{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from pandas import Series,DataFrame" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "sns.set_style('whitegrid')\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.datasets import load_boston" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "boston = load_boston()" ] }, { "cell_type": "code", "execution_count": 5, "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": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAERCAYAAAB2CKBkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAHnBJREFUeJzt3XuYHHWd7/F3wWaASIgRDWu8ZLzsfJVzZIEeoytokgdW\n", "DwdcNHNWdGOA7Lqah8hlHznohkvAxVUWyQox5HACGlhZXWBCXKKBeLgkex4fiTRsuH8BOQybmBCI\n", "IZjbkmT6/FHVpDPpS/Wkq6p76vN6nnnSdf92Tae/U/X71fcXlEolREQkvw7KOgAREcmWEoGISM4p\n", "EYiI5JwSgYhIzikRiIjknBKBiEjO/UHSBzCz8UAROAkYBBZH/z4OzHZ39V8VEclQolcEZjYKuAHY\n", "BgTAPGCOu38imj49yeOLiEhjSd8auhpYCKyPpo9391XR6+XAyQkfX0REGkgsEZjZ2cDL7r4imhVE\n", "P2VbgbFJHV9EROJJso1gJlAys5OBY4GbgbdVLB8DvJrg8UVEJIbEEoG7Ty6/NrP7gVnA1WY22d1X\n", "AqcA9zbaT7FYVGOyiMgwFAqFoPFaKfQaqlACvgYsMrMu4Engjjgbxn0zaSkWiyXF1Fg7xgTtGZdi\n", 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"plt.xlabel('Prices in $1000s')\n", "plt.ylabel('Number of houses')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAERCAYAAAB2CKBkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXt4FeWZwH8DBKKtQne3ZVvbVVuZb3d7UYOKgkQQS/CC\n", "t6LSgkZFC4pgVaCIyE2sVK1aAYkLKlG0KKxSUTEotyioQBC7vX2gVltta28KVUlCYPaPdw5z7jkn\n", "Odec9/c88+Rkzsw375ycfO9879XxPA9FURSldOmUbwEURVGU/KKKQFEUpcRRRaAoilLiqCJQFEUp\n", "cVQRKIqilDiqCBRFUUqcLtkc3BhzIzAUKAPmARuBxcB+4JfAWGutxq8qiqLkkaytCIwxA4CTrLV9\n", "gQHAV4GfAFOstZWAA5yTresriqIoqZFN09Bg4P+MMSuAlcDTQG9rbb3//irgtCxeX1EURUmBbJqG\n", "Pg98BTgLWQ2sRFYBIT4Gumfx+oqiKEoKZFMR/A34jbW2BdhhjGkEDgt7/xDgoyxeX1EURUmBbCqC\n", "l4FrgbuMMV8CDgbWGGNOsdZuAE4H1rQ2SENDgzqTFUVR2kDv3r2d1o/KoiKw1j5rjKk0xmxGfBFX\n", 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20.0272907.0700.4697.18561.14.9671224217.8392.834.03
30.0323702.1800.4586.99845.86.0622322218.7394.632.94
40.0690502.1800.4587.14754.26.0622322218.7396.905.33
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" ], "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": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston_df = DataFrame(boston.data)\n", "\n", "boston_df.columns = boston.feature_names\n", "\n", "boston_df.head()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "boston_df['Price'] = boston.target" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTATPrice
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10.0273107.0700.4696.42178.94.9671224217.8396.909.1421.6
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" ], "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": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston_df.head()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAWEAAAFhCAYAAACh/xvXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"IIJdEASh6xDBLgiC0GWIYBcEQegyRLALgiB0GSLYBUEQugwR7IIgCF2GCHZBEIQu4/8HIZdgX+6d\n", "R0gAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(boston_df.RM,boston_df.Price,'o')\n", "\n", "x = boston_df.RM\n", "\n", "plt.plot(x, m*x + b,'r',label='Best Fit Line')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " The root mean square error was 6.60\n" ] } ], "source": [ "result = np.linalg.lstsq(X,Y)\n", "\n", "error_total = result[1]\n", "\n", "rmse = np.sqrt(error_total/len(X))\n", "\n", "print ' The root mean square error was %.2f' %rmse" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import sklearn\n", "from sklearn.linear_model import LinearRegression" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "lreg = LinearRegression()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X_multi = boston_df.drop('Price',1)\n", "\n", "Y_target = boston_df.Price" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "LinearRegression(copy_X=True, fit_intercept=True, normalize=False)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lreg.fit(X_multi,Y_target)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " The estimated intercept coefficient is 36.49 \n", " The number of coefficients used was 13 \n" ] } ], "source": [ "print ' The estimated intercept coefficient is %.2f ' % lreg.intercept_\n", "\n", "print ' The number of coefficients used was %d ' %len(lreg.coef_)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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FeaturesCoefficient Estimate
0CRIM-0.107171
1ZN0.046395
2INDUS0.020860
3CHAS2.688561
4NOX-17.795759
5RM3.804752
6AGE0.000751
7DIS-1.475759
8RAD0.305655
9TAX-0.012329
10PTRATIO-0.953464
11B0.009393
12LSTAT-0.525467
13PriceNaN
\n", "
" ], "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": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coeff_df = DataFrame(boston_df.columns)\n", "coeff_df.columns = ['Features']\n", "\n", "coeff_df['Coefficient Estimate'] = Series(lreg.coef_)\n", "\n", "coeff_df" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X_train,X_test,Y_train,Y_test = sklearn.cross_validation.train_test_split(X,boston_df.Price)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(379L, 2L) (127L, 2L) (379L,) (127L,)\n" ] } ], "source": [ "print X_train.shape, X_test.shape , Y_train.shape , Y_test.shape" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "LinearRegression(copy_X=True, fit_intercept=True, normalize=False)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lreg = LinearRegression()\n", "\n", "lreg.fit(X_train,Y_train)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pred_train = lreg.predict(X_train)\n", "pred_test = lreg.predict(X_test)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Fit a model X_train, and calculate the MSE with Y_train: 47.30 \n", " Fit a model X_train, and calculate MSE with X_test and Y_test: 32.75 \n" ] } ], "source": [ "print \" Fit a model X_train, and calculate the MSE with Y_train: %.2f \" % np.mean((Y_train-pred_train)**2)\n", "\n", "print \" Fit a model X_train, and calculate MSE with X_test and Y_test: %.2f \" % np.mean((Y_test - pred_test)**2)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEKCAYAAAD3tSVSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXl8VNX5/9/nzpJMVkIWIAsBES5hx4QEEJVNQKDaRLRY\n", "1NrWfrVKl2/prxatXb51r1i1YLVqtVZbrUisgojKIkaBQNgCJFd2yAJZyJ5MJjP3/v64MzCEsGRB\n", "knDer9e8MnOXM8+9d/K55z7nOc8jDMNAIpFIJN0T5VIbIJFIJJKLhxR5iUQi6cZIkZdIJJJujBR5\n", "iUQi6cZIkZdIJJJujBR5iUQi6cZYL7UBkssbVVV1YBfgAQwgCKgGfqxpWk4b23wZ+LemaWuaLU8B\n", "3tU0rX8b2+0H5GqaFtrCuubHYQPe0jTtCVVVJwJ/0TRt+Hna/y2wXdO0D9pin0TSElLkJZ2BiZqm\n", 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"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": "2.7.7" } }, "nbformat": 4, "nbformat_minor": 0 }