Example 1: SelectionRegression

This example uses a data set from Draper and Smith (1981, pp. 629-630). Class SelectionRegression is invoked to find the best regression for each subset size using the criterion.

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.PrintMatrix;
import com.imsl.math.PrintMatrixFormat;

public class SelectionRegressionEx1 {

    public static void main(String[] args)  throws Exception {
        double x[][] = { {7., 26., 6., 60.},
                         {1., 29., 15., 52.},
                         {11., 56., 8., 20.},
                         {11., 31., 8., 47.},
                         {7., 52., 6., 33.},
                         {11., 55., 9., 22.},
                         {3., 71., 17., 6.},
                         {1., 31., 22., 44.},
                         {2., 54., 18., 22.},
                         {21., 47., 4., 26},
                         {1., 40., 23., 34.},
                         {11., 66., 9., 12.},
                         {10.0, 68., 8., 12.}};
        
        double y[] = { 78.5, 74.3, 104.3, 87.6,
                       95.9, 109.2, 102.7, 72.5,
                       93.1, 115.9, 83.8, 113.3, 109.4};

        String criterionOption;
        MessageFormat critMsg =
           new MessageFormat("Regressions with {0} variable(s) ({1})");
        MessageFormat critLabel =
           new MessageFormat("   Criterion               Variables");
        MessageFormat coefMsg =
           new MessageFormat("Best Regressions with {0} variable(s) ({1})");
        MessageFormat coefLabel = new MessageFormat("Variable   Coefficient" +
           "   Standard Error  t-statistic   p-value");
        MessageFormat critData = new MessageFormat("{0}   {1}   {2}   {3}" +
           "   {4}   {5}");

        SelectionRegression sr = new SelectionRegression(4);
        sr.compute(x, y);
        SelectionRegression.Statistics stats =
                sr.getStatistics();
        
        criterionOption = new String("R-squared");
        
        for (int i=1; i <= 4 ; i++) {
            double[] tmpCrit = stats.getCriterionValues(i);
            int[][] indvar = stats.getIndependentVariables(i);
            
            Object p[] = {new Integer(i), criterionOption};
            System.out.println(critMsg.format(p));
            Object p1[] = {null};
            System.out.println(critLabel.format(p1));
            
            for (int j=0; j< tmpCrit.length; j++) {
                System.out.print("     "+tmpCrit[j]+"        ");
                for (int k = 0; k < indvar[j].length ; k++) {
                    System.out.print(indvar[j][k]+"   ");
                }
                System.out.println("");
            }
            System.out.println("");
        }
        
        for (int i=0; i < 4; i++) {
            System.out.println("");
            Object p[] = {new Integer(i+1), criterionOption};
            System.out.println(coefMsg.format(p));
            Object p2[] = {null};
            System.out.println(coefLabel.format(p2));
            
            double[][] tmpCoef= stats.getCoefficientStatistics(i);
            PrintMatrix pm = new PrintMatrix();
            pm.setColumnSpacing(10);
            PrintMatrixFormat tst = new PrintMatrixFormat();
            tst.setNoColumnLabels();
            tst.setNoRowLabels();
            pm.print(tst, tmpCoef);
            System.out.println("");
            System.out.println("");
        }
    }
}

Output

Regressions with 1 variable(s) (R-squared)
   Criterion               Variables
     67.45419641316094        4   
     66.62682576332938        2   
     53.39480238350332        1   
     28.58727312298116        3   

Regressions with 2 variable(s) (R-squared)
   Criterion               Variables
     97.86783745356314        1   2   
     97.24710477169312        1   4   
     93.52896406158074        3   4   
     68.00604079500502        2   4   
     54.81667488448575        1   3   

Regressions with 3 variable(s) (R-squared)
   Criterion               Variables
     98.23354512004263        1   2   4   
     98.22846792190859        1   2   3   
     98.12810925873434        1   3   4   
     97.28199593862728        2   3   4   

Regressions with 4 variable(s) (R-squared)
   Criterion               Variables
     98.23756204076797        1   2   3   4   


Best Regressions with 1 variable(s) (R-squared)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                   
4          -0.738          0.155          -4.775          0.001          




Best Regressions with 2 variable(s) (R-squared)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                              
1          1.468          0.121          12.105          0          
2          0.662          0.046          14.442          0          




Best Regressions with 3 variable(s) (R-squared)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                   
1           1.452          0.117          12.41           0              
2           0.416          0.186           2.242          0.052          
4          -0.237          0.173          -1.365          0.205          




Best Regressions with 4 variable(s) (R-squared)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                   
1           1.551          0.745           2.083          0.071          
2           0.51           0.724           0.705          0.501          
3           0.102          0.755           0.135          0.896          
4          -0.144          0.709          -0.203          0.844