MULTIPLE COMPARISONS WITH A CONTROL IN RESPONSE-SURFACE METHODOLOGY

Quadratic response surface methodology often focuses on finding the le vels of some (coded) predictor variables x = (x(1), x(2), ..., X(k)) t hat optimize the expected value of a response variable y. Typically th e experimenter starts from some best guess or ''control'' combination of the predictors (usually coded to x = 0) and performs an experiment varying them in a region around this center point. The question of int erest addressed here is whether any x in the experimental region provi des an E(Y) preferable to that of the control, and if so, by what amou nt? This article approaches the question via simultaneous confidence i ntervals for E(y/x)-E(y/0) for all x within a specified distance of 0. Exact results for the quadratic regression case (k = 1) are obtained using existing results for linear regression. A conservative solution for rotatable designs in k > 1 predictors is obtained using a result o f Casella and Strawderman. Several examples are provided.