Evaluating the power of Minitab's data subsetting lack of fit test in multiple linear regression

Abstract

Minitab's data subsetting lack of fit test (denoted XLOF) is a combination of Burn and Ryan's test and Utts’ test for testing lack of fit in linear regression models. As an alternative to the classical or pure error lack of fit test, it does not require replicates of predictor variables. However, due to the uncertainty about its performance, XLOF still remains unfamiliar to regression users while the well-known classical lack of fit test is not applicable to regression data without replicates. So far this procedure has not been mentioned in any textbooks and has not been included in any other software packages. This study assesses the performance of XLOF in detecting lack of fit in linear regressions without replicates by comparing the power with the classic test. The power of XLOF is simulated using Minitab macros for variables with several forms of curvature. These comparisons lead to pragmatic suggestions on the use of XLOF. The performance of XLOF was shown to be superior to the classical test based on the results. It should be noted that the replicates required for the classical test made itself unavailable for most of the regression data while XLOF can still be as powerful as the classic test even without replicates.