The MTEST statement described in the section MTEST Statement can test hypotheses involving several dependent variables in the form

where is a linear function on the regressor side, is a matrix of parameters, is a column vector of constants, is a row vector of ones, and is a linear function on the dependent side. The special case where the constants are zero is

To test this hypothesis, PROC REG constructs two matrices called and that correspond to the numerator and denominator of a univariate test:

These matrices are displayed for each MTEST statement if the PRINT option is specified.

Four test statistics based on the eigenvalues of or are formed. These are Wilks’ lambda, Pillai’s trace, the Hotelling-Lawley trace, and Roy’s greatest root. These test statistics are discussed in Chapter 4, Introduction to Regression Procedures.

The following code creates MANOVA data from Morrison (1976):

 
* Manova Data from Morrison (1976, 190);
data a;
input sex $ drug $ @;
do rep=1 to 4;
   input y1 y2 @;
   sexcode=(sex='m')-(sex='f');
   drug1=(drug='a')-(drug='c');
   drug2=(drug='b')-(drug='c');
   sexdrug1=sexcode*drug1;
   sexdrug2=sexcode*drug2;
   output;
end;
datalines;
m a  5  6  5  4  9  9  7  6
m b  7  6  7  7  9 12  6  8
m c 21 15 14 11 17 12 12 10
f a  7 10  6  6  9  7  8 10
f b 10 13  8  7  7  6  6  9
f c 16 12 14  9 14  8 10  5
;

The following statements perform a multivariate analysis of variance and produce Figure 74.60 through Figure 74.63:

proc reg;
   model y1 y2=sexcode drug1 drug2 sexdrug1 sexdrug2;
   y1y2drug: mtest y1=y2, drug1,drug2;
   drugshow: mtest drug1, drug2 / print canprint;
run;

The four multivariate test statistics are all highly significant, giving strong evidence that the coefficients of drug1 and drug2 are not the same across dependent variables y1 and y2.

The four multivariate test statistics are all highly significant, giving strong evidence that the coefficients of drug1 and drug2 are not zero for both dependent variables.