Selecting Check Points for Testing Lack of Fit in Response Surface Models

Abstract

In modeling a response as a function of a set of explanatory variables, one way to check lack of fit in a fitted model of the form E(Y) = Xβ₁, when the true model is E(Y) = Xβ₁ + X₂2β₂, is to use additional check points. The question of choosing check points has not often been addressed, so we propose a method of selecting check points to maximize the power of the lack-of-fit test. Two examples illustrate the procedure.

KEY WORDS:

• Response surface
• Polynomial model
• Lack of fit
• Check points
• Mixture experiments
• Noncentral F distribution
• Doubly noncentral F distribution