The Prediction Properties of Classical and Inverse Regression for the Simple Linear Calibration Problem

Abstract

The calibration of measurement systems is a fundamental but understudied problem within industrial statistics. In the classical context of this problem, standards produced by the National Institute of Standards and Technology (NIST) are used in chemical, mechanical, electrical, and materials-engineering analyses. Often, applications cast into this calibration framework do not provide “gold standards” such as the standards provided by NIST. This paper considers the classical calibration approach, in which the experiment treats the standards as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to inverse regression, which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it is simple and easily implemented in most software. However, it violates some of the basic regression assumptions. In this paper, we study the properties of classical and inverse regression applied to calibration problems, compare their performance, and provide guidance to practitioners.