Regional residual plots for assessing the fit of linear regression models

An intuitively appealing lack-of-fit test to assess the adequacy of a regression model is introduced together with a graphical diagnostic tool. The graphical method itself includes a formal testing procedure, and, it is particularly useful to detect the location of lack-of-fit. The procedure is based on regional residuals, using subsets of the space of the independent variables. A simulation study shows that, the proposed procedures in simple linear regression have similar power as those of some popular classical lack-of-fit tests. In case of local departures from the hypothesized regression model, the new tests are shown to be more powerful. Therefore, when it becomes difficult to discriminate between systematic deviations and noise, regional residual plots are very helpful in formally locating areas of lack-of-fit in the predictor space. Data examples illustrate the ability of the new methods to detect and to locate lack-of-fit.