Example 1: StepwiseRegression

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

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

public class StepwiseRegressionEx1 {

   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};

         StepwiseRegression sr = new StepwiseRegression(x,y);
         sr.compute();

         PrintMatrix pm = new PrintMatrix();
         pm.setTitle("*** ANOVA *** "); pm.print(sr.getANOVA().getArray());
         
         StepwiseRegression.CoefficientTTests coefT =
            sr.getCoefficientTTests();
         double coef[][] = new double[4][4];
         for (int i=0; i<4; i++) {
            coef[i][0] = coefT.getCoefficient(i);
            coef[i][1] = coefT.getStandardError(i);
            coef[i][2] = coefT.getTStatistic(i);
            coef[i][3] = coefT.getPValue(i);
         }
         pm.setTitle("*** Coef *** "); pm.print(coef);
         pm.setTitle("*** Swept *** "); pm.print(sr.getSwept());
         pm.setTitle("*** History *** "); pm.print(sr.getHistory());
         pm.setTitle("*** VIF *** "); pm.print(sr.getCoefficientVIF());
         pm.setTitle("*** CovS *** "); pm.print(sr.getCovariancesSwept());
   }
}

Output

*** ANOVA *** 
        0      
 0      2      
 1     10      
 2     12      
 3  2,641.001  
 4     74.762  
 5  2,715.763  
 6  1,320.5    
 7      7.476  
 8    176.627  
 9      0      
10     97.247  
11     96.697  
12      2.734  
13      ?      
14      ?      

          *** Coef *** 
     0       1       2       3    
0   1.44   0.138   10.403  0      
1   0.416  0.186    2.242  0.052  
2  -0.41   0.199   -2.058  0.07   
3  -0.614  0.049  -12.621  0      

*** Swept *** 
   0   
0   1  
1  -1  
2  -1  
3   1  
4  -1  

*** History *** 
   0  
0  2  
1  0  
2  0  
3  1  
4  0  

*** VIF *** 
     0     
0   1.064  
1  18.78   
2   3.46   
3   1.064  

                 *** CovS *** 
     0        1         2        3        4     
0   0.003    -0.029    -0.946   0        1.44   
1  -0.029   154.72   -142.8     0.907   64.381  
2  -0.946  -142.8     142.302   0.07   -58.35   
3   0         0.907     0.07    0       -0.614  
4   1.44     64.381   -58.35   -0.614   74.762