) + (theta_opt.item(2,0) * beds_scaled)\n",
    "\n",
    "# Now we re-re-scale the price to convert it back to the right order of magnitude\n",
    "pred_price_real = (pred_price * data2.std()[2]) + data2.mean()[2]\n",
    "\n",
    "# Format and print the result\n",
    "print \"Predicted Price: \", '{:20,.0f}'.format(math.ceil(pred_price_real))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll notice that the predicted prices are mostly driven by the size of the house; the number of bedrooms don't matter as much. In fact, there's something strange going on in our model; for a fixed house size, the price seems to go down as the number of bedrooms goes up! "
   ]
  }
 ],
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