Analytical Use of Linear Regression. Part I: Regression Procedures for Calibration and Quantitation

Abstract

Although commonly used by analysts, linear regression requires careful attention to 5 fundamental assumptions. This paper summarizes these assumptions and describes the effects of deviations from these assumptions and various approaches to correct for such deviations. Specific cases are defined where classical unweighted or weighted linear regression methods are still applicable in calibration experiments, even though the independent x-variable contains random error. Another topic of this paper is the proper construction of confidence intervals, not only for the relatively easy case of predicting a response value given an analyte concentration (or amount) value but also for the theoretically more difficult case of predicting a concentration (or amount) value given a response value. Various approaches based on single-use discrimination intervals (SDI), multiple-use discrimination intervals (MDI), and unlimited-use discrimination intervals (UDI) are discussed for the latter case. This discussion examines both the theory and analytical applicability of each approach. A simplified procedure based on calculated g-values is introduced for guidance on whether or not to use the SDI approximation. The lengths of the MDIs and UDIs are compared for several test data sets, and the modified Scheffe UDI approach is found to be advantageous because of its relative simplicity and short intervals. Its use is recommended when neither of the described SDI approaches is appropriate, i.e., when the comparison of several predicted analyte concentration (or amount) values obtained from the same calibration curve is desired.