Hierarchical models. Several times we have used the hierarchy principle in selecting a model; that is, we have included nonsignificant lower order terms in a model because they were factors involved in significant higher order terms.

Hierarchy is certainly not an absolute principle that must be followed in all cases. To illustrate, consider the model resulting from Problem 6.5, which required that a nonsignificant main effect be included to achieve hierarchy. Using the data from Problem 6.5.

(a) Fit both the hierarchical and the nonhierarchical models.

(b) Calculate the PRESS statistic, the adjusted R2, and the mean square error for both models.

(c) Find a 95 percent confidence interval on the estimate of the mean response at a cube corner (x1 = x2 = x3 = ±1).

Hint: Use the results of Problem 6.40.

(d) Based on the analyses you have conducted, which model do you prefer?