APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

3.8. General Linear Hypotheses

Sometimes our interest may be in comparing the regression coefficients from the models corresponding to different variables. For example, in a multivariate linear model with two response variables, it may be interesting to test if the intercepts, means, or some other regression coefficients are equal in the respective models corresponding to these two response variables. Such a hypothesis cannot be expressed in the form of Equation 3.11. This hypothesis can, however, be formulated as a general linear hypothesis which can be written as

H₀: LBM=0 vs. H₁: LBM ≠0,

where r by (k+1) matrix L is, as earlier, of rank r and the p by s matrix M is of rank s. These two matrices have different roles to play and need to be ...