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This is an *extremely* bad idea.
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.display import HTML"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python2.7/dist-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": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"from scipy import stats\n",
"import pandas as pd\n",
"from patsy import dmatrices\n",
"import seaborn as sns\n",
"from statsmodels import api as sm"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<blockquote class=\"twitter-tweet\" lang=\"en\"><p lang=\"en\" dir=\"ltr\">Get better regressions most of the time with this one weird trick:&#10;<a href=\"https://t.co/vLB0GeShTm\">https://t.co/vLB0GeShTm</a>&#10;&#10;via <a href=\"https://twitter.com/johnmyleswhite\">@johnmyleswhite</a></p>&mdash; fastml extra (@fastml_extra) <a href=\"https://twitter.com/fastml_extra/status/674364084654055424\">December 8, 2015</a></blockquote>\n",
"<script async src=\"//platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"HTML(\"\"\"<blockquote class=\"twitter-tweet\" lang=\"en\"><p lang=\"en\" dir=\"ltr\">Get better regressions most of the time with this one weird trick:&#10;<a href=\"https://t.co/vLB0GeShTm\">https://t.co/vLB0GeShTm</a>&#10;&#10;via <a href=\"https://twitter.com/johnmyleswhite\">@johnmyleswhite</a></p>&mdash; fastml extra (@fastml_extra) <a href=\"https://twitter.com/fastml_extra/status/674364084654055424\">December 8, 2015</a></blockquote>\n",
"<script async src=\"//platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>\"\"\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generate uncorrelated data"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 500"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df = pd.DataFrame({\n",
" 'x': stats.uniform.rvs(0, 1, size=N),\n",
" 'y': stats.uniform.rvs(0, 1, size=N)\n",
" })"
]
},
{
"cell_type": "code",
"execution_count": 7,
"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>x</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.445872</td>\n",
" <td>0.823346</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.008912</td>\n",
" <td>0.420028</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.555452</td>\n",
" <td>0.462420</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.312182</td>\n",
" <td>0.160712</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.552521</td>\n",
" <td>0.237752</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x y\n",
"0 0.445872 0.823346\n",
"1 0.008912 0.420028\n",
"2 0.555452 0.462420\n",
"3 0.312182 0.160712\n",
"4 0.552521 0.237752"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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05B59AXIFlELPQ6rgpPREY2FhDnNzC1InGiyRNbkwi0qJJi94BDFRgkKuZBRY3OTp9tic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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe42c771f50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6));\n",
"\n",
"ax.scatter(df.x, df.y, c='k', alpha=0.5);\n",
"\n",
"ax.set_xlim(0, 1);\n",
"ax.set_ylim(0, 1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fit a correct model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y, X = dmatrices('y ~ x', data=df)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"model = sm.OLS(y, X)\n",
"results = model.fit()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.002</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> -0.000</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 0.8514</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 09 Dec 2015</td> <th> Prob (F-statistic):</th> <td> 0.357</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>13:57:24</td> <th> Log-Likelihood: </th> <td> -85.466</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 500</td> <th> AIC: </th> <td> 174.9</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 498</td> <th> BIC: </th> <td> 183.4</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</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> 0.5216</td> <td> 0.026</td> <td> 20.127</td> <td> 0.000</td> <td> 0.471 0.572</td>\n",
"</tr>\n",
"<tr>\n",
" <th>x</th> <td> -0.0422</td> <td> 0.046</td> <td> -0.923</td> <td> 0.357</td> <td> -0.132 0.048</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>259.586</td> <th> Durbin-Watson: </th> <td> 2.098</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 28.584</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td>-0.016</td> <th> Prob(JB): </th> <td>6.21e-07</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 1.829</td> <th> Cond. No. </th> <td> 4.47</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.002\n",
"Model: OLS Adj. R-squared: -0.000\n",
"Method: Least Squares F-statistic: 0.8514\n",
"Date: Wed, 09 Dec 2015 Prob (F-statistic): 0.357\n",
"Time: 13:57:24 Log-Likelihood: -85.466\n",
"No. Observations: 500 AIC: 174.9\n",
"Df Residuals: 498 BIC: 183.4\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"Intercept 0.5216 0.026 20.127 0.000 0.471 0.572\n",
"x -0.0422 0.046 -0.923 0.357 -0.132 0.048\n",
"==============================================================================\n",
"Omnibus: 259.586 Durbin-Watson: 2.098\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 28.584\n",
"Skew: -0.016 Prob(JB): 6.21e-07\n",
"Kurtosis: 1.829 Cond. No. 4.47\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"results.summary()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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hZUXwTvSOz+XLaxAIBHD77R/DihUrDZdjVucLz2lc1nRiMsyK5LFmgBPGQKPI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\nxSYwXB+uAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe42c68c450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6));\n",
"\n",
"ax.scatter(df.x, df.y, c='k', alpha=0.5, label=None);\n",
"\n",
"xs = np.linspace(0, 1, 20)\n",
"ax.plot(xs, results.predict(sm.add_constant(xs)), c='r', label='OLS estimate');\n",
"\n",
"ax.set_xlim(0, 1);\n",
"ax.set_ylim(0, 1);\n",
"\n",
"ax.legend(bbox_to_anchor=(1.25, 1.));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fit a sorted model"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sorted_df = df.apply(lambda s: s.sort_values().values)"
]
},
{
"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>x</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.002298</td>\n",
" <td>0.004737</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.004193</td>\n",
" <td>0.005661</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.008912</td>\n",
" <td>0.006825</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.010693</td>\n",
" <td>0.010308</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.012882</td>\n",
" <td>0.011007</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x y\n",
"0 0.002298 0.004737\n",
"1 0.004193 0.005661\n",
"2 0.008912 0.006825\n",
"3 0.010693 0.010308\n",
"4 0.012882 0.011007"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sorted_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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dAUA8XshLL73cOQqnXrP0ZQd99AdB8I5/19fXc8kllzBw4ECuuOIKXnjhBWbN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\nYrs5vAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe42c644150>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6));\n",
"\n",
"ax.scatter(sorted_df.x, sorted_df.y, c='k', alpha=0.5);\n",
"\n",
"ax.set_xlim(0, 1);\n",
"ax.set_ylim(0, 1);"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sorted_y, sorted_X = dmatrices('y ~ x', data=sorted_df)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sorted_model = sm.OLS(sorted_y, sorted_X)\n",
"sorted_results = sorted_model.fit()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.997</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.997</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td>1.786e+05</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 09 Dec 2015</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>13:57:25</td> <th> Log-Likelihood: </th> <td> 1385.4</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 500</td> <th> AIC: </th> <td> -2767.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 498</td> <th> BIC: </th> <td> -2758.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</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> -0.0009</td> <td> 0.001</td> <td> -0.676</td> <td> 0.500</td> <td> -0.004 0.002</td>\n",
"</tr>\n",
"<tr>\n",
" <th>x</th> <td> 1.0207</td> <td> 0.002</td> <td> 422.627</td> <td> 0.000</td> <td> 1.016 1.025</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td> 5.624</td> <th> Durbin-Watson: </th> <td> 0.029</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.060</td> <th> Jarque-Bera (JB): </th> <td> 5.860</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.182</td> <th> Prob(JB): </th> <td> 0.0534</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 3.386</td> <th> Cond. No. </th> <td> 4.47</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.997\n",
"Model: OLS Adj. R-squared: 0.997\n",
"Method: Least Squares F-statistic: 1.786e+05\n",
"Date: Wed, 09 Dec 2015 Prob (F-statistic): 0.00\n",
"Time: 13:57:25 Log-Likelihood: 1385.4\n",
"No. Observations: 500 AIC: -2767.\n",
"Df Residuals: 498 BIC: -2758.\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"Intercept -0.0009 0.001 -0.676 0.500 -0.004 0.002\n",
"x 1.0207 0.002 422.627 0.000 1.016 1.025\n",
"==============================================================================\n",
"Omnibus: 5.624 Durbin-Watson: 0.029\n",
"Prob(Omnibus): 0.060 Jarque-Bera (JB): 5.860\n",
"Skew: 0.182 Prob(JB): 0.0534\n",
"Kurtosis: 3.386 Cond. No. 4.47\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sorted_results.summary()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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7ooSzOI4EtBBCnAO6rpOaugaA5OQOrFy5nMWLF5NdmEXhIA9GcwPNq9F2Szt6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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe42c45d450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6));\n",
"\n",
"ax.scatter(sorted_df.x, sorted_df.y, c='k', alpha=0.5, label=None);\n",
"\n",
"\n",
"ax.plot(xs, sorted_results.predict(sm.add_constant(xs)),\n",
" c='g', label='Sorted OLS estimate');\n",
"\n",
"ax.set_xlim(0, 1);\n",
"ax.set_ylim(0, 1);\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<img src=\"http://media3.giphy.com/media/12MQeyrNxQT2s8/giphy.gif\"/>"
],
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%giphy facepalm"
]
},
{
"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": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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