Use the model and the general form of estimable functions in Exercise 17.7 to answer each of the following. In each case, explain how you arrived at your answer. (Note: In the nested model, the nested...

Use the model and the general form of estimable functions in Exercise 17.7 to answer each of the following. In each case, explain how you arrived at your answer. (Note: In the nested model, the nested effects β_ij
“contain” the α_i
effects.)

(a) How many degrees of freedom are there for SS(A)?

(b) How many degrees of freedom are there for SS(B(A))?

(c) Which coefficients will be zero for the Type I sum of squares SS(A)? For the Type III SS(A)?

(d) Which coefficients will be zero for the Type I sum of squares SS(B(A))? For the Type III SS(B(A))?

Exercise 17.7

Construct the general form of estimable functions L’β for the nested model

(You need to define X for this model, eliminate any non unique rows, and then use row operations to reduce X to the “near identity” form.) You should obtain