37         PROC REG DATA=ONE;   TITLE2 'Sub Models';
38            MODEL Y = X1;
39            MODEL Y = X2;
40            MODEL Y = X3;
41            MODEL Y = X1 X2 / SS2;
42            MODEL Y = X1 X3 / SS2;
43            MODEL Y = X2 X3 / SS2;
44            MODEL Y = X1 X2 X3 / SS2; RUN;

 
Model: MODEL1  Analysis of Variance
                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            1   5957.02249   5957.02249       14.817       0.0014
Error           16   6432.58862    402.03679
C Total         17  12389.61111

 
Model: MODEL2  Analysis of Variance
                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            1   1556.70846   1556.70846        2.299       0.1489
Error           16  10832.90265    677.05642
C Total         17  12389.61111

 
Model: MODEL3  Analysis of Variance
                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            1   1620.75928   1620.75928        2.408       0.1403
Error           16  10768.85183    673.05324
C Total         17  12389.61111

 
Model: MODEL4  Analysis of Variance
                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            2   5975.66853   2987.83427        6.988       0.0072
Error           15   6413.94258    427.59617
C Total         17  12389.61111

 
Model: MODEL5  Analysis of Variance
                         Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            2   6790.21357   3395.10678        9.095       0.0026
Error           15   5599.39754    373.29317
C Total         17  12389.61111

 
Model: MODEL6 
Analysis of Variance     Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            2   2411.96162   1205.98081        1.813       0.1971
Error           15   9977.64949    665.17663
C Total         17  12389.61111

 
Model: MODEL7 
Analysis of Variance     Sum of         Mean
Source          DF      Squares       Square      F Value       Prob>F
Model            3   6806.11145   2268.70382        5.689       0.0092
Error           14   5583.49966    398.82140
C Total         17  12389.61111


Model and Error SS for different combinations of variables. 

          SSR(X1) = 5957.02249                                         SSE = 6432.58862

          SSR(X2) = 1556.70846                                         SSE = 10832.90265

          SSR(X3) = 1620.75928                                         SSE = 10768.85183

          SSR(X1,X2) = 5975.66853                          SSE = 6413.94258

          SSR(X1,X3) = 6790.21357                          SSE = 5599.39754

          SSR(X2,X3) = 2411.96162                          SSE = 9977.64949

          SSR(X1,X2,X3) = 6806.11145                     SSE = 5583.49966

 

Model SS for each term adjusted for one other. 

These values are calculated as SSR(Xk|Xl) = SSR(Xk,Xl) - SSR(Xl)

          SSR(X1|X2) = 4418.960069

          SSR(X1|X3) = 5169.454291

          SSR(X2|X1) = 18.646037

          SSR(X2|X3) = 791.202345

          SSR(X3|X1) = 833.191073

          SSR(X3|X2) = 855.253158

 

Model SS for each term adjusted for two others.  These are the partial SS for a 3 factor multiple regression. 

These values are calculated as SSR(Xk|Xl,Xm) = SSR(Xk,Xl,Xm) - SSR(Xk,Xl)

          SSR(X1|X2,X3) = 4394.149832

          SSR(X2|X1,X3) = 15.897886

          SSR(X3|X1,X2) = 830.442921



Modified: August 16, 2004
James P. Geaghan