The $2^{5-2}$ design with 5 factors A, B, C, D, E is based on 2 generators that can be equivalently written as I=-ABC=-ADE. Deduce the full defining relation before procedure to the questions below.
Part a)
Suppose we use the 3 columns A,B,D to generate the 8 treatment combinations.
(a1) How is the column C expressed in terms of A,B,D?
(a2) How is the column E expressed in terms of A,B,D?

Part b)
Suppose we use the 3 columns C,D,E to generate the 8 treatment combinations.
(b1) How is the column A expressed in terms of C,D,E?
(b2) How is the column B expressed in terms of C,D,E?

Part c)
What are the treatment combinations in your quarter fraction?
(The notation abc, for example, indicates that factors A, B, and C are at their +1 levels. There is no d or e in abc, indicating that factors D and E are at their -1 levels.)

A. c ae b abce cde ad bde abcd
B. ce a be abc cd ade bd abcde
C. (1) ace bc abe de acd bcde abd
D. e ac bce ab d acde bcd abde
E. e cde bd bc a ac abde abcde
F. None of the above


Part d)
Which of the following 2-way interactions are not aliased to a main effect? Choose all that apply

A. DE
B. AD
C. BD
D. BC
E. CD
F. None of the above


Part e)
There are 7 estimable quantities: 5 main effects and 10 2-way interactions.
Which main effect(s) is/are aliased to two 2-way interactions? Choose all that apply

A. A,D,E
B. A
C. D
D. E
E. B
F. A,B,C
G. C
H. None of the above

Hint: