An unreplicated 24−1 fractional factorial experiment with four center points has been run. The experimenter has used the following factors:

Factor Natural Levels Coded Levels (x’s)

A - time 10, 50 (minutes) −1, 1 B - temperature 200, 300 (deg C) −1, 1 C - concentration 70, 90 (percent) −1, 1 D - pressure 260, 300 (psi) −1, 1

(a) Suppose that the average of the 16 factorial design points is 100 and the average of the center points is 120, what is the sum of squares for pure quadratic curvature?

(b) Suppose that the prediction equation that results from this experiment is ̂y = 50 + 5x1 + 2x2 − 2x1x2. Find the predicted response at A = 20, B = 250, C = 80, and D = 275.