Orthogonal contrasts (see Section 9.1.2): Consider the equation F = XB (-1 relating the parameters flF of the full-rank ANOVA model to the cell means „. Suppose that X(1 B is constructed so that its...

Orthogonal contrasts (see Section 9.1.2): Consider the equation

_F
= X_B
(^-1

relating the parameters flF of the full-rank ANOVA model to the cell means „. Suppose that X(1 B is constructed so that its rows are orthogonal. Show that the columns of the row basis X_B
of the model matrix are also orthogonal and further that each column of XB is equal to the corresponding row of X(1 B divided by the sum of squared entries in that row. (Hint: Multiply X(1 B by its transpose.)