Multiple-Use Calibration for All Future Values and Exact Two-Sided Simultaneous Tolerance Intervals in Linear Regression

Multiple-use calibration using regression is an important statistical tool. Confidence sets for the <i>x</i>-values associated with all future <i>y</i>-values should guarantee a <i>key property</i>, which can be satisfied by simultaneous tolerance intervals (STI’s), and so multiple-use calibration requires the construction of STI’s. In this article, exact two-sided STI’s have been constructed for polynomial regression over any given covariate interval. There is a misconception that two-sided pointwise tolerance intervals (PTI’s) can be employed for multiple-use calibration. This article shows that the confidence sets based on the two-sided PTI’s do not satisfy the <i>key property</i> and so should not be used. Real-world data examples are given in this article for illustration. Supplementary materials for this article are available online.