Contains the parameter estimates for each response variable (without details like standard errors or t tests). There is a column for each response variable.
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The elements of the E matrix are the cross products of the residuals.
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The H matrices correspond to hypothesis sums of squares and cross products.
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There is an H matrix for the whole model and for each effect in the model. Diagonal elements of the E and H matrices correspond to the hypothesis (numerator) and error (denominator) sum of squares for the univariate F tests. New E and H matrices for any given response design are formed from these initial matrices, and the multivariate test statistics are computed from them.