Question: Consider a design which is a 231 III with 2 center runs. Consider yf as the average response at the design parameter and y0 as

Consider a design which is a 23−1 III 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

(a) Give (and verify) E(¯yf − y¯0).

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

(a).

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