8.44. A 26!2 factorial experiment with three replicates has been run in a pharmaceutical drug manufacturing process.

The experimenter has used the following factors:

(a) If two main effects and one two-factor interaction are included in the final model, how many degrees of freedom for error will be available?

(b) Suppose that the significant factors are A, C, AB, and AC. What other effects need to be included to obtain a hierarchical model?

Factor Natural levels Coded levels (x's) A 50, 100 -1, 1 B 20, 60 -1,1 C 10,30 -1, 1 D 12, 18 -1,1 E 15,30 -1,1 F 60, 100 -1,1