Suppose that you want to replicate 2 of the 8 runs in a 23 factorial design. How many ways are there to choose the 2 runs to replicate? Suppose that you decide to replicate the run with all three factors at the high level and the run with all three factors at the low level.

(a) Is the resulting design orthogonal?

(b) What are the relative variances of the model coefficients if the main effects plus two-factor interaction model are fit to the data from this design?

(c) What is the power for detecting effects of two standard deviations in magnitude?