15.46 Consider a design which is a 23−1 I I I with 2 center runs. Consider ¯yf as the average response at the design parameter and ¯y0 as the average response at the design center. Suppose the true regression model is E(Y ) = β0 + β1x1 + β2x2 + β3x3

+ β11x21

+ β22x22

+ β33x23

.

(a) Give (and verify) E(¯yf − ¯y0 ).

(b) Explain what you have learned from the result in

(a).