.ipynb_checkpoints/Untitled2-checkpoint.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:d2d9d9999df0d82e05a34bd3e5e4f35dd2e89adfdd7af344e29965ceb7cefa2b"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# load numpy and pandas for data manipulation\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "\n",
      "# load statsmodels as alias ``sm``\n",
      "import statsmodels.api as sm\n",
      "\n",
      "# load the longley dataset into a pandas data frame - first column (year) used as row labels\n",
      "df = pd.read_csv('http://vincentarelbundock.github.io/Rdatasets/csv/datasets/longley.csv', index_col=0)\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>GNP.deflator</th>\n",
        "      <th>GNP</th>\n",
        "      <th>Unemployed</th>\n",
        "      <th>Armed.Forces</th>\n",
        "      <th>Population</th>\n",
        "      <th>Year</th>\n",
        "      <th>Employed</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1947</th>\n",
        "      <td> 83.0</td>\n",
        "      <td> 234.289</td>\n",
        "      <td> 235.6</td>\n",
        "      <td> 159.0</td>\n",
        "      <td> 107.608</td>\n",
        "      <td> 1947</td>\n",
        "      <td> 60.323</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1948</th>\n",
        "      <td> 88.5</td>\n",
        "      <td> 259.426</td>\n",
        "      <td> 232.5</td>\n",
        "      <td> 145.6</td>\n",
        "      <td> 108.632</td>\n",
        "      <td> 1948</td>\n",
        "      <td> 61.122</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1949</th>\n",
        "      <td> 88.2</td>\n",
        "      <td> 258.054</td>\n",
        "      <td> 368.2</td>\n",
        "      <td> 161.6</td>\n",
        "      <td> 109.773</td>\n",
        "      <td> 1949</td>\n",
        "      <td> 60.171</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1950</th>\n",
        "      <td> 89.5</td>\n",
        "      <td> 284.599</td>\n",
        "      <td> 335.1</td>\n",
        "      <td> 165.0</td>\n",
        "      <td> 110.929</td>\n",
        "      <td> 1950</td>\n",
        "      <td> 61.187</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1951</th>\n",
        "      <td> 96.2</td>\n",
        "      <td> 328.975</td>\n",
        "      <td> 209.9</td>\n",
        "      <td> 309.9</td>\n",
        "      <td> 112.075</td>\n",
        "      <td> 1951</td>\n",
        "      <td> 63.221</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "      GNP.deflator      GNP  Unemployed  Armed.Forces  Population  Year  \\\n",
        "1947          83.0  234.289       235.6         159.0     107.608  1947   \n",
        "1948          88.5  259.426       232.5         145.6     108.632  1948   \n",
        "1949          88.2  258.054       368.2         161.6     109.773  1949   \n",
        "1950          89.5  284.599       335.1         165.0     110.929  1950   \n",
        "1951          96.2  328.975       209.9         309.9     112.075  1951   \n",
        "\n",
        "      Employed  \n",
        "1947    60.323  \n",
        "1948    61.122  \n",
        "1949    60.171  \n",
        "1950    61.187  \n",
        "1951    63.221  "
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import statsmodels.formula.api as smf\n",
      "# formula: response ~ predictors\n",
      "est = smf.ols(formula='Employed ~ GNP + Population + Year', data=df).fit()\n",
      "est.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table class=\"simpletable\">\n",
        "<caption>OLS Regression Results</caption>\n",
        "<tr>\n",
        "  <th>Dep. Variable:</th>        <td>Employed</td>     <th>  R-squared:         </th> <td>   0.979</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.974</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   190.1</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Date:</th>             <td>Thu, 22 Jan 2015</td> <th>  Prob (F-statistic):</th> <td>2.22e-10</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Time:</th>                 <td>11:44:49</td>     <th>  Log-Likelihood:    </th> <td> -11.227</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   30.45</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Df Residuals:</th>          <td>    12</td>      <th>  BIC:               </th> <td>   33.55</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Df Model:</th>              <td>     3</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>  416.9465</td> <td>  740.264</td> <td>    0.563</td> <td> 0.584</td> <td>-1195.950  2029.843</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>GNP</th>        <td>    0.0679</td> <td>    0.015</td> <td>    4.436</td> <td> 0.001</td> <td>    0.035     0.101</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Population</th> <td>   -0.3597</td> <td>    0.193</td> <td>   -1.860</td> <td> 0.088</td> <td>   -0.781     0.062</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Year</th>       <td>   -0.1718</td> <td>    0.388</td> <td>   -0.443</td> <td> 0.666</td> <td>   -1.016     0.673</td>\n",
        "</tr>\n",
        "</table>\n",
        "<table class=\"simpletable\">\n",
        "<tr>\n",
        "  <th>Omnibus:</th>       <td> 1.348</td> <th>  Durbin-Watson:     </th> <td>   1.219</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Prob(Omnibus):</th> <td> 0.510</td> <th>  Jarque-Bera (JB):  </th> <td>   0.640</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Skew:</th>          <td> 0.489</td> <th>  Prob(JB):          </th> <td>   0.726</td>\n",
        "</tr>\n",
        "<tr>\n",
        "  <th>Kurtosis:</th>      <td> 2.934</td> <th>  Cond. No.          </th> <td>1.05e+07</td>\n",
        "</tr>\n",
        "</table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<class 'statsmodels.iolib.summary.Summary'>\n",
        "\"\"\"\n",
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:               Employed   R-squared:                       0.979\n",
        "Model:                            OLS   Adj. R-squared:                  0.974\n",
        "Method:                 Least Squares   F-statistic:                     190.1\n",
        "Date:                Thu, 22 Jan 2015   Prob (F-statistic):           2.22e-10\n",
        "Time:                        11:44:49   Log-Likelihood:                -11.227\n",
        "No. Observations:                  16   AIC:                             30.45\n",
        "Df Residuals:                      12   BIC:                             33.55\n",
        "Df Model:                           3                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept    416.9465    740.264      0.563      0.584     -1195.950  2029.843\n",
        "GNP            0.0679      0.015      4.436      0.001         0.035     0.101\n",
        "Population    -0.3597      0.193     -1.860      0.088        -0.781     0.062\n",
        "Year          -0.1718      0.388     -0.443      0.666        -1.016     0.673\n",
        "==============================================================================\n",
        "Omnibus:                        1.348   Durbin-Watson:                   1.219\n",
        "Prob(Omnibus):                  0.510   Jarque-Bera (JB):                0.640\n",
        "Skew:                           0.489   Prob(JB):                        0.726\n",
        "Kurtosis:                       2.934   Cond. No.                     1.05e+07\n",
        "==============================================================================\n",
        "\n",
        "Warnings:\n",
        "[1] The condition number is large, 1.05e+07. This might indicate that there are\n",
        "strong multicollinearity or other numerical problems.\n",
        "\"\"\""
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}