An unreplicated 2⁴¹ fractional factorial experiment has been run. The experimenter has used the following factors:

(a)Suppose that this design has four center runs that average 100. The average of the 16 factorial design points is 95. What is the sum of squares for pure quadratic curvature?

(b)Suppose that the prediction equation that results from this experiment is y = 100 2 x ₁ + 10 x ₂ 4 x ₁ x ₂ . What is the predicted response at A = 41, B = 280, C = 60, and D = 185?

Factor Natural levels Coded levels (x's) A 20, 50 -1,1 B 200, 280 -1,1 50, 100 -1,1 D 150, 200 -1, 1 Factor Natural levels Coded levels (x's) A 20, 50 -1,1 B 200, 280 -1,1 50, 100 -1,1 D 150, 200 -1, 1