Suppose the dummy regressors (see Section XXXXXXXXXXfor factor A are named (A1, A2) and the dummy regressors for factor B are named (B 1 , B 2 , B 3 ). Write the mean function  in Wilkinson–Rogers...

Suppose the dummy regressors (see Section 5.1.1) for factor A are named (A1, A2) and the dummy regressors for factor B are named (B₁, B₂, B₃). Write the mean function
 in Wilkinson–Rogers notation (e.g., (3.19) in Chapter 3).

The model in has six regression coefficients, including an intercept. Express the βs as functions of the μ_ij.

We write
  to be the “main effect” of the jth level of factor B, obtained by averaging over the levels of factor A. For the model of, show that the main effects of B depend on all six β-parameters. Show how the answer simplifies for the model of Problem 5.5.3.