Measures of Lack of Fit for Response Surface Designs and Predictor Variable Transformations

Abstract

Some first-order (2 ^k–p two-level factorials and fractional factorials plus center points) and second-order (cube plus star plus center-point composite) response surface designs are discussed from the point of view of their ability to detect certain likely kinds of lack of fit of degree one higher than has been fitted. This leads to consideration of conditions for representationa adequacy of first- and second-order models in transformed predictor variables. It is shown how to use the estimated regression coefficients from the higher degree model to check if power transformations of the predictor variables could eliminate the lack of fit, and also actually to estimate the transformations.

KEY WORDS:

• First-order designs
• Lack of fit
• Response surface designs
• Second-order designs
• Transformations on predictors