The process of determining the adequacy of the fitted model is referred to as testing for lack of fit. When replicate measurements are not available, there are several approaches to testing for lack of fit. This article presents some of these approaches on a continuum so as to provide a basis for a meaningful comparison. The issue of grouping data is also discussed. A usual approach of forming groups by arbitrary cutoffs in the space of predictor variables is questioned, and a data-splitting algorithm is recommended for separating groups.