RPD -- Example 9.2 -- Numerical Example

       X1                                 XTXINV1

        1         0         0         0       0.5         0         0         0
        1         0         0         0         0       0.5         0         0
        0         1         0         0         0         0       0.5         0
        0         1         0         0         0         0         0       0.5
        0         0         1         0                                        
        0         0         1         0                                        
        0         0         0         1                                        
        0         0         0         1                                        
                                    BETAHAT1

                                        8.83
                                      11.925
                                       13.49
                                       16.68


       X2                                 XTXINV2

        1         1         0         0     0.125         0         0         0
        1         1         0         0         0     0.375    -0.125    -0.125
        1         0         1         0         0    -0.125     0.375    -0.125
        1         0         1         0         0    -0.125    -0.125     0.375
        1         0         0         1                                        
        1         0         0         1                                        
        1        -1        -1        -1                                        
        1        -1        -1        -1                                        
                               BETAHAT2   TAUHAT4

                               12.73125   3.94875
                               -3.90125          
                               -0.80625          
                                0.75875          


       X3                                 XTXINV3

        1         1         0         0       0.5      -0.5      -0.5      -0.5
        1         1         0         0      -0.5         1       0.5       0.5
        1         0         1         0      -0.5       0.5         1       0.5
        1         0         1         0      -0.5       0.5       0.5         1
        1         0         0         1                                        
        1         0         0         1                                        
        1         0         0         0                                        
        1         0         0         0                                        
                                    BETAHAT3

                                       16.68
                                       -7.85
                                      -4.755
                                       -3.19
                    RPD -- Example 9.2 -- Numerical Example

                               The GLM Procedure

                            Class Level Information
 
                        Class         Levels    Values

                        group              4    1 2 3 4 


                    Number of Observations Read           8
                    Number of Observations Used           8
                    RPD -- Example 9.2 -- Numerical Example

                               The GLM Procedure
 
Dependent Variable: y   

                                       Sum of
 Source                     DF        Squares    Mean Square   F Value   Pr > F

 Model                       3    64.07623750    21.35874583     40.37   0.0019

 Error                       4     2.11625000     0.52906250                   

 Corrected Total             7    66.19248750                                  


               R-Square     Coeff Var      Root MSE        y Mean

               0.968029      5.713240      0.727367      12.73125


 Source                     DF      Type I SS    Mean Square   F Value   Pr > F

 group                       3    64.07623750    21.35874583     40.37   0.0019


 Source                     DF    Type III SS    Mean Square   F Value   Pr > F

 group                       3    64.07623750    21.35874583     40.37   0.0019


                                           Standard
     Parameter           Estimate             Error    t Value    Pr > |t|

     Intercept        16.68000000 B      0.51432602      32.43      <.0001
     group     1      -7.85000000 B      0.72736683     -10.79      0.0004
     group     2      -4.75500000 B      0.72736683      -6.54      0.0028
     group     3      -3.19000000 B      0.72736683      -4.39      0.0118
     group     4       0.00000000 B       .                .         .    

NOTE: The X'X matrix has been found to be singular, and a generalized inverse 
      was used to solve the normal equations.  Terms whose estimates are 
      followed by the letter 'B' are not uniquely estimable.
                    RPD -- Example 9.2 -- Numerical Example

                               The GLM Procedure

                            Class Level Information
 
                        Class         Levels    Values

                        group              4    1 2 3 4 


                    Number of Observations Read           8
                    Number of Observations Used           8
                    RPD -- Example 9.2 -- Numerical Example

                               The GLM Procedure
 
Dependent Variable: y   

                                       Sum of
 Source                     DF        Squares    Mean Square   F Value   Pr > F

 Model                       4    1360.754050     340.188513    643.00   <.0001

 Error                       4       2.116250       0.529063                   

 Uncorrected Total           8    1362.870300                                  


               R-Square     Coeff Var      Root MSE        y Mean

               0.968029      5.713240      0.727367      12.73125


 Source                     DF      Type I SS    Mean Square   F Value   Pr > F

 group                       4    1360.754050     340.188513    643.00   <.0001


 Source                     DF    Type III SS    Mean Square   F Value   Pr > F

 group                       4    1360.754050     340.188513    643.00   <.0001


                                          Standard
      Parameter           Estimate           Error    t Value    Pr > |t|

      group     1       8.83000000      0.51432602      17.17      <.0001
      group     2      11.92500000      0.51432602      23.19      <.0001
      group     3      13.49000000      0.51432602      26.23      <.0001
      group     4      16.68000000      0.51432602      32.43      <.0001