MANOVA CRF-32 Example Using PROC REG
Same data as Assignment 8

data crf32;
input a b y1 y2 x1 x2 x3;
  x4 = x1*x3; output;
  x5 = x2*x3; output;
cards;
1 1 10 21  1  1  1
1 1 12 22  1  1  1
1 1  9 19  1  1  1
1 1 10 21  1  1  1
1 1 14 23  1  1  1
1 2  9 14  1  1 -1
1 2  8 15  1  1 -1
1 2 11 16  1  1 -1
1 2  9 17  1  1 -1
1 2  9 17  1  1 -1
2 1 11 23 -1  1  1
2 1 14 27 -1  1  1
2 1 13 24 -1  1  1
2 1 15 26 -1  1  1
2 1 14 24 -1  1  1
2 2 11 15 -1  1 -1
2 2 12 18 -1  1 -1
2 2 10 16 -1  1 -1
2 2  9 17 -1  1 -1
2 2  9 18 -1  1 -1
3 1  8 17  0 -2  1
3 1  7 15  0 -2  1
3 1 10 18  0 -2  1
3 1  8 17  0 -2  1
3 1  7 19  0 -2  1
3 2  9 22  0 -2 -1
3 2  8 18  0 -2 -1
3 2 10 17  0 -2 -1
3 2  9 19  0 -2 -1
3 2  8 19  0 -2 -1
;
proc reg;
  model y1 y2 = x1 x2 x3 x4 x5;
  a:mtest x1, x2;
  b:mtest x3;
  axb:mtest x4, x5;
run;

----------------------------------------------------------------------------

Model: MODEL1
Dependent Variable: Y1

                           Analysis of Variance
                           Sum of         Mean
  Source          DF      Squares       Square      F Value       Prob>F
  Model            5     93.10000     18.62000        9.800       0.0001
  Error           24     45.60000      1.90000
  C Total         29    138.70000

      Root MSE       1.37840     R-square       0.6712
      Dep Mean      10.10000     Adj R-sq       0.6027
      C.V.          13.64757


                    Parameter      Standard    T for H0:
   Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
   INTERCEP   1     10.100000    0.25166115        40.133        0.0001
   X1         1     -0.850000    0.30822070        -2.758        0.0109
   X2         1      0.850000    0.17795130         4.777        0.0001
   X3         1      0.700000    0.25166115         2.782        0.0104
   X4         1     -0.350000    0.30822070        -1.136        0.2674
   X5         1      0.550000    0.17795130         3.091        0.0050


Dependent Variable: Y2

                           Analysis of Variance
                           Sum of         Mean
  Source          DF      Squares       Square      F Value       Prob>F
  Model            5    283.46667     56.69333       24.297       0.0001
  Error           24     56.00000      2.33333
  C Total         29    339.46667

      Root MSE       1.52753     R-square       0.8350
      Dep Mean      19.13333     Adj R-sq       0.8007
      C.V.           7.98358

                    Parameter      Standard    T for H0:
   Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
   INTERCEP   1     19.133333    0.27888668        68.606        0.0001
   X1         1     -1.150000    0.34156503        -3.367        0.0026
   X2         1      0.516667    0.19720266         2.620        0.0150
   X3         1      1.933333    0.27888668         6.932        0.0001
   X4         1     -0.650000    0.34156503        -1.903        0.0691
   X5         1      1.416667    0.19720266         7.184        0.0001

Multivariate Test: A

               Multivariate Statistics and F Approximations
                          S=2    M=-0.5    N=10.5

Statistic                    Value          F      Num DF    Den DF  Pr > F
Wilks' Lambda             0.36855473     7.4429         4        46  0.0001
Pillai's Trace            0.69074032     6.3310         4        48  0.0004
Hotelling-Lawley Trace    1.55241585     8.5383         4        44  0.0001
Roy's Greatest Root       1.44074791    17.2890         2        24  0.0001

       NOTE: F Statistic for Roy's Greatest Root is an upper bound.
               NOTE: F Statistic for Wilks' Lambda is exact.


Multivariate Test: B

              Multivariate Statistics and Exact F Statistics
                           S=1    M=0    N=10.5

Statistic                    Value          F      Num DF    Den DF  Pr > F
Wilks' Lambda             0.33304572    23.0298         2        23  0.0001
Pillai's Trace            0.66695428    23.0298         2        23  0.0001
Hotelling-Lawley Trace    2.00259072    23.0298         2        23  0.0001
Roy's Greatest Root       2.00259072    23.0298         2        23  0.0001

Multivariate Test: AXB

               Multivariate Statistics and F Approximations
                          S=2    M=-0.5    N=10.5

Statistic                    Value          F      Num DF    Den DF  Pr > F
Wilks' Lambda             0.30092873     9.4636         4        46  0.0001
Pillai's Trace            0.70226819     6.4938         4        48  0.0003
Hotelling-Lawley Trace    2.31242251    12.7183         4        44  0.0001
Roy's Greatest Root       2.30781925    27.6938         2        24  0.0001

       NOTE: F Statistic for Roy's Greatest Root is an upper bound.
               NOTE: F Statistic for Wilks' Lambda is exact.