Tolerance Factors in Multiple and Multivariate Linear Regressions

In this article, an improved method of computing tolerance factors for constructing tolerance regions in a multivariate linear regression model is proposed. The method is based on a chi-square approximation to the distribution of a linear function of noncentral chi-square variables and simulation. The merits of the proposed approach and the usual simulation method considered in Lee and Mathew (2004 Lee , Y. , Mathew , T. ( 2004 ). Tolerance regions in multivariate linear regression . Journal of Statistical Planning Inference 126 : 253 – 271 . Google Scholar]) are evaluated using Monte Carlo simulation. The study indicates that the proposed approach is stable and accurate even for small samples, and better than available methods. For constructing two-sided tolerance intervals in multiple linear regression, coverage level adjusted one-sided tolerance factors are shown to be better than available approximate tolerance factors. The results based on the coverage level adjusted one-sided tolerance factors are as good as the ones based on the exact two-sided tolerance factors in many cases.