COMPARISON OF SIMULTANEOUS CONFIDENCE BANDS FOR QUADRATIC-REGRESSION OVER A FINITE INTERVAL

This article considers a quadratic regression model with one independe nt variable and iid normal errors. Exact simultaneous confidence bound s are developed for the expected response over a finite interval of th e independent variable. These are compared with conservative approxima tions due to Wynn and Bloomfield and to Naiman. Neither of the conserv ative methods are uniformly better than the other, but the better of t he two is almost as good as the exact method. An application arises in the bounding of a quadratic response surface for a two-component mixt ure experiment. For this application, the exact confidence bands are a pproximately 3% narrower than the Wynn-Bloomfield bands but only .1% n arrower than Naiman bands.