Calibration and Simultaneous Tolerance Intervals for Regression

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Abstract
Simultaneous calibration (or discrimination) intervals in regression were proposed by Lieberman, Miller, and Hamilton (1967) and by Scheffe (1973). Those procedures enable one to construct confidence intervals for the unobserved values of the independent variable corresponding to an unlimited sequence of observations of the dependent variable in a regression model. These calibration intervals are conservative in that they are obtained from simultaneous tolerance intervals for which the actual confidence level exceeds the nominal level. Furthermore, all other existing simultaneous tolerance intervals in regression are likewise conservative. In this article, we propose simultaneous tolerance intervals that are narrower than previous intervals. Given the tables of factors included in this article, they are also simple to construct and use in straightline calibration applications.

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