Example 2: SelectionRegression

This example uses the same data set as the first example, but Mallow's statistic is used as the criterion rather than . Note that when Mallow's statistic (or adjusted ) is specified, the method setMaximumBestFound is used to indicate the total number of "best" regressions (rather than indicating the number of best regressions per subset size, as in the case of the criterion). In this example, the three best regressions are found to be (1, 2), (1, 2, 4), and (1, 2, 3).

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

public class SelectionRegressionEx2 {

    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");

        SelectionRegression sr = new SelectionRegression(4);
        sr.setCriterionOption(SelectionRegression.MALLOWS_CP_CRITERION);
        sr.setMaximumBestFound(3);
        sr.compute(x, y);
        SelectionRegression.Statistics stats = sr.getStatistics();

        criterionOption = "Mallows Cp";

        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 < 3; i++) {
            System.out.println("");

            double[][] tmpCoef = stats.getCoefficientStatistics(i);

            Object p[] = {new Integer(tmpCoef.length), criterionOption};
            System.out.println(coefMsg.format(p));
            Object p2[] = {null};
            System.out.println(coefLabel.format(p2));

            PrintMatrix pm = new PrintMatrix();
            pm.setColumnSpacing(10);
            NumberFormat nf = NumberFormat.getInstance();
            nf.setMinimumFractionDigits(4);
            PrintMatrixFormat tst = new PrintMatrixFormat();
            tst.setNoColumnLabels();
            tst.setNoRowLabels();
            tst.setNumberFormat(nf);
            pm.print(tst, tmpCoef);
            System.out.println();
            System.out.println();
        }
    }
}

Output

Regressions with 1 variable(s) (Mallows Cp)
   Criterion               Variables
     138.73083349167362        4   
     142.4864069369577        2   
     202.54876912344534        1   
     315.154284140073        3   

Regressions with 2 variable(s) (Mallows Cp)
   Criterion               Variables
     2.6782415983184045        1   2   
     5.495850824758396        1   4   
     22.37311196469674        3   4   
     138.22591975463834        2   4   
     198.09465256956904        1   3   

Regressions with 3 variable(s) (Mallows Cp)
   Criterion               Variables
     3.0182334734873084        1   2   4   
     3.04127972306423        1   2   3   
     3.4968244423483164        1   3   4   
     7.337473995655756        2   3   4   

Regressions with 4 variable(s) (Mallows Cp)
   Criterion               Variables
     5.0        1   2   3   4   


Best Regressions with 2 variable(s) (Mallows Cp)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                           
1.0000          1.4683          0.1213          12.1047          0.0000          
2.0000          0.6623          0.0459          14.4424          0.0000          




Best Regressions with 3 variable(s) (Mallows Cp)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                            
1.0000           1.4519          0.1170          12.4100          0.0000          
2.0000           0.4161          0.1856           2.2418          0.0517          
4.0000          -0.2365          0.1733          -1.3650          0.2054          




Best Regressions with 3 variable(s) (Mallows Cp)
Variable   Coefficient   Standard Error  t-statistic   p-value
                                                                                           
1.0000          1.6959          0.2046           8.2895          0.0000          
2.0000          0.6569          0.0442          14.8508          0.0000          
3.0000          0.2500          0.1847           1.3536          0.2089