Course_2/Week_2_1_Multiple_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week 2_1: Multiple regression (Interpretation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of this first notebook is to explore multiple regression and feature engineering with existing graphlab functions.\n",
    "\n",
    "In this notebook you will use data on house sales in King County to predict prices using multiple regression. You will:\n",
    "* Use SFrames to do some feature engineering\n",
    "* Use built-in graphlab functions to compute the regression weights (coefficients/parameters)\n",
    "* Given the regression weights, predictors and outcome write a function to compute the Residual Sum of Squares\n",
    "* Look at coefficients and interpret their meanings\n",
    "* Evaluate multiple models via RSS"
   ]
  },
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] This non-commercial license of GraphLab Create is assigned to chengjun@chem.ku.dk and will expire on January 27, 2017. For commercial licensing options, visit https://dato.com/buy/.\n",
      "\n",
      "[INFO] Start server at: ipc:///tmp/graphlab_server-32502 - Server binary: /usr/local/lib/python2.7/site-packages/graphlab/unity_server - Server log: /tmp/graphlab_server_1454915892.log\n",
      "[INFO] GraphLab Server Version: 1.8.1\n",
      "[WARNING] Unable to create session in specified location: '/Users/jcj/.graphlab/artifacts'. Using: '/var/tmp/graphlab-jcj/32502/tmp_session_8970c4c9-d1e7-48be-8719-3cd9dca9b4db'\n"
     ]
    }
   ],
   "source": [
    "import graphlab\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = graphlab.SFrame('kc_house_data.gl/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sales['bedrooms_squared'] = sales['bedrooms']**2\n",
    "sales['bed_bath_rooms'] = sales['bedrooms']*sales['bathrooms']\n",
    "sales['log_sqft_living'] = np.log(sales['sqft_living'])\n",
    "sales['lat_plus_long'] = sales['lat'] + sales['long']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_data, test_data = sales.random_split(0.8, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.4466777016\n",
      "7.50390163159\n",
      "7.55027467965\n",
      "-74.6533349722\n"
     ]
    }
   ],
   "source": [
    "print test_data['bedrooms_squared'].mean()\n",
    "print test_data['bed_bath_rooms'].mean()\n",
    "print test_data['log_sqft_living'].mean()\n",
    "print test_data['lat_plus_long'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Model 1: ‘sqft_living’, ‘bedrooms’, ‘bathrooms’, ‘lat’, and ‘long’\n",
    "#Model 2: ‘sqft_living’, ‘bedrooms’, ‘bathrooms’, ‘lat’,‘long’, and ‘bed_bath_rooms’\n",
    "#Model 3: ‘sqft_living’, ‘bedrooms’, ‘bathrooms’, ‘lat’,‘long’, ‘bed_bath_rooms’, ‘bedrooms_squared’, ‘log_sqft_living’, and ‘lat_plus_long’"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning a multiple regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 17384\n",
      "PROGRESS: Number of features          : 4\n",
      "PROGRESS: Number of unpacked features : 4\n",
      "PROGRESS: Number of coefficients    : 5\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.037443     | 5853449.620139     | 294260.514511 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "# model 1\n",
    "model_1 = graphlab.linear_regression.create(train_data,\n",
    "                                           target='price',\n",
    "                                           features=['bedrooms', 'bathrooms', 'lat', 'long'],\n",
    "                                           validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 17384\n",
      "PROGRESS: Number of features          : 5\n",
      "PROGRESS: Number of unpacked features : 5\n",
      "PROGRESS: Number of coefficients    : 6\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.044404     | 5700638.852504     | 290492.952343 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "# model 2\n",
    "model_2 = graphlab.linear_regression.create(train_data,\n",
    "                                           target='price',\n",
    "                                           features=['bedrooms', 'bathrooms', 'lat', 'long', 'bed_bath_rooms'],\n",
    "                                           validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PROGRESS: Linear regression:\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: Number of examples          : 17384\n",
      "PROGRESS: Number of features          : 8\n",
      "PROGRESS: Number of unpacked features : 8\n",
      "PROGRESS: Number of coefficients    : 9\n",
      "PROGRESS: Starting Newton Method\n",
      "PROGRESS: --------------------------------------------------------\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: | 1         | 2        | 0.036926     | 5251970.041717     | 257390.979477 |\n",
      "PROGRESS: +-----------+----------+--------------+--------------------+---------------+\n",
      "PROGRESS: SUCCESS: Optimal solution found.\n",
      "PROGRESS:\n"
     ]
    }
   ],
   "source": [
    "# model 3\n",
    "model_3 = graphlab.linear_regression.create(train_data,\n",
    "                                           target='price',\n",
    "                                           features=['bedrooms', 'bathrooms', 'lat', 'long', 'bed_bath_rooms', 'bedrooms_squared', 'log_sqft_living', 'lat_plus_long'],\n",
    "                                           validation_set=None)"
   ]
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       "|      lat       |  None | 715304.419626  | 16072.4954437 |\n",
       "|      long      |  None | -92554.3230669 | 16247.8626679 |\n",
       "| bed_bath_rooms |  None | 51546.9605159  | 2394.21790502 |\n",
       "+----------------+-------+----------------+---------------+\n",
       "[6 rows x 4 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_2.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'max_error': 5853449.620139115, 'rmse': 294260.5145112174}\n",
      "{'max_error': 5700638.852503888, 'rmse': 290492.9523426828}\n",
      "{'max_error': 5251970.041716702, 'rmse': 257390.97947653994}\n"
     ]
    }
   ],
   "source": [
    "print model_1.evaluate(train_data)\n",
    "print model_2.evaluate(train_data)\n",
    "print model_3.evaluate(train_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'max_error': 4894438.0333952755, 'rmse': 282171.3588745187}\n",
      "{'max_error': 4212529.507538155, 'rmse': 277503.88834027527}\n",
      "{'max_error': 15371303.52558896, 'rmse': 339617.6663557775}\n"
     ]
    }
   ],
   "source": [
    "print model_1.evaluate(test_data)\n",
    "print model_2.evaluate(test_data)\n",
    "print model_3.evaluate(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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