Regression Tolerance Intervals

In this article, we discuss the utility of tolerance intervals for various regression models. We begin with a discussion of tolerance intervals for linear and nonlinear regression models. We then introduce a novel method for constructing nonparametric regression tolerance intervals by extending the well-established procedure for univariate data. Simulation results and application to real datasets are presented to help visualize regression tolerance intervals and to demonstrate that the methods we discuss have coverage probabilities very close to the specified nominal confidence level.