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sherdim/regression blog2

Created February 28, 2016 23:31
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regression blog2.ipynb
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regression blog2
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test a Basic Linear Regression Model"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas"
]
},
{
"cell_type": "code",
"execution_count": 3,
"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>attempt</th>\n",
" <th>bukv</th>\n",
" <th>bukv0</th>\n",
" <th>host</th>\n",
" <th>kr</th>\n",
" <th>naextra</th>\n",
" <th>ncextra</th>\n",
" <th>nfscan</th>\n",
" <th>npause</th>\n",
" <th>nscan</th>\n",
" <th>...</th>\n",
" <th>tclast</th>\n",
" <th>texit</th>\n",
" <th>u</th>\n",
" <th>userid</th>\n",
" <th>var</th>\n",
" <th>vt</th>\n",
" <th>cmid</th>\n",
" <th>course</th>\n",
" <th>grade</th>\n",
" <th>result</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1795</td>\n",
" <td>257</td>\n",
" <td>147</td>\n",
" <td>up11</td>\n",
" <td>0.432422</td>\n",
" <td>-3</td>\n",
" <td>-2</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>64.556</td>\n",
" <td>66.461</td>\n",
" <td>UP11__4103478780151029</td>\n",
" <td>540</td>\n",
" <td>5</td>\n",
" <td>12.972669</td>\n",
" <td>1706</td>\n",
" <td>9</td>\n",
" <td>0.25</td>\n",
" <td>correct</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1795</td>\n",
" <td>283</td>\n",
" <td>49</td>\n",
" <td>up11</td>\n",
" <td>1.662998</td>\n",
" <td>4</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>1</td>\n",
" <td>...</td>\n",
" <td>158.545</td>\n",
" <td>159.532</td>\n",
" <td>UP11__4106285050151029</td>\n",
" <td>540</td>\n",
" <td>3</td>\n",
" <td>49.889946</td>\n",
" <td>1706</td>\n",
" <td>9</td>\n",
" <td>0.00</td>\n",
" <td>incorrect</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1795</td>\n",
" <td>81</td>\n",
" <td>27</td>\n",
" <td>up11</td>\n",
" <td>1.431508</td>\n",
" <td>-2</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>17.633</td>\n",
" <td>18.453</td>\n",
" <td>UP11__4106480830151029</td>\n",
" <td>540</td>\n",
" <td>4</td>\n",
" <td>42.945239</td>\n",
" <td>1706</td>\n",
" <td>9</td>\n",
" <td>0.00</td>\n",
" <td>incorrect</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1795</td>\n",
" <td>251</td>\n",
" <td>21</td>\n",
" <td>up11</td>\n",
" <td>1.870821</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>...</td>\n",
" <td>23.561</td>\n",
" <td>24.441</td>\n",
" <td>UP11__4107136770151029</td>\n",
" <td>540</td>\n",
" <td>4</td>\n",
" <td>56.124639</td>\n",
" <td>1706</td>\n",
" <td>9</td>\n",
" <td>0.25</td>\n",
" <td>correct</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1795</td>\n",
" <td>117</td>\n",
" <td>75</td>\n",
" <td>up11</td>\n",
" <td>0.275338</td>\n",
" <td>-1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>32.652</td>\n",
" <td>33.450</td>\n",
" <td>UP11__4107482870151029</td>\n",
" <td>540</td>\n",
" <td>3</td>\n",
" <td>8.260141</td>\n",
" <td>1706</td>\n",
" <td>9</td>\n",
" <td>0.25</td>\n",
" <td>correct</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 26 columns</p>\n",
"</div>"
],
"text/plain": [
" attempt bukv bukv0 host kr naextra ncextra nfscan npause \\\n",
"0 1795 257 147 up11 0.432422 -3 -2 0 1 \n",
"1 1795 283 49 up11 1.662998 4 0 0 2 \n",
"2 1795 81 27 up11 1.431508 -2 0 0 0 \n",
"3 1795 251 21 up11 1.870821 1 0 0 0 \n",
"4 1795 117 75 up11 0.275338 -1 0 0 1 \n",
"\n",
" nscan ... tclast texit u userid var \\\n",
"0 0 ... 64.556 66.461 UP11__4103478780151029 540 5 \n",
"1 1 ... 158.545 159.532 UP11__4106285050151029 540 3 \n",
"2 0 ... 17.633 18.453 UP11__4106480830151029 540 4 \n",
"3 1 ... 23.561 24.441 UP11__4107136770151029 540 4 \n",
"4 0 ... 32.652 33.450 UP11__4107482870151029 540 3 \n",
"\n",
" vt cmid course grade result \n",
"0 12.972669 1706 9 0.25 correct \n",
"1 49.889946 1706 9 0.00 incorrect \n",
"2 42.945239 1706 9 0.00 incorrect \n",
"3 56.124639 1706 9 0.25 correct \n",
"4 8.260141 1706 9 0.25 correct \n",
"\n",
"[5 rows x 26 columns]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"D=pandas.read_table('..\\StiReac\\D.tsv')\n",
"\n",
"D.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will test a linear regression model for the association between our primary explanatory variable - number of pauses (`npause`) and a response variable - time of exit (`texit`)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we have a quantitative explanatory variable, let us center it so that the mean = 0."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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7PH4aEdsBJG2meKJr/R6OBJaouPa5gBdI+r2I+O0E929ziFs39iwRcRNFYWhd\ngO3nwLFlS0LA69hVOCa7iNJEV7K8FhiIiLMpPghiwqtdSnojsJyyCJfTdwEfjeLTdN5PcQZ8F7C4\nvM2LgIk+Bu/nFFctPBH4KHBTOX8NRRH9hKSF5dy/L9s5B5b3dXfbGj8JrIqId1Oc5bevffee9gDw\nSES8i+ITxQ4s559h139vD0g6stxeVh7rWfcVEXdQPNmcTXEBq91dR/HJXosj4nvl/Z0WEX8GXEDx\nBNFa50SP02SPx6slHajihfFjKf7Saf3sLuAb5e/zT4EbXOSbwWf0NpELKVokRMTPJN0AbKT4D35D\nRAxJ6tvtNjHJdstXgRFJ2ylaFIdNcvvVwBbgH8oz7b8HPgxcI2l/irPmD0bET8ue+maKM+4HJzjm\nfwG+WhatZ4D3SvoAxV8cKyQ9QVHwrqY4+72Zotf/yYj4raTWmm4ArpB0EcWZcOv1gIkyfx/4uqTj\ngB3A3ZJeSnGJ6osl/Q/gHODq8onzaeC9E9wfFB8E8vaIuGv3YBFxf7m+NeXUvcB2FVczFEXx3v13\n3G6yx+M3wLcoWlffjIift/0e/htwraRhinbZl6a4f5tDfPVKe94rX1T884g4c7bX0k7Shyk+s3Zw\nttdizeYzerM5SNL1FJ8YdOpsr8Waz2f0ZmbJ+cVYM7PkXOjNzJJzoTczS86F3swsORd6M7PkXOjN\nzJL7/1oWG46ld34uAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11b100f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = D.npause\n",
"x = x - x.mean()\n",
"D['x']=x\n",
"x.hist();\n",
"xlabel('Normalized explanatory variable');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us use `statsmodel` module to test a linear regression model."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import statsmodels.api as sm\n",
"import statsmodels.formula.api as smf"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>texit</td> <th> R-squared: </th> <td> 0.485</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.485</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 6230.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Mon, 29 Feb 2016</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>02:03:07</td> <th> Log-Likelihood: </th> <td> -28193.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 6611</td> <th> AIC: </th> <td>5.639e+04</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 6609</td> <th> BIC: </th> <td>5.640e+04</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> 34.7437</td> <td> 0.212</td> <td> 164.092</td> <td> 0.000</td> <td> 34.329 35.159</td>\n",
"</tr>\n",
"<tr>\n",
" <th>x</th> <td> 27.8682</td> <td> 0.353</td> <td> 78.931</td> <td> 0.000</td> <td> 27.176 28.560</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>2583.402</td> <th> Durbin-Watson: </th> <td> 1.694</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td>14650.850</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 1.784</td> <th> Prob(JB): </th> <td> 0.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 9.361</td> <th> Cond. No. </th> <td> 1.67</td> \n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: texit R-squared: 0.485\n",
"Model: OLS Adj. R-squared: 0.485\n",
"Method: Least Squares F-statistic: 6230.\n",
"Date: Mon, 29 Feb 2016 Prob (F-statistic): 0.00\n",
"Time: 02:03:07 Log-Likelihood: -28193.\n",
"No. Observations: 6611 AIC: 5.639e+04\n",
"Df Residuals: 6609 BIC: 5.640e+04\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"Intercept 34.7437 0.212 164.092 0.000 34.329 35.159\n",
"x 27.8682 0.353 78.931 0.000 27.176 28.560\n",
"==============================================================================\n",
"Omnibus: 2583.402 Durbin-Watson: 1.694\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 14650.850\n",
"Skew: 1.784 Prob(JB): 0.00\n",
"Kurtosis: 9.361 Cond. No. 1.67\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"reg1 = smf.ols('texit ~ x', data=D).fit()\n",
"reg1.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results of the linear regression model indicated that time of exit is proportional to the number of pauses (k=27.9, p<.001). So simple linear model is\n",
"$$ t_{exit} = 34.74 + 27.86 n_{pause}$$\n",
"where $t_{exit}$ - time of exit, $n_{pause}$ - number of pauses\n",
"\n",
"We can conclude that a single pause lasts at average near 28 sec.\n",
"\n",
"To estimate regression fit let us scatter data."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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/wB/FKSG3aBEcd5z/WrQo6GgSTyecRciiRdC9u9+vKD/ffz9unJJCipW3x3A58DOginPu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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ed2690>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"y=D.texit\n",
"plot(x, y, '.')\n",
"xx=xlim()\n",
"yy=reg1.predict(dict(x=xx))\n",
"plot(xx,yy,'r')\n",
"text(.8,.9, '$r^2 = {:.2f}$'.format(reg1.rsquared), transform=gca().transAxes);\n",
"xlabel('$n_{pause}$'); ylabel('$t_{exit}$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Time of exit definitely grows with the number of pauses."
]
}
],
"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
}
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