Confidence Bands for Linear Regression with Restricted Predictor Variables

Abstract

Abstract The classic procedure for constructing a confidence band around a regression function is that of Scheffé (1959), which provides a band of infinite length. This band can be unnecessarily wide if the region of interest to the experimenter is finite. A class of sets is defined that restricts the range of the predictor variables. Confidence bands for a regression function over are constructed, which, for fixed α, are narrower than the Scheffé bands. Also, a procedure is illustrated by which sets that are not in the class can be embedded in Tables are provided to facilitate the use of the procedure.