Skip to content

Instantly share code, notes, and snippets.

@sente
Last active November 23, 2015 05:38
Show Gist options
  • Save sente/9340872 to your computer and use it in GitHub Desktop.
Save sente/9340872 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Display the source blob
Display the rendered blob
Raw
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Polynomial Regression with Python\n",
"\n",
"\n",
"In this example we look at the Boston housing dataset and try to predict housing prices using the lsat variable, defined as the \u201cproportion of the adults without some high school education and proportion of male workes classified as laborers\u201d.\n",
"\n",
"We can clearly see that the relationship between medv and lstat is non-linear: the blue (straight) line is a poor fit; a better fit can be obtained by including higher order terms."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import numpy as np\n",
"import statsmodels.formula.api as smf\n",
"\n",
"# load the boston housing dataset - median house values in the Boston area\n",
"df = pd.read_csv('http://vincentarelbundock.github.io/Rdatasets/csv/MASS/Boston.csv')\n",
"print df.head()\n",
"\n",
"# plot lstat (% lower status of the population) against median value\n",
"plt.figure(figsize=(6 * 1.618, 6))\n",
"plt.scatter(df.lstat, df.medv, s=10, alpha=0.3)\n",
"plt.xlabel('lstat')\n",
"plt.ylabel('medv')\n",
"\n",
"# points linearlyd space on lstats\n",
"x = pd.DataFrame({'lstat': np.linspace(df.lstat.min(), df.lstat.max(), 100)})\n",
"\n",
"# 1-st order polynomial\n",
"poly_1 = smf.ols(formula='medv ~ 1 + lstat', data=df).fit()\n",
"plt.plot(x.lstat, poly_1.predict(x), 'b-', label='Poly n=1 $R^2$=%.2f' % poly_1.rsquared, \n",
" alpha=0.9)\n",
"\n",
"# 2-nd order polynomial\n",
"poly_2 = smf.ols(formula='medv ~ 1 + lstat + I(lstat ** 2.0)', data=df).fit()\n",
"plt.plot(x.lstat, poly_2.predict(x), 'g-', label='Poly n=2 $R^2$=%.2f' % poly_2.rsquared, \n",
" alpha=0.9)\n",
"\n",
"# 3-rd order polynomial\n",
"poly_3 = smf.ols(formula='medv ~ 1 + lstat + I(lstat ** 2.0) + I(lstat ** 3.0)', data=df).fit()\n",
"plt.plot(x.lstat, poly_3.predict(x), 'r-', alpha=0.9,\n",
" label='Poly n=3 $R^2$=%.2f' % poly_3.rsquared)\n",
"\n",
"plt.legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n",
" Unnamed: 0 crim zn indus chas nox rm age dis rad tax \\\n",
"0 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 \n",
"1 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 \n",
"2 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 \n",
"3 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 \n",
"4 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 \n",
"\n",
" ptratio black lstat medv \n",
"0 15.3 396.90 4.98 24.0 \n",
"1 17.8 396.90 9.14 21.6 \n",
"2 17.8 392.83 4.03 34.7 \n",
"3 18.7 394.63 2.94 33.4 \n",
"4 18.7 396.90 5.33 36.2 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"<matplotlib.legend.Legend at 0x10206ddd0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAF/CAYAAACVJ7fPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLmEuXgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10761b990>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"poly_2.summary()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>medv</td> <th> R-squared: </th> <td> 0.641</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.639</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 448.5</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Mon, 03 Mar 2014</td> <th> Prob (F-statistic):</th> <td>1.56e-112</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>11:00:57</td> <th> Log-Likelihood: </th> <td> -1581.3</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 506</td> <th> AIC: </th> <td> 3169.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 503</td> <th> BIC: </th> <td> 3181.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 2</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> 42.8620</td> <td> 0.872</td> <td> 49.149</td> <td> 0.000</td> <td> 41.149 44.575</td>\n",
"</tr>\n",
"<tr>\n",
" <th>lstat</th> <td> -2.3328</td> <td> 0.124</td> <td> -18.843</td> <td> 0.000</td> <td> -2.576 -2.090</td>\n",
"</tr>\n",
"<tr>\n",
" <th>I(lstat ** 2.0)</th> <td> 0.0435</td> <td> 0.004</td> <td> 11.628</td> <td> 0.000</td> <td> 0.036 0.051</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>107.006</td> <th> Durbin-Watson: </th> <td> 0.921</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 228.388</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 1.128</td> <th> Prob(JB): </th> <td>2.55e-50</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 5.397</td> <th> Cond. No. </th> <td>1.13e+03</td>\n",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: medv R-squared: 0.641\n",
"Model: OLS Adj. R-squared: 0.639\n",
"Method: Least Squares F-statistic: 448.5\n",
"Date: Mon, 03 Mar 2014 Prob (F-statistic): 1.56e-112\n",
"Time: 11:00:57 Log-Likelihood: -1581.3\n",
"No. Observations: 506 AIC: 3169.\n",
"Df Residuals: 503 BIC: 3181.\n",
"Df Model: 2 \n",
"===================================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"-----------------------------------------------------------------------------------\n",
"Intercept 42.8620 0.872 49.149 0.000 41.149 44.575\n",
"lstat -2.3328 0.124 -18.843 0.000 -2.576 -2.090\n",
"I(lstat ** 2.0) 0.0435 0.004 11.628 0.000 0.036 0.051\n",
"==============================================================================\n",
"Omnibus: 107.006 Durbin-Watson: 0.921\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 228.388\n",
"Skew: 1.128 Prob(JB): 2.55e-50\n",
"Kurtosis: 5.397 Cond. No. 1.13e+03\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] The condition number is large, 1.13e+03. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n",
"\"\"\""
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
Display the source blob
Display the rendered blob
Raw
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment