regression blog2.ipynb

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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\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": {
      "image/png": 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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
}