Testing regression lack of fit without replication: a tutorial around Minitab's XLOF procedures

The tutorial is concerned with two types of test for the general lack of fit of a linear regression model, as found in the Minitab software package, and which do not require replicated observations. They aim to identify non-specified curvature and interaction in predictors, by comparing fits over the predictor region divided into two parts. Minitab's regression subcommand XLOF which gives the tests is only briefly documented in the manual and, unlike virtually all other statistical procedures in the software, it is not standard and cannot be readily found in textbooks. The two types of test are described here; they concern the predictors one-at-a-time and the predictors all-at-once. An example of their use is given. A suite of macros is available which reproduces the results of the XLOF tests in much more detail than is given by the XLOF subcommand.