Machine Learning - Supervised - Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Steps "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    1. Getting and setting up the data.\n",
    "    2. Visualizing current data.\n",
    "    3. The mathematics behind the Least Squares Method.\n",
    "    4. Using Numpy for a Univariate Linear Regression.\n",
    "    5. Getting the error.\n",
    "    6. Using scikit learn to implement a multivariate regression.\n",
    "    7. Using Training and Validation.  \n",
    "    8. Predicting Prices\n",
    "    9. Residual Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pandas import Series, DataFrame\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Grab boston dataset from the scikit learn\n",
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston House Prices dataset\n",
      "\n",
      "Notes\n",
      "------\n",
      "Data Set Characteristics:  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive\n",
      "    \n",
      "    :Median Value (attribute 14) is usually the target\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "http://archive.ics.uci.edu/ml/datasets/Housing\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      "**References**\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print boston.DESCR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 2 - Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10b234a90>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAERCAYAAAB7FtAjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b1e2150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of Prices\n",
    "# target is specific to boston dataset\n",
    "plt.hist(boston.target, bins = 50)\n",
    "\n",
    "plt.xlabel('Prices in $1000s')\n",
    "plt.ylabel('Number of Houses')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10b1c6bd0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAERCAYAAAB7FtAjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEARBEABRCIIgCIKFKARBEAQBgP8H8dPM3Q75hKMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b51fb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# single feature vs the targe \n",
    "# housing price vs the average room per dwelling\n",
    "\n",
    "plt.scatter(boston.data[:,5], boston.target)\n",
    "plt.ylabel('Price in 1000s')\n",
    "plt.xlabel('Number of Rooms')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM  ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  \n",
       "0  396.90   4.98  \n",
       "1  396.90   9.14  \n",
       "2  392.83   4.03  \n",
       "3  394.63   2.94  \n",
       "4  396.90   5.33  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Grab Data with pandas\n",
    "boston_df = DataFrame(boston.data)\n",
    "# set columns names fron boston datset\n",
    "boston_df.columns = boston.feature_names\n",
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM  ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  Price  \n",
       "0  396.90   4.98   24.0  \n",
       "1  396.90   9.14   21.6  \n",
       "2  392.83   4.03   34.7  \n",
       "3  394.63   2.94   33.4  \n",
       "4  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add a new columb to demonstrate the price\n",
    "boston_df['Price']=boston.target\n",
    "\n",
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x10b6dafd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWEAAAFhCAYAAACh/xvXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b3f4c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# linear fit room vs the price\n",
    "\n",
    "sns.lmplot('RM','Price', data=boston_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3: The mathematics LSM\n",
    "https://www.youtube.com/watch?v=Qa2APhWjQPc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Step 4 : Using Numpy for a Univariate Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      6.575\n",
       "1      6.421\n",
       "2      7.185\n",
       "3      6.998\n",
       "4      7.147\n",
       "5      6.430\n",
       "6      6.012\n",
       "7      6.172\n",
       "8      5.631\n",
       "9      6.004\n",
       "10     6.377\n",
       "11     6.009\n",
       "12     5.889\n",
       "13     5.949\n",
       "14     6.096\n",
       "15     5.834\n",
       "16     5.935\n",
       "17     5.990\n",
       "18     5.456\n",
       "19     5.727\n",
       "20     5.570\n",
       "21     5.965\n",
       "22     6.142\n",
       "23     5.813\n",
       "24     5.924\n",
       "25     5.599\n",
       "26     5.813\n",
       "27     6.047\n",
       "28     6.495\n",
       "29     6.674\n",
       "       ...  \n",
       "476    6.484\n",
       "477    5.304\n",
       "478    6.185\n",
       "479    6.229\n",
       "480    6.242\n",
       "481    6.750\n",
       "482    7.061\n",
       "483    5.762\n",
       "484    5.871\n",
       "485    6.312\n",
       "486    6.114\n",
       "487    5.905\n",
       "488    5.454\n",
       "489    5.414\n",
       "490    5.093\n",
       "491    5.983\n",
       "492    5.983\n",
       "493    5.707\n",
       "494    5.926\n",
       "495    5.670\n",
       "496    5.390\n",
       "497    5.794\n",
       "498    6.019\n",
       "499    5.569\n",
       "500    6.027\n",
       "501    6.593\n",
       "502    6.120\n",
       "503    6.976\n",
       "504    6.794\n",
       "505    6.030\n",
       "Name: RM, dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = boston_df.RM  #Room Values\n",
    "X.shape\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.vstack(boston_df.RM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.575],\n",
       "       [ 6.421],\n",
       "       [ 7.185],\n",
       "       [ 6.998],\n",
       "       [ 7.147],\n",
       "       [ 6.43 ],\n",
       "       [ 6.012],\n",
       "       [ 6.172],\n",
       "       [ 5.631],\n",
       "       [ 6.004],\n",
       "       [ 6.377],\n",
       "       [ 6.009],\n",
       "       [ 5.889],\n",
       "       [ 5.949],\n",
       "       [ 6.096],\n",
       "       [ 5.834],\n",
       "       [ 5.935],\n",
       "       [ 5.99 ],\n",
       "       [ 5.456],\n",
       "       [ 5.727],\n",
       "       [ 5.57 ],\n",
       "       [ 5.965],\n",
       "       [ 6.142],\n",
       "       [ 5.813],\n",
       "       [ 5.924],\n",
       "       [ 5.599],\n",
       "       [ 5.813],\n",
       "       [ 6.047],\n",
       "       [ 6.495],\n",
       "       [ 6.674],\n",
       "       [ 5.713],\n",
       "       [ 6.072],\n",
       "       [ 5.95 ],\n",
       "       [ 5.701],\n",
       "       [ 6.096],\n",
       "       [ 5.933],\n",
       "       [ 5.841],\n",
       "       [ 5.85 ],\n",
       "       [ 5.966],\n",
       "       [ 6.595],\n",
       "       [ 7.024],\n",
       "       [ 6.77 ],\n",
       "       [ 6.169],\n",
       "       [ 6.211],\n",
       "       [ 6.069],\n",
       "       [ 5.682],\n",
       "       [ 5.786],\n",
       "       [ 6.03 ],\n",
       "       [ 5.399],\n",
       "       [ 5.602],\n",
       "       [ 5.963],\n",
       "       [ 6.115],\n",
       "       [ 6.511],\n",
       "       [ 5.998],\n",
       "       [ 5.888],\n",
       "       [ 7.249],\n",
       "       [ 6.383],\n",
       "       [ 6.816],\n",
       "       [ 6.145],\n",
       "       [ 5.927],\n",
       "       [ 5.741],\n",
       "       [ 5.966],\n",
       "       [ 6.456],\n",
       "       [ 6.762],\n",
       "       [ 7.104],\n",
       "       [ 6.29 ],\n",
       "       [ 5.787],\n",
       "       [ 5.878],\n",
       "       [ 5.594],\n",
       "       [ 5.885],\n",
       "       [ 6.417],\n",
       "       [ 5.961],\n",
       "       [ 6.065],\n",
       "       [ 6.245],\n",
       "       [ 6.273],\n",
       "       [ 6.286],\n",
       "       [ 6.279],\n",
       "       [ 6.14 ],\n",
       "       [ 6.232],\n",
       "       [ 5.874],\n",
       "       [ 6.727],\n",
       "       [ 6.619],\n",
       "       [ 6.302],\n",
       "       [ 6.167],\n",
       "       [ 6.389],\n",
       "       [ 6.63 ],\n",
       "       [ 6.015],\n",
       "       [ 6.121],\n",
       "       [ 7.007],\n",
       "       [ 7.079],\n",
       "       [ 6.417],\n",
       "       [ 6.405],\n",
       "       [ 6.442],\n",
       "       [ 6.211],\n",
       "       [ 6.249],\n",
       "       [ 6.625],\n",
       "       [ 6.163],\n",
       "       [ 8.069],\n",
       "       [ 7.82 ],\n",
       "       [ 7.416],\n",
       "       [ 6.727],\n",
       "       [ 6.781],\n",
       "       [ 6.405],\n",
       "       [ 6.137],\n",
       "       [ 6.167],\n",
       "       [ 5.851],\n",
       "       [ 5.836],\n",
       "       [ 6.127],\n",
       "       [ 6.474],\n",
       "       [ 6.229],\n",
       "       [ 6.195],\n",
       "       [ 6.715],\n",
       "       [ 5.913],\n",
       "       [ 6.092],\n",
       "       [ 6.254],\n",
       "       [ 5.928],\n",
       "       [ 6.176],\n",
       "       [ 6.021],\n",
       "       [ 5.872],\n",
       "       [ 5.731],\n",
       "       [ 5.87 ],\n",
       "       [ 6.004],\n",
       "       [ 5.961],\n",
       "       [ 5.856],\n",
       "       [ 5.879],\n",
       "       [ 5.986],\n",
       "       [ 5.613],\n",
       "       [ 5.693],\n",
       "       [ 6.431],\n",
       "       [ 5.637],\n",
       "       [ 6.458],\n",
       "       [ 6.326],\n",
       "       [ 6.372],\n",
       "       [ 5.822],\n",
       "       [ 5.757],\n",
       "       [ 6.335],\n",
       "       [ 5.942],\n",
       "       [ 6.454],\n",
       "       [ 5.857],\n",
       "       [ 6.151],\n",
       "       [ 6.174],\n",
       "       [ 5.019],\n",
       "       [ 5.403],\n",
       "       [ 5.468],\n",
       "       [ 4.903],\n",
       "       [ 6.13 ],\n",
       "       [ 5.628],\n",
       "       [ 4.926],\n",
       "       [ 5.186],\n",
       "       [ 5.597],\n",
       "       [ 6.122],\n",
       "       [ 5.404],\n",
       "       [ 5.012],\n",
       "       [ 5.709],\n",
       "       [ 6.129],\n",
       "       [ 6.152],\n",
       "       [ 5.272],\n",
       "       [ 6.943],\n",
       "       [ 6.066],\n",
       "       [ 6.51 ],\n",
       "       [ 6.25 ],\n",
       "       [ 7.489],\n",
       "       [ 7.802],\n",
       "       [ 8.375],\n",
       "       [ 5.854],\n",
       "       [ 6.101],\n",
       "       [ 7.929],\n",
       "       [ 5.877],\n",
       "       [ 6.319],\n",
       "       [ 6.402],\n",
       "       [ 5.875],\n",
       "       [ 5.88 ],\n",
       "       [ 5.572],\n",
       "       [ 6.416],\n",
       "       [ 5.859],\n",
       "       [ 6.546],\n",
       "       [ 6.02 ],\n",
       "       [ 6.315],\n",
       "       [ 6.86 ],\n",
       "       [ 6.98 ],\n",
       "       [ 7.765],\n",
       "       [ 6.144],\n",
       "       [ 7.155],\n",
       "       [ 6.563],\n",
       "       [ 5.604],\n",
       "       [ 6.153],\n",
       "       [ 7.831],\n",
       "       [ 6.782],\n",
       "       [ 6.556],\n",
       "       [ 7.185],\n",
       "       [ 6.951],\n",
       "       [ 6.739],\n",
       "       [ 7.178],\n",
       "       [ 6.8  ],\n",
       "       [ 6.604],\n",
       "       [ 7.875],\n",
       "       [ 7.287],\n",
       "       [ 7.107],\n",
       "       [ 7.274],\n",
       "       [ 6.975],\n",
       "       [ 7.135],\n",
       "       [ 6.162],\n",
       "       [ 7.61 ],\n",
       "       [ 7.853],\n",
       "       [ 8.034],\n",
       "       [ 5.891],\n",
       "       [ 6.326],\n",
       "       [ 5.783],\n",
       "       [ 6.064],\n",
       "       [ 5.344],\n",
       "       [ 5.96 ],\n",
       "       [ 5.404],\n",
       "       [ 5.807],\n",
       "       [ 6.375],\n",
       "       [ 5.412],\n",
       "       [ 6.182],\n",
       "       [ 5.888],\n",
       "       [ 6.642],\n",
       "       [ 5.951],\n",
       "       [ 6.373],\n",
       "       [ 6.951],\n",
       "       [ 6.164],\n",
       "       [ 6.879],\n",
       "       [ 6.618],\n",
       "       [ 8.266],\n",
       "       [ 8.725],\n",
       "       [ 8.04 ],\n",
       "       [ 7.163],\n",
       "       [ 7.686],\n",
       "       [ 6.552],\n",
       "       [ 5.981],\n",
       "       [ 7.412],\n",
       "       [ 8.337],\n",
       "       [ 8.247],\n",
       "       [ 6.726],\n",
       "       [ 6.086],\n",
       "       [ 6.631],\n",
       "       [ 7.358],\n",
       "       [ 6.481],\n",
       "       [ 6.606],\n",
       "       [ 6.897],\n",
       "       [ 6.095],\n",
       "       [ 6.358],\n",
       "       [ 6.393],\n",
       "       [ 5.593],\n",
       "       [ 5.605],\n",
       "       [ 6.108],\n",
       "       [ 6.226],\n",
       "       [ 6.433],\n",
       "       [ 6.718],\n",
       "       [ 6.487],\n",
       "       [ 6.438],\n",
       "       [ 6.957],\n",
       "       [ 8.259],\n",
       "       [ 6.108],\n",
       "       [ 5.876],\n",
       "       [ 7.454],\n",
       "       [ 8.704],\n",
       "       [ 7.333],\n",
       "       [ 6.842],\n",
       "       [ 7.203],\n",
       "       [ 7.52 ],\n",
       "       [ 8.398],\n",
       "       [ 7.327],\n",
       "       [ 7.206],\n",
       "       [ 5.56 ],\n",
       "       [ 7.014],\n",
       "       [ 8.297],\n",
       "       [ 7.47 ],\n",
       "       [ 5.92 ],\n",
       "       [ 5.856],\n",
       "       [ 6.24 ],\n",
       "       [ 6.538],\n",
       "       [ 7.691],\n",
       "       [ 6.758],\n",
       "       [ 6.854],\n",
       "       [ 7.267],\n",
       "       [ 6.826],\n",
       "       [ 6.482],\n",
       "       [ 6.812],\n",
       "       [ 7.82 ],\n",
       "       [ 6.968],\n",
       "       [ 7.645],\n",
       "       [ 7.923],\n",
       "       [ 7.088],\n",
       "       [ 6.453],\n",
       "       [ 6.23 ],\n",
       "       [ 6.209],\n",
       "       [ 6.315],\n",
       "       [ 6.565],\n",
       "       [ 6.861],\n",
       "       [ 7.148],\n",
       "       [ 6.63 ],\n",
       "       [ 6.127],\n",
       "       [ 6.009],\n",
       "       [ 6.678],\n",
       "       [ 6.549],\n",
       "       [ 5.79 ],\n",
       "       [ 6.345],\n",
       "       [ 7.041],\n",
       "       [ 6.871],\n",
       "       [ 6.59 ],\n",
       "       [ 6.495],\n",
       "       [ 6.982],\n",
       "       [ 7.236],\n",
       "       [ 6.616],\n",
       "       [ 7.42 ],\n",
       "       [ 6.849],\n",
       "       [ 6.635],\n",
       "       [ 5.972],\n",
       "       [ 4.973],\n",
       "       [ 6.122],\n",
       "       [ 6.023],\n",
       "       [ 6.266],\n",
       "       [ 6.567],\n",
       "       [ 5.705],\n",
       "       [ 5.914],\n",
       "       [ 5.782],\n",
       "       [ 6.382],\n",
       "       [ 6.113],\n",
       "       [ 6.426],\n",
       "       [ 6.376],\n",
       "       [ 6.041],\n",
       "       [ 5.708],\n",
       "       [ 6.415],\n",
       "       [ 6.431],\n",
       "       [ 6.312],\n",
       "       [ 6.083],\n",
       "       [ 5.868],\n",
       "       [ 6.333],\n",
       "       [ 6.144],\n",
       "       [ 5.706],\n",
       "       [ 6.031],\n",
       "       [ 6.316],\n",
       "       [ 6.31 ],\n",
       "       [ 6.037],\n",
       "       [ 5.869],\n",
       "       [ 5.895],\n",
       "       [ 6.059],\n",
       "       [ 5.985],\n",
       "       [ 5.968],\n",
       "       [ 7.241],\n",
       "       [ 6.54 ],\n",
       "       [ 6.696],\n",
       "       [ 6.874],\n",
       "       [ 6.014],\n",
       "       [ 5.898],\n",
       "       [ 6.516],\n",
       "       [ 6.635],\n",
       "       [ 6.939],\n",
       "       [ 6.49 ],\n",
       "       [ 6.579],\n",
       "       [ 5.884],\n",
       "       [ 6.728],\n",
       "       [ 5.663],\n",
       "       [ 5.936],\n",
       "       [ 6.212],\n",
       "       [ 6.395],\n",
       "       [ 6.127],\n",
       "       [ 6.112],\n",
       "       [ 6.398],\n",
       "       [ 6.251],\n",
       "       [ 5.362],\n",
       "       [ 5.803],\n",
       "       [ 8.78 ],\n",
       "       [ 3.561],\n",
       "       [ 4.963],\n",
       "       [ 3.863],\n",
       "       [ 4.97 ],\n",
       "       [ 6.683],\n",
       "       [ 7.016],\n",
       "       [ 6.216],\n",
       "       [ 5.875],\n",
       "       [ 4.906],\n",
       "       [ 4.138],\n",
       "       [ 7.313],\n",
       "       [ 6.649],\n",
       "       [ 6.794],\n",
       "       [ 6.38 ],\n",
       "       [ 6.223],\n",
       "       [ 6.968],\n",
       "       [ 6.545],\n",
       "       [ 5.536],\n",
       "       [ 5.52 ],\n",
       "       [ 4.368],\n",
       "       [ 5.277],\n",
       "       [ 4.652],\n",
       "       [ 5.   ],\n",
       "       [ 4.88 ],\n",
       "       [ 5.39 ],\n",
       "       [ 5.713],\n",
       "       [ 6.051],\n",
       "       [ 5.036],\n",
       "       [ 6.193],\n",
       "       [ 5.887],\n",
       "       [ 6.471],\n",
       "       [ 6.405],\n",
       "       [ 5.747],\n",
       "       [ 5.453],\n",
       "       [ 5.852],\n",
       "       [ 5.987],\n",
       "       [ 6.343],\n",
       "       [ 6.404],\n",
       "       [ 5.349],\n",
       "       [ 5.531],\n",
       "       [ 5.683],\n",
       "       [ 4.138],\n",
       "       [ 5.608],\n",
       "       [ 5.617],\n",
       "       [ 6.852],\n",
       "       [ 5.757],\n",
       "       [ 6.657],\n",
       "       [ 4.628],\n",
       "       [ 5.155],\n",
       "       [ 4.519],\n",
       "       [ 6.434],\n",
       "       [ 6.782],\n",
       "       [ 5.304],\n",
       "       [ 5.957],\n",
       "       [ 6.824],\n",
       "       [ 6.411],\n",
       "       [ 6.006],\n",
       "       [ 5.648],\n",
       "       [ 6.103],\n",
       "       [ 5.565],\n",
       "       [ 5.896],\n",
       "       [ 5.837],\n",
       "       [ 6.202],\n",
       "       [ 6.193],\n",
       "       [ 6.38 ],\n",
       "       [ 6.348],\n",
       "       [ 6.833],\n",
       "       [ 6.425],\n",
       "       [ 6.436],\n",
       "       [ 6.208],\n",
       "       [ 6.629],\n",
       "       [ 6.461],\n",
       "       [ 6.152],\n",
       "       [ 5.935],\n",
       "       [ 5.627],\n",
       "       [ 5.818],\n",
       "       [ 6.406],\n",
       "       [ 6.219],\n",
       "       [ 6.485],\n",
       "       [ 5.854],\n",
       "       [ 6.459],\n",
       "       [ 6.341],\n",
       "       [ 6.251],\n",
       "       [ 6.185],\n",
       "       [ 6.417],\n",
       "       [ 6.749],\n",
       "       [ 6.655],\n",
       "       [ 6.297],\n",
       "       [ 7.393],\n",
       "       [ 6.728],\n",
       "       [ 6.525],\n",
       "       [ 5.976],\n",
       "       [ 5.936],\n",
       "       [ 6.301],\n",
       "       [ 6.081],\n",
       "       [ 6.701],\n",
       "       [ 6.376],\n",
       "       [ 6.317],\n",
       "       [ 6.513],\n",
       "       [ 6.209],\n",
       "       [ 5.759],\n",
       "       [ 5.952],\n",
       "       [ 6.003],\n",
       "       [ 5.926],\n",
       "       [ 5.713],\n",
       "       [ 6.167],\n",
       "       [ 6.229],\n",
       "       [ 6.437],\n",
       "       [ 6.98 ],\n",
       "       [ 5.427],\n",
       "       [ 6.162],\n",
       "       [ 6.484],\n",
       "       [ 5.304],\n",
       "       [ 6.185],\n",
       "       [ 6.229],\n",
       "       [ 6.242],\n",
       "       [ 6.75 ],\n",
       "       [ 7.061],\n",
       "       [ 5.762],\n",
       "       [ 5.871],\n",
       "       [ 6.312],\n",
       "       [ 6.114],\n",
       "       [ 5.905],\n",
       "       [ 5.454],\n",
       "       [ 5.414],\n",
       "       [ 5.093],\n",
       "       [ 5.983],\n",
       "       [ 5.983],\n",
       "       [ 5.707],\n",
       "       [ 5.926],\n",
       "       [ 5.67 ],\n",
       "       [ 5.39 ],\n",
       "       [ 5.794],\n",
       "       [ 6.019],\n",
       "       [ 5.569],\n",
       "       [ 6.027],\n",
       "       [ 6.593],\n",
       "       [ 6.12 ],\n",
       "       [ 6.976],\n",
       "       [ 6.794],\n",
       "       [ 6.03 ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y = boston_df.Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# It is required  y =mx +c, y=Ap, A =[x,1],p =[m b] we need A=[x,1] matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# in the form of[X,1] , for every value in x set ast [x,1]\n",
    "\n",
    "X = np.array([[value,1] for value in X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[array([ 6.575]), 1],\n",
       "       [array([ 6.421]), 1],\n",
       "       [array([ 7.185]), 1],\n",
       "       ..., \n",
       "       [array([ 6.976]), 1],\n",
       "       [array([ 6.794]), 1],\n",
       "       [array([ 6.03]), 1]], dtype=object)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Best Fit Values with p =[m b ]\n",
    "\n",
    "m, b = np.linalg.lstsq(X,Y)[0] #care about only first index\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10b68ba10>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAECCAYAAAD0JMwBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnX18VOWZ938zSZSAGSIECW4gAWpvRdSGcZWlGMRqfUPA\nRawvaKHaWrVUZck+anUfW9d2tyC1S6v10QX0oS5dpLy2FFtEA7VUO6RaCnsXkQDRAIEYEyVAkpn9\nY3ImZ+acM3POnDNzZk5+38/Hj8w95+U6M5Pfuc51X/d1+SKRCAghhHgPv9sGEEIIyQwUeEII8SgU\neEII8SgUeEII8SgUeEII8SgUeEII8SiFdnYWQoQAfNLzch+A7wNYBiAMYKeU8n5b1hFCCEmbtD14\nIcTpACClvKLnv7sALALwqJRyEgC/EGKaQ3YSQgixiB0P/iIAA4QQmwAUAPgOgHFSyq09728EcBWA\ntfZMJIQQkg52YvDHASyQUl4N4F4APwfgU73fDmCgjeMTQgixgR2B/xuiog4p5R4AxwAMVb1fAqDV\nxvEJIYTYwE6IZg6ACwHcL4Q4G0AAwGtCiElSyjcBXAvg9WQHCIVCLIRDCCFpEAwGfam2sSPw/wlg\niRCiDkAEwGxEvfgXhRBFAHYDeNWEkTZMyG1CoZBnrm/uwi1oaGrTjFcNC2Dx/MkuWJQ+Zq/FzPeX\nrc/FqfNk83t04lxGx0gHM+c1e76iQj8evKUaNdUVps+f7NhWP/9QKGRqu7RDNFLKLinlnVLKGinl\nJCnlH6WU70spL5dSflFKebeUkh66R5j5pXMsjecyTl5Ltj4Xp86Tze/RiXOlY1e1GJL2scyer7Mr\njAXLQ6irbzRtV7JjZ+rvqOCJJ57IyIHN0NTU9MTZZ5/t2vkzTVNTE7xyfZXDAqg46wx81PwZ2o+f\nQmV5AF+6cACmXXGB26ZZRu9avj59rMYbM/P9mT1Wtmy2cpy2z06iclhm7HXKZvUxWj89qbuN3xcN\nIRQV+nHdhCrUzroYpz5tRkdXkenz1tU3YuHPQ/jN9v0YPLAYA/oV4eSpblSWBzDxC2dj30dtCIe1\n/upHzZ/hugkjLV3LngOtOH6iCwBQVlqM+2+6yPLn3/Pb/G6q7Xxu1oMPhUIRr4Qw9PBSiEYPXl9+\nk2/XZyXkY+Xa6uobsWC5NuRROysYE95ptet0Bb7A78OaBVNNncdJeq4vZQyepQoIIXnBgcPtuuMH\nDcbNsnLznpTjI4aW6G4z3GA8V6DAE0LygkyJrJkbR77OQVHgCSF5QaZE1syNo6a6ArWzgqgaFkCB\n34eqYYG4EE6uYqvYGCGEZAtFTFdu3oODh9sxfGgJZn7pHNsiO/NL5+jG4BNvHDXVFTkv6IlQ4Akh\nOUFdfSNWbt6DA4fbMcJAvDMhspm6ceQCFHhCiOskZrI0NLXFXmdDaPPROzcDY/CEEFepq2/EMyvq\ndd8zynAh5qAHTwhxDaMcdAW7KZB9HXrwhBDXSOWh53qeea5DD54Q4hpGOegKSiaLmQlYooUCTwhx\njRFDS3TLD6irNbo9AZvPMERDCHENo0VK6lK8ZkoJOEFdfSPmLtyCabXrMHfhFkuVItOmuRm4/XZg\n27aMHJ4ePCHENczkoGeqBo2arD8lRCLA7NnAyy9HX4fDwMSJjp+GAk8IcZVUOehGYRwnJ2CTPSU4\nLvC1tcDChfFjixc7e44eKPCEEMdxclLUbCkBO2TjKQENDcDIhNrxa9YA06Y5d44EKPCEEEdxOtxR\nU12B3Q0t2LR9Pzq7wigq9OPq8ZWOetYZf0rw6ZRu7+4G/JmdBuUkKyHEUYzCHUs37ErreHX1jdiw\nbR86u8IAou3yNmzb5+gkaMbKAS9YoBX3t9+OxuAzLO4APXhCiMMYhTuOtnZg6vy1qCwPWArZZCM+\n7njBseZm4Kyz4seuvRb49a9tWmoNCjwhxFGMwh1A1HG1GrLJSnxche0mpnrhmFOngKIiu0e2DEM0\nhBBHMRvWMJvHno12ecq8QUNTtLm2chOyFAZatkwr7q+9Fr2ruSDuAAWeEOIwNdUVKCstTrndgUNt\nphYWZaNdnq3FVO3tUWGfM6d37IILosJ+1VUOWZgeFHhCiOPMmTIm5TbhnnBNKo85G+3y0g4DjRgB\nBALxY599Brz3nkOW2YMxeEKI46gnLQ8cakPYZGDbaOI00w05jOYN/H4fptWu0+byr1unzV//xS+A\nm2/OmI3pQIEnhGQEtSgrC5+UDJX9h9oQ0RF9t+q/Gy2mUlIzlScM36mTuGz85+I3OvNMoKUlG2Za\nhgJPiMfJhVK7iR743IVbMl5+wAqJaZJ+vy8m7gr/vuIRjFm0O37HlpaowOcojMET4mEcyQ7JANmY\nOLVKTXUFFs+fjDULpqJbFVMa0/hXrF80HWM+Uon7s89GJ1FzWNwBevCEeJpk2SGzJwd038sGji8s\ncpgRQ0tw4MOPsfaZGdo39WJLOYotgRdCnAXgTwCuBNANYBmAMICdUsr7bVtHCLFF8uwQ9wQeyPzE\nqR3+5bVFGPLbDXFjX/3GEtz1zatQ45JN6ZB2iEYIUQjgZwCO9wwtAvColHISAL8QInMl0gghpsjG\nIiFP8e67gM8XJ+6vTLgVcxe8HhX3HL0hGWHHg18I4DkAjwDwARgnpdza895GAFcBWGvPPEKIHZKW\n2g0fdsGiHMWo+FckgtsA3JZ1g5whLQ9eCDEbwBEp5W8RFffEY7UDGGjPNEKIXbKxSChTZK2F3re/\nrRX3PXvyKtZuRLoe/BwAYSHEVQAuAvAygCGq90sAtNq0jRDiALkc6zYiKy30PvgAGD06fuy++4Cf\n/tSZ4+cAvojNu5QQ4nUA3wSwAMDTUso6IcRzAF6XUq5Mtm8oFMr/WyQhxHGe/fVhHGnt1IwPLS3C\nvdcNtX384MUXa8ZC77yjXwkyRwkGgymNdTJNcj6AF4QQRQB2A3jVzE7BYNBBE3KLUCjE68tjeH3u\ncXTFOv3xti5TNhte2/e/D3znO/FjO3YA1dXIzU9Cn1BIO6+ih22Bl1JeoXp5ud3jEUKIUy30lFW8\nbR8cwEvPzY5/c/p0YPVqG1bmPlzoRAjJOZxotK3E8dcvmq59s7MTKPS+/Hn/CgkheYcTK119992H\n9dvXx409MvNJfHrJF7G4D4g7QIEnhCSQC8XJABvZP0eO6E6i3jBvDQCgwKWKlW5AgSeExMhKemIm\n0cmCmfmt/8KJ03o7TPWlVbwUeEL6CImeeXBkIRITTZIVJ8tpgX/qKeCxx+KGXpo4C69ecpNmUzcr\nVmYbCjwhfYDnV7+HDdv2xV43NLWhoQkYNaoxTrj3H9JmriQbd532dm3LPAB3fe9Xunn0Q0qLc/tG\n5TCsB0+Ix6mrb4wTdzWJHnthgb4kGI27is+nFfcjR4BIBM2faMUdAFraTmTBsNwhB781QoiTGIVd\nAG2LvK7usO52nV3hzNaDscKSJdpY+333RWvHDIlWTBkysEh3174UfwcYoiHEMrmSZWIWo5rwgFbw\nKssDuguMgN4J16UbdmHOlDHZv+ZTp4DTT9eO65RbuWxMCVa9pe2T2pfi7wAFnhBL5GOWidGqUEAr\neGNHDzbcVuFoawcWLA9hd0MLdu49lp0bnV6NmL17gVGjdDe/oKo/Ro0ambMdo7IFBZ4QC+RjlonR\nqtBLPj9AY/POvcdMHzdx0jYjN7pf/QqYMiV+7LrrouMpyMcqmk5DgSfEAslb4OUmisgt3bALR1s7\nAABlpcUYXqYNdyQL55jBsRtdOAwUFGjHPVCjPZtwkpUQC+RqCzwzzTEUcVf+veqtFs12RtdnFjs3\nOuUamgNDtOIeClHc04ACT4gFjCbp3Jy8U+YFGpraEA5HYuEStXgbhZYWLA/F3RDsXke6N7q6+kas\n++ErWFx7BYa0H42NfzbynKiwjxtny66+CkM0hFjAiSJYTmNmXiDZQiW9+Lk6nGOFdG8QNeOGoyZh\n7IaHVqPq7IFYnNYRCUCBJ8QyuTZ5Z2ZeoLDAj84u/Rx3BeWGUFNdgaUbdpk+v98HjCgPpHeju/xy\n4M0344Yem/FdvFt5EYDcntvIByjwhOQ5ZppjGC1gUqMWUyve+4jyABbPn2x6ewCAlMC558YNdfkL\ncOODq+LG3J7byHcYgyckzzEzL1BZrq3Xkki6YmrZy/b5NOJe9/Y+jbgDfW9hktPQgyckzzEzL2CU\nC69GLaZlpcWmvXj1jSHpKt/Zs4GXXorf+ZVXgFtvjcbfCwtzam7DC1DgCfEAapE/cLg9NvGqjNdU\nV2B3Q4tu0bEhpcWYnVB6YM6UMSlvCApjRw8GYLzK97TmQxh/9d9rd0xIe8y1uQ0vQIEnxAOYKaGw\nfech3X0VmZ27cAv2H2pDYYHfVMxeYcO2fTivapDuxOz6RdOBRQmDn30G9O9v+vgkfRiDJ8QDJEuV\nVDAKuSi1ZRqa2hCJRCtHWl1TtHLznrjj3/77n2ubXT/9dNRrp7hnDXrwhOQQVipVqrcNh/UVOVtp\nhsp5+p/8DL/46e3aDbgK1RUo8ITkCFYqVSZua4R6AtTKxKlVhg8tweLaKzTjt977/9Fv2FlYmpGz\nklQwRENIjmAmzJJq20SUCVAgOnGaCa59d6NG3FcHp+KGeWvwaXFJxs5LUkMPnpAcwUqlSrNVH5UJ\nUHWGipKKWBYoRDcKU3r1BX4funVCQIVdnVj9HzM149Pnr0V3OIKiQj+uHl/JzBgXocATkiMMCvTT\nFdszA/00Y8maeCSirkmjFvpQKITvrfgw5f564q6ZQAXwtbtfiFaC7Nm+syscd4Mh2YchGkJyHJ1e\nRpZWeCYrNGalPHBRoR8T9m7XiPu2cybghnlrouKug9lwEnEeevCE5AgtbSd0x5tbO1BX3xjnBSsF\nwcxMmkYiiNtfyb7Zf6gNgwcWm7LNH+7GL3+o9dpvmLcm5b4sGOYeFHhCcoRkYZfEbBq9hh7JUMI0\nidk3yg1iSGkxWtpOYPjQEnza0Rl349ALx3x/3ov4A8pMnZsFw9wjbYEXQvgBvABAAAgD+CaAkwCW\n9bzeKaW83wEbCekTpKoXYyTSZlC86GThkuFDS3DgcDsG9cT8r35vE771u+e0G0Yi+GPtulisPRUs\nGOYedmLwNwCISCknAngcwPcRXZT8qJRyEgC/EGKaAzYS0ieoqa5A7ayg4ftKLN1KrXYFxYs2yr5p\nbu2IdYQ6+vFxrF80XSvu4XBswZJR7L7A70NZaTEK/D5UDQugdlaQE6wukrYHL6VcK4RY3/OyEsDH\nAK6UUm7tGdsI4CoAa+2ZSEhuYWW1aToUFeo354hEgOdXv5fWYqUzA6djzpOvGa54VdALx+BnPwPu\nuSduyOhpY95t4yjoOYStGLyUMiyEWArgRgAzERV0hXYAA+0cn5Bcw8pqU6s8v/o93WqPajZt35/W\nsetlc9L3L/ufrfjnXz+tfcOgxEAuti4kWnwRB2pECCHOAvAOgDOklIN7xqYi6tF/22i/UCjEAhUk\nr3j214dxpLVTMz60tAj3XjfU8vH+0nAcW3e1o7m1E3b/GHyA5WMU+oHVC7Ve+7QHV2HIoH5pXRPJ\nDsFgUC+DNg47k6x3AKiQUv4AwAkA3QD+JISYJKV8E8C1AF43YWS6JuQ8oVCI15fH6F3f0RXrdLc9\n2tZl+bOoq2/EqresTZYahW+GlBZjQHGR6cVPgH44Zsu5k7DouocAAHdOuRDBPPXI+8Jv0wx2QjSv\nAlgmhHiz5zjfBvA/AF4UQhQB2N2zDSGewUz/01QoMXwrYqzQZdA4+9Kx5TivapCp7JqL9r+Lf131\nfzXjSk67XgMQkp/YmWTtAPAVnbcuT9saQnIco8lFs6mA6aQ4qjEKwezcewz33HghAOBnv3wP7cej\nYaQCvw8XnlMWi8Hree1fuf/nOH76gNjr5gxVnCTZhwudCLFAupOLdrx2Myh57rsbWmLiDkTryNTL\nZl1hP1VQhBkPrNQ9nrp+DclfKPAkb8l0uqIRVnuH2vXazTAo0A919Y2aLJyKYwfx3EtzNdvPXfB6\n0psNywt4gz4p8G4JA3GOTKYrOo3ZYltVwwKx3+LU+WstNUGK6JxHN6f9/feB0aMxM8VNh+UFvEGf\nE/h8EgZiTLLmGLn2PZqp3Z644rOyPGApnHPskw4c+yQaO9cVdgB1Ow6iZnRv2eAPPtiHul0dujF3\nlhfwBn1O4PNJGIgxVppjZAK9p0AAuk+GyYqIqb129TEH6dSAT0ZhgR+B459g2U/u0LynZMdUJfzG\nL6jqj9kzLoudlwuWvEefE3i3hYE4gxPpiumS7ClQb8wo80bttRtVeTTLL384VTP2f25+Crsqzo+z\naVrtutjNR8mbsTqnQPKHPifwbgoDcQ676Yp2sNLAYuXmPVg8f3Ls34lest3smh8tn4fPHflAM25U\npz0cjsRuPjMmDIKH1wIR9EGBd1MYiDcw2w8V6H0y1POS7WTXFHWdwi//42bNuJkGHArbdrVj9oy0\nTk/yhD4n8CyS5A3cnEux0g812ZNhuq3s9CZRF13zALaMmRx77fcBBQX6ZQ0Umj/R1tQh3qLPCTzA\nmKMXcHMuJVVjjsRtjbDyJAAAD6//d3xxzx8043pe+9qF0VYM02rXGZYIHjKwyNL5Sf7RJwWe5D9u\nzqXUVFdgd0MLNm3fj86uMIoK/bh6fCXOqxpk6ckwVXZNrHVeJIL1P7pRs41ROKaosLePT7JzTBzD\neSevQ4EneYmbcymJK0Y7u8LYsG0ftu88hJa2E6YXz6XKrqmrb0TNuOGa939x6Uws/+Lthse9enxl\nynNMmTgSF4xgiMbrUOBJXpLtuRR1jnqBX78Mt5LaqGSpLN2wK07wgWi7PXUKZEn/IgA+tB8/FXu9\ndMMufHh/LW79wwrNOZJNohb4fbh2QhXOqxqEuQu3xPLxp0wciZ17j2k+p1AoxFXdHocCT/IWp+ZS\nFJHbf6gNhQV+dHWHUVkeQHBkIYJBbbZLqrZ3ComCr4e6MJjy+pV/vV6z3bQHVyHsLwAAlJUWwwdt\n1cfuHrsSc/Qbmtp0e6P+peF4XD16rur2HhR40qdJFG8l6yQqjEBo3+toaMrOIji97Jj3zxqFh2Yt\nihs79kkHKssDuiUGjFr66WUXbd2lf11c1e0dKPCkT5MqVTEb4j551xbM+82PNeNG4ZjCAr9hBo5R\nWqRedpFRmiRXdXsHCjzJKbIVE850fXaz6Hntt9y3HJ/1O8Nwn2S57UYt/YYPLdF8tiXFBWg73q27\nLfEGFHiSM2Sr0mc26rOnwqjio5WVqHqMHT041r0pcTzxszWCq7q9gz/1JoRkh2SrU7Nxnmww+vD7\nuuJ+w7w1tsUdAD5uO4naWUFUDQugwO9D1bAAamcFsXPvsaT7+X2Ibcv4u3egB58GTC3LDGZXp1op\n1avH/kPuhGX0hP0bc55F05lnO3aOg4fbdbOLnn5lR9L9RpQHYkXRiHegwFuEDUMyh5nVqc+vfi9u\nkVGqUr1634nf50O3lXZJNslUOEYPo/h5qvo5nFj1JhR4i7BhSOZItTpVr+doMpTvpK6+UbPAKBsM\nbj+KZS/crRnPhLArGMXPU9XP4cSqN6HAW4QNQzJHqtWpVmPnBw+3uzahque1z7/l3yDPPjcj5ysq\n9OPBW6oNnQxlfNmGXWzR14egwFukLzcMSYx9Kys9nSTZ6lSr1ReHDy3J+oTq8ufuxMAO7e8jk147\nEE2dfPqVHVi5eY9uC0BlXmLJ41/uHT/UhhHlAc4huUim5/Mo8Bbpqw1D9OYeGpqAUaMasyYOVuqw\nA9EVn4mlADLF6Z0n8OriWzTjmRZ2NepuTbsbWgznKpSbaCgUQpAtnVwjG/N5TJO0SE11hW4amtc9\noGylMCbD6CY6ZeJI1M4KYkhpcdx4tsR9/aLpGnFfeO1DaYm7T7+OmWWSlSwguUE2/qbowadBX2wY\nkgtzD2Zi9Hrx5Uzx+Jp/xSUf/EkzbsdrX7dwGqbOXwujJB+fDxg8MFpsrKXtRKzAWCJWShYQd8jG\n3xQFnpgik3MPVuKQRr1Ns1l2wBcJY92P/lEzbjccozyBVJYHDK8lEumtUlk7K2h43clKFpDcIBvz\neQzREFMkS7+zgxKHbGhqi4sh19U3Wt4/G6xfNF0j7isuvdmRWPvsKWMAmP9MlQlVPdRNP9R4fa4o\nn8jU35SatDx4IUQhgCUAqgCcBuApALsALAMQBrBTSnm/MyaSXEAvPBIcWWg7VGUUb1y2YZcprz5b\nMeU7ti3HzW+/qhl3QthL+hfh9NMK47JgFO/84OF2wzCMsmoV0A9bWW0hSLJLNprWpBuimQXgqJTy\nTiFEKYB3AfwZwKNSyq1CiOeEENOklGsds5S4TmJ4JBSyn19uVDagubUjFk9Pll2QKnXS54NhPNss\nejntUx/6JSI+aw/ABX4fBgX6xa6rrLQY48eWY8O2fbEJYeVaa2cFY6UD5i7ckvRR3mhOqC/OFeUb\nmf6O0hX4/wawsuffBQC6AIyTUm7tGdsI4CoAFHhiSF19oyXx1VstnCp10o646wn79tGX4Klpj6Z1\nvHAkgiWPfzn2uq6+Ec+sqNfdVn2tfTU1l9gnLYGXUh4HACFECaJC/x0AC1WbtAMYaNs64mnSWZmq\npq6+EZ92OJ8KeeXO3+GB136iGbcbjikb2JvGmWqFrfpas91/lngHXyRNF0cIMRzALwH8REr5khDi\ngJRyRM97UwFcKaX8drJjhEKh7FV8IjnHd//Lmgc/tLQI9143FIDST7TFcZv0vPab5q7AyaJ+jhx/\nxoRBuKCqPxatadJttqGgvlZC9AgGgylXTaQ7yToUwCYA90spt/QM1wshaqSUdQCuBfC6SSPTMSEv\n8PpKQbvXV7mlzVL2y51TLkRQqamyZUuKra2hJ+wnC07DTQ/8t6PnCe3rwqhRQ9F2PHmWkPpaM4WX\nf59evjbA/PxXujH4RwCUAnhcCPEvACIAHgCwWAhRBGA3AG3KASEqUlU4VKgapq2XYrUujRFjD+7E\nD1Y+phnPVIkBvfLGalIVDSPECunG4B8E8KDOW5fbsob0KdSx5WSevF4jCqt1afTQ89pnf/1FHCsp\ns3VcO1w9vpLiThyDK1mJqyhpYnOefE23XntifRmFsaMHpy3w2WzAYZUN2/bhvKpBFHniCBR4j+Nm\ne0Er554zZYxu6EJZ3ZlIqh6jegz7uAn/b+m9mvFcEHY1+dg8hm0scxMKvIdxs72g1XNbTQW02ldV\nz2ufd9sC7CnPvVzyfCsIxjaWuQsF3sO42V4wnXObXdX3/Or3TKdX5nI4xoh8KwjGNpa5CwXew7hZ\n4jdT5zbbl7X45HH8909v04znsrArJK5QzfXwRy6Ukib6UOA9jJvtBTN1bjOrX/W89n+bUovff/6L\nts5thQK/z7BIWLJ9rp1QFSfe+RD+6MttLHMdlgv2MNkoR5rtcyfLf5+7abGuuM98eH1WxR0A5t02\nLtb5yyzd4Qg2bNuHqfPXYu7CLTHPXY9c6szk5u+MJIcevIdxu4ZJWWlxLPWxrLQYc6aMsX1uPW/R\nH+7G2mdmaLaNhWNOGZcEcAIfgMphAd3PWGl+bWZBl0Ik0uupG7Xwa2hqw9yFW3IiXOP274wYQ4H3\nOE6WI02MBQdHFkJvNbieoOnluKdD4upXPY990TUPYMsY7eKoTFE5LBC3GKuuvhFzF26Ji5mrb3ZW\nKCzQ78wE5Fa4hqWJcxOGaIgp9DovrXqrRbfzUibDCkrT8yl/e0NX3G+Ytyar4g7EhyKMOlSNH1ue\n1rG7uvXFXU0uhWtIbkEPnpjCSiqcU1kVRtkjNeOGoyZh2xseWg3DeIYBJf2L0O+0QtONupUw09IN\nu+JCT2qMPqede4+hpH9RrLGHWSrLo3V4kpVzYLYKMYIePDGFkWgrsWC1Jz/CIHvCSlbF86vf03jC\nNeOGa0T8+cl3R2PtFsUdACaNqzAt7kB0tS0QH2462toR10M22c3tsxNdlm00M1HJbBViBD14Yopk\nxb0SY8F2OxAl5rp/Yf+f8eSqJzTbpZvTrlSnNBvaUFeznPPka7rbLNuwCzXVFYafk9WUSeWcAFJO\n0I4dPdjSsZ0g13PzSRQKPEmJ2c5JSrjGblaFWnj14uz/+NAqdPoKTFofj8/XW53y6Vd2pNy+rLQY\nBw63x2wymihtbu1AXX2j6RLIySjw++L6saYi2wXK8iE3n0ShwJOkWEnxS2wzZ/WPXfEKG5ra8PyS\ne3F2a1Pc+2vH3YDf3foQ/g5Iu5JkJIJYemGyp5IhpcVobu2ICXqqOu4AYs2y082YUVCHXMzWvc9m\nWQCWJsgfKPAkKVYyNAYF0m9rp9xIhn38EdYvvU/zvhKOqTUZtkiGItZTJo7UFfgpE0di0/b9aR17\n5eY9aGk7kbZtAPBpRyfq6huThnwSOXi4PWthE5YmyB8o8C6QT/FLK1Ub7TTYXbl5T8p+qFMmjox9\nTrsbWkzVpEnGzr3HUDsrGBdKGjt6sK3jHjjUhhHlAVvNSJSJW8B816tBgX5ZC5uwNEH+wCyaLGOU\nJ62XT+42dfXWmmJ/nK7n+sgjWFx7RdzQ+i9cjxvmrYkT93tuvBBANMMmmQj7fNr0RT0OHm6PTQoP\nH1qCA4fbsfGthvSuIXZun2NL9K08PRl9TZnIkWdpgvyBHnyWyaf4pVVxsOzBtbYCZ56pGdbLjlEa\nfJipJllZHl1Zqo7p69Edjhh2kkqX7nAk9j0+s6LecBWqGQ4ebsfSDbt03ysq9KO7O4yCnpWuRteQ\nibAJSxPkDxT4LJNP8UsjW30+6Hr2Zjw4RXQTPXYAuOW+5fis3xm6+ymfj5mbzqcdnZhWuy4W/gKM\nY/ZOirsaRezszBUMCvQzzNPv6g4jEgHCKW4gmQqbsDRBfsAQTZZxYhFQtjCytbI8gNpZQQwtLUKB\n34eqYdHXqf7g6+obseufvqcR94NfvRdzF7xuKO5A7+djJqvkaGtHXPhrd0OL5cqO6aIODSllFYz6\nyqYiWXSssMDcny7DJn0bCnyWyaf4ZTJba6orcO91Q7FmwVQsnj85tTd34gRqxg3HN7e8EDd8w7w1\n+OHYmSkuWbEFAAAR50lEQVSFW7HF6KaTDCWks3j+ZPj91le8WmVa7brY6t6a6goMKC6ytL9yw0yW\njWOmRo2Zmy7xNgzRZJl8il86ZqtOGYHZX38Rx0rKAETDL0aZGUWFfjx4SzWAaP661V6sCsoch9m0\nQzVWasjo5c2bzWUH4hc5Gc0fDCktxoDioqTXUTUskJO/KZJdKPAuYietMFvYirW++iowc2bc0Jvi\nMiy8/p/ixvx+H8aOHqwrWIq4210dqsTw01lpevpphZaLhCms3LzH0k1FHaozsnV2T02cZNeRi0+E\nJPtQ4LNMvi3zTitnv7sbKNT+tOp2HMRCHVHq7Apjw7Z9mDJxJHbuPaZ5WjCzXD8VinDWVFfEVYM0\ng7py5MdtJ2L58jv3HsOBQ22xTBY9Dh5ux7zbxpm+qaiF2cwT1MrNe2I2dHWHY9Unc/G3RLIPBT7L\n5FOaZFo3o0AAaE8ISfz1r8CYMbESv0bpg3/ceQgDios0TzZWQhxGqIVzzpQxaT0RnFFchKWPfzn2\nWvl8kmWyDB9agprqCix6ZUfKgmPqhVwKyZ6gmMlCUkGBzzL5lCZp6Wb0xhvA5IRGG+PHA3/4Q9xQ\nTXWFYZGv5taOWFqg+maSKsRRVOhHOByJebiKjUZer5FnrIyZrbtuJmVTOW7YxIoxJdefEKegwGeZ\nfFrmbepmFIkAfp1krHDYsEa7lZj0ys17UsbNw+EI1iyYGjeWzLNNFnZSQkJmvqNkE77qEsNANLU0\n1TUfONSmafVHD53YgWmSWSaf0iRT5eyfO2uWVty3bo2KfpIGHFauVSknkKz0gJWbo5lSEWa+o2Rl\nHIaUFmtSR81cc7in2Xaul7Ag+YMtD14IcSmAf5NSThZCjAawDEAYwE4p5f0O2Oc53EqTTGey1Mhz\n/uqILsDnwwD1YFkZ0Nxsypaa6grsbmjBpu370dkVRlGhH/1OK9DNVFHEO1lOuJVGIs+sqNd9Tx12\nUv7/8ob3cLSty3By0wg93Vd/7/sPtZmu8ePk3IzZpunEO6Qt8EKIWgB3APi0Z2gRgEellFuFEM8J\nIaZJKdc6YaTXyPbkWDqTpYoY+HzRVZNKhoZeiQF0d+uHaZLYo64n09kVNsxCUS9w0gtxlJUWm/os\nU9W1T4yv11RXYED4MIIGCphs4rflE/0MHfX3rny+yk3eSPSdmpvR+w00NAGjRjUyDORh7IRo3gdw\no+p1UEq5teffGwFcaePYxEGSTZbqoQ5jRCJRAZ7+zhqNuL+/cKFxDD4Ne4aUFqNqWEC3/IGRl670\nSU33nApW50CSragNR5AytFJTXYHF8yfHVgJXluuXUXBqbsbqb4B4g7Q9eCnlaiFEpWpIHXRtBzAw\nbauIo1jN3FH/0fc71YGVP7k1foNrrgE2bsS2VVvx4zQmBY3saWk7gSWqNEQ1dkNbZkshmCXVxG9i\naCUxPBLLo1e91ntCcWpuJp+yt4hzOJlFo37GLgHQamanUMjeCsVcJxeuryxQiCOt2vh2WaBQ1z4l\nO+TWt/4Lt23/Rdx7oe3bgcJC/GXVVqx6qyU2roR9PvhgHy6o6u+oPQoDAMyeHADQ4+2GDyMUOpz0\nXKnOCUQ9kwEGxzKyZwCAGRMGxX0Gag4caovt+5eG45rPSi3myutLPj8A+4+cQvMnnRgysAgTx5QY\n2mWVdD/zfMar12UFJwV+hxCiRkpZB+BaAK+b2ckoxukFQqFQTlzfV/368ec7p1yIoI4HPGH5Djz8\nzDfixh6f8QRax9dg8aWXAgCWbdFfXRra14XZM5Jfs1V7nMDonABQOSyg+z2l+v6CQSC0Tz+lckR5\n7zGNPqtEjrQX4MXHrzO1rVXc+MzdJFf+9jKF2ZuXkwI/H8ALQogiALsBvOrgsfs8dtr8mQ5vnDwJ\nXHABHt7TG6J59kv3YONF1wLo7YcK2HvkdyOTSMnc0WsWMvNL5+h+vgN0jgPEfxdGfWhnmvisEslk\nuETvMw+OLOQEq8exJfBSyv0AJvT8ew+Ayx2wiSTgRP2alJk7zzwDPPRQ7OWn55yH79z1Y+w/2oEq\nHQG2u2ArnUwiqzc5ve3PqxqkubEkCr/y+c6YMEiTRpj4XejVqTH7WSVid0I11eeT+JkzhOF9uJI1\nD8ho/RopgXPPjR/buRNnnH8+fpxkN6NJxv09qzHNeuRmRdvqTc5o+9pZwVg53rr6xqSFx7btasfs\nGfFjRt9FYp0aNWYrWNqZUM23InYkO3Alax6QkQyIrq5orRi1uP/gB9G0x/PPT7l7TXUFZkwYhKph\ngbhFq5EITK/CtNKA3GqaX6px5dzJqko2f6KdlEznu1A6O6lTQKdMHGmYEpoOTIMketCDzwMcr1+z\nZAlw112qAw2PevLF1lrLXVDVH7NnBA1rt6R6wrDyZGJVWFNtb0b4hgzUdmJK97vI9OI2pkESPSjw\neYDRI77lR/oDB4DKyvixt98G/v7vLR1GCavsP9SGyi1thkW3UomLFVGyKqyptjcz8TlxjPbYjn0X\nDqF8F2GDUsS5WMSOZA8KfB5gO+skHAauvx74zW96xx5+OBqSsYherNcIPXFRx9wL/D5dYdLbz6qw\npto+1cTnlIkjccEIbYjG6nehN8eg7G+3amSq8gtAbhaxI9mDAp8npHrEN5ysXLkSuPnm3g3POAP4\n6COgJD3PzkpMN1FcEgXJyOv8tKMT02rXxV2HVWFNtb3RDWBIaTFmTxmDmuoKwywTs+GWZBOfemNW\nRT7Zd5FYrpj0TSjwHkBPSF54fjNqnp8dv+EbbwCTJtk6l1Fow+eL1jxPJr5GgqQ07Dgz0A9HWzt0\nG1crompFsFJ1Q1JsylQuvpWbYToZUUbfhbpxN+nbUOA9QJyQRCKY/+tFmBSr+wbgG98Ann/ekXMZ\nhTYqywMpRcVIkJSGHXMXbtHNaslkydxMerlWWg2mMxmaT81jiDswTdIDKEIS3BfC+h/dGC/uR486\nJu6AvYYlqRqIZDoTxEpaphMkqziZSDqinE/NY4g7UOA9gCgB1i+ajidWPxkb++70xzB3wevA4MGO\nnkud0+33wVIOdypBSnUDsEu2c8WtCG06oqyXX283n554C4Zo8p1vfQs//OlPYy+3fv6L+OH18wGf\nL652jJMosW2rBZ3SnfjMZslcdQinLFCIr/rTb4iRqrm3E7H/bDePIfkFBT5f2boVqKmJG/rO4yvx\n147TdGvH5ApuTnymilknTlYfae20vdzf6Hpz8bsh3oMCn298+ilQUQF88knv2IoVwFe+gqfcs8ox\nFEFUPOmnX9mBlZv3mBL6VBOoqZ4QMlrzhxAXoMDnE489BjylkvGrroouXrLYMi/XSbeHbKp9Uj0h\ncLk/8RoU+Hxgxw5o6tbu2wdUVbliTqZJx5M2u0+yEBHTDonX8Jbr5zVOnABGjowX9xdeiJZs9Ki4\nA+l50k5430w7JF6DAp+rLFgQre7Y0BB9ffHFQGcncPfdrpqVDdJJl3QixTIx7XBoaRHTDklewxBN\nrrF7NzBmTPzYrl3Aeee5Y48LpJMu6VSKpTqEEwqFPNmvlPQdKPC5QlcXcMklQH1979iCBcD8+e7Z\n5BLppEu60eeVkFyHAp8LvPBCtF6MwqhRwF//CvTTb+jcF0hnAQ8X/RASDwXeTfbti4q5mlAIGDfO\nHXsIIZ6Ck6xuEA4DV14ZL+6PPRbNjqG4E0Icgh58tlmxArj11t7XZ54ZbaV3xhnu2UQI8SQU+GzR\n1AScfXb82NatwMSJ7thDCPE8DNFkmkgEmDkzXty/9a3oOMWdEJJB6MFnkIFbt0YXKKlpaYmGZQgh\nJMNQ4DPBsWNAWRk+px7buBG45hq3LCKE9EEYonGae+4Bysp6X99+ezRrhuJOCMky9OCd4o03gMnx\nTaff3bQJF335y+7YQwjp8zgq8EIIH4BnAVwE4ASAu6WUHzh5jpyjvR0oLweOH+8dW7kSuOkmdIW0\ntVEIISRbOB2imQ7gdCnlBACPAFjk8PFzi4cfBgKBXnG/7jqguxu46SZ37SKEEDgfopkI4DcAIKX8\noxDi4hTb5yfvvBMtDKZm/35gxAh37CGEEB2c9uADAFTNQtElhPDORG5HR7QfqlrclyyJ5rRT3Akh\nOYbT4tsGQN1hwS+lDDt8Dnf4wQ+A/v2BDz+Mvv6Hf4iW+J0zx127CCHEAF8kEnHsYEKIfwQwRUr5\nNSHEeACPSymvN9o+FAo5d/IM0e/993H+LbfEje1ctQonKytdsogQQoBgMOhLtY3TMfjVAK4SQvy+\n53VK9zaY2Ew6V+jsjFZ23Lmzd+yZZ4AHHsBYk4cIhUK5e30OwOvLb7x8fV6+NiB6fWZwVOCllBEA\n9zp5TFd47jngvvt6XwsBvPcecNpp7tlECCEW4UInNXv3Ap/7XPzYn/8MXHSRO/YQQogNvJPhYofu\nbmDSpHhxf+KJaHYMxZ0QkqfQg1++HLjjjt7XZ50VbaXXv797NhFCiAP0XYH/8MNoTruat96Kpj8S\nQogH6JshmqNH48X9oYei4RiKOyHEQ/RdD76yEvjoI6C5GRg40G1rCCHEcfqmwJeVAQ0NbltBCCEZ\npW+GaAghpA9AgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9C\ngSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeEEI9CgSeE\nEI9CgSeEEI9CgSeEEI9CgSeEEI9SaGdnIcSNAG6SUt7e8/pSAD8G0Angt1LK79k3kRBCSDqk7cEL\nIZ4B8BQAn2r4ZwBukVJeBuBSIcRFNu0jhBCSJnZCNL8HcK/yQghRAuA0KWVDz9AmAFfaOD4hhBAb\npAzRCCG+BuAhABFEvfUIgDlSypVCiEmqTQMA2lSv2wGMdNBWQgghFkgp8FLKJQCWmDhWG6Iir1AC\noDVNuwghhNjEF4lE0t65x4O/R0p5W8/rHQBmAGgAsAHAE1LKd4z2D4VC6Z+cEEL6MMFg0JdqG1tZ\nNDp8E8AriMb2X0sm7oA5AwkhhKSHLQ+eEEJI7sKFToQQ4lEo8IQQ4lEo8IQQ4lEo8IQQ4lGczqIx\nhRDCD+AFAAJAGMA3pZS73LAlUwghzgLwJwBXSin/5rY9TiOECAH4pOflPinlXW7a4yRCiIcBTEX0\n7+MnUsqXXTbJMYQQXwUwG9EFi8UALgJQLqVsS7ZfviCE8AF4EVFt6QbwdS/9/QkhihC9vnMAnALw\ngJTyXaPt3fLgbwAQkVJOBPA4gO+7ZEdGEEIUIlqX57jbtmQCIcTpACClvKLnPy+J+yQA/yClnABg\nMoBRLpvkKFLKl6SUk6WUVwAIAZjrFXHv4csABvRoy5PwmLYA+DqAjp7f5zeQYhGqKwIvpVyLqHEA\nUAXgYzfsyCALATwH4CO3DckQFwEYIITYJIT4XU8VUa9wNYCdQog1ANb1/Oc5hBAXAxgjpfxPt21x\nmBMABvZ48gMR9XK9xPkANgJAz5PJ3wkhAkYbuxaDl1KGhRBLES0v/HO37HAaIcRsAEeklL9FfKVN\nL3EcwAIp5dWIFpz7eU/YzQuUAQgCuAnRa3vFXXMyxiMAvuu2ERlgG6Khp/8B8DyA/3DXHMf5M4Ap\nACCEGI/o73WA0cau/lFKKecA+DyAF4UQxW7a4iBzAFwlhNgC4AsAXu6Jx3uJv6Hnpiyl3APgGIBh\nrlrkHMcAbJJSdvV4SCeEEGVuG+UkQoiBAD4vpXzTbVsywD8D+L2UUiD6pPmyEOI0l21ykiUA2oUQ\ndQCmI/q32GK0sSsCL4S4QwjxSM/LE4hOhoTdsMVppJSTemKckxG9294ppTzitl0OMwfA0wAghDgb\n0cJyTa5a5BzbAFwDxK6tP6Ki7yVqAGx224gMcQZ6J/9bEZ0oL3DPHMe5BMDrUsoaACsBHJJSnjTa\n2JUsGgCvAlgmhHizx4YHkhmZx3i1DsR/AljS40VEAHxNSumVG/SvhBCXCSHeRjTEdp+U0mvfowDw\ngdtGZIgFAJYKIbYiqi2PSCk7XLbJSSSAXwghHgXQgeikqyGsRUMIIR7FKxNjhBBCEqDAE0KIR6HA\nE0KIR6HAE0KIR6HAE0KIR6HAE0KIR6HAE0KIR6HAE0KIR/lfJZ6QYPXpgHIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10baeb210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot original plot\n",
    "\n",
    "plt.plot(boston_df.RM,boston_df.Price,'o')\n",
    "# plot best fit line\n",
    "\n",
    "x = boston_df.RM\n",
    "plt.plot(x,m*x + b,'r',label='Best Fit Line')  #y =mx +c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10bbea5d0>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAECCAYAAAD0JMwBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nuk4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b5858d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 5 : Get the error and do the multi variate regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMS Error is 6.60\n"
     ]
    }
   ],
   "source": [
    "result = np.linalg.lstsq(X,Y)\n",
    "#Error are stored in index 1\n",
    "error_total = result[1]\n",
    "\n",
    "rmse = np.sqrt(error_total/len(X))\n",
    "\n",
    "print ('RMS Error is %.2f'%rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approx to std dev, the price of house wont vary more than 2 times the RMSE value for 95% of the time\n",
    " i.e 6.60 * 2 in thousands\n",
    "\n",
    " 68–95–99.7 rule\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 6: scikit learn multi variable regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# scikit learn regression as estimator. \n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lreg = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# lreg.fit()\n",
    "# lreg.predict()\n",
    "# lreg.score() - coefficient of determination (R^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_multi = boston_df.drop('Price',1)\n",
    "Y_target = boston_df.Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# linear regresstion\n",
    "lreg.fit(X_multi,Y_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated intercept coefficient is 36.49 \n",
      "The number of coefficient used is 13.00\n"
     ]
    }
   ],
   "source": [
    "print'Estimated intercept coefficient is %.2f '%lreg.intercept_\n",
    "print'The number of coefficient used is %.2f'%len(lreg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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>Features</th>\n",
       "      <th>Coefficient Estimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CRIM</td>\n",
       "      <td>-0.107171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ZN</td>\n",
       "      <td>0.046395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>INDUS</td>\n",
       "      <td>0.020860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>CHAS</td>\n",
       "      <td>2.688561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NOX</td>\n",
       "      <td>-17.795759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RM</td>\n",
       "      <td>3.804752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE</td>\n",
       "      <td>0.000751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIS</td>\n",
       "      <td>-1.475759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>RAD</td>\n",
       "      <td>0.305655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>TAX</td>\n",
       "      <td>-0.012329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PTRATIO</td>\n",
       "      <td>-0.953464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>B</td>\n",
       "      <td>0.009393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LSTAT</td>\n",
       "      <td>-0.525467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Price</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Features  Coefficient Estimate\n",
       "0      CRIM             -0.107171\n",
       "1        ZN              0.046395\n",
       "2     INDUS              0.020860\n",
       "3      CHAS              2.688561\n",
       "4       NOX            -17.795759\n",
       "5        RM              3.804752\n",
       "6       AGE              0.000751\n",
       "7       DIS             -1.475759\n",
       "8       RAD              0.305655\n",
       "9       TAX             -0.012329\n",
       "10  PTRATIO             -0.953464\n",
       "11        B              0.009393\n",
       "12    LSTAT             -0.525467\n",
       "13    Price                   NaN"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show\n",
    "# create coeffdf based on dataframe columns\n",
    "coeff_df = DataFrame(boston_df.columns)\n",
    "\n",
    "# rename that column as Features\n",
    "coeff_df.columns = ['Features']\n",
    "\n",
    "# newcolumn\n",
    "coeff_df['Coefficient Estimate'] = Series(lreg.coef_)\n",
    "\n",
    "coeff_df\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 7:Training and Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[array([ 6.575]), 1],\n",
       "       [array([ 6.421]), 1],\n",
       "       [array([ 7.185]), 1],\n",
       "       ..., \n",
       "       [array([ 6.976]), 1],\n",
       "       [array([ 6.794]), 1],\n",
       "       [array([ 6.03]), 1]], dtype=object)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      24.0\n",
       "1      21.6\n",
       "2      34.7\n",
       "3      33.4\n",
       "4      36.2\n",
       "5      28.7\n",
       "6      22.9\n",
       "7      27.1\n",
       "8      16.5\n",
       "9      18.9\n",
       "10     15.0\n",
       "11     18.9\n",
       "12     21.7\n",
       "13     20.4\n",
       "14     18.2\n",
       "15     19.9\n",
       "16     23.1\n",
       "17     17.5\n",
       "18     20.2\n",
       "19     18.2\n",
       "20     13.6\n",
       "21     19.6\n",
       "22     15.2\n",
       "23     14.5\n",
       "24     15.6\n",
       "25     13.9\n",
       "26     16.6\n",
       "27     14.8\n",
       "28     18.4\n",
       "29     21.0\n",
       "       ... \n",
       "476    16.7\n",
       "477    12.0\n",
       "478    14.6\n",
       "479    21.4\n",
       "480    23.0\n",
       "481    23.7\n",
       "482    25.0\n",
       "483    21.8\n",
       "484    20.6\n",
       "485    21.2\n",
       "486    19.1\n",
       "487    20.6\n",
       "488    15.2\n",
       "489     7.0\n",
       "490     8.1\n",
       "491    13.6\n",
       "492    20.1\n",
       "493    21.8\n",
       "494    24.5\n",
       "495    23.1\n",
       "496    19.7\n",
       "497    18.3\n",
       "498    21.2\n",
       "499    17.5\n",
       "500    16.8\n",
       "501    22.4\n",
       "502    20.6\n",
       "503    23.9\n",
       "504    22.0\n",
       "505    11.9\n",
       "Name: Price, dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df.Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sklearn\n",
    "X_train,X_test,Y_train,Y_test=sklearn.cross_validation.train_test_split(X,boston_df.Price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(379, 2) (127, 2) (379,) (127,)\n"
     ]
    }
   ],
   "source": [
    "# output\n",
    "print X_train.shape, X_test.shape,Y_train.shape,Y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 8 Predicting the house prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lreg = LinearRegression()\n",
    "lreg.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# run prediction on x train and x test\n",
    "\n",
    "pred_train = lreg.predict(X_train)\n",
    "pred_test = lreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit a model X_train and calculate the MSE with Y_train : 44.21 \n",
      "Fit a model X_train and calculate the MSE with X_test and Y_test : 42.54 \n"
     ]
    }
   ],
   "source": [
    "# take means squared error\n",
    "\n",
    "print 'Fit a model X_train and calculate the MSE with Y_train : %.2f '% np.mean((Y_train-pred_train)**2)  #this is the length of d line\n",
    "print 'Fit a model X_train and calculate the MSE with X_test and Y_test : %.2f '% np.mean((Y_test-pred_test)**2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 9: Residual plot to visualize \n",
    "Residual = Observed value - predicted value  i.e pred_train-Y_train\n",
    "More here http://blog.minitab.com/blog/adventures-in-statistics/why-you-need-to-check-your-residual-plots-for-regression-analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10c4de490>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEKCAYAAAAcgp5RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRCTgVPQiIgH3f0iggnbICF3RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2e3e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train = plt.scatter(pred_train,(pred_train- Y_train),c ='b', alpha =0.5)\n",
    "test = plt.scatter(pred_test,(pred_test-Y_test),c='r',alpha =0.5)\n",
    "\n",
    "plt.hlines(y=0,xmin=-10,xmax=40)\n",
    "plt.legend((train,test),('Training','Test'),loc='lower left')\n",
    "\n",
    "plt.title('Residual Plots')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}