Interactive Regression Modelling
Murray A. Aitkin, Brian J. Francis, Paul F. Velleman, Harold Victor Henderson · Biometrics · 1982
We read with interest the paper by Henderson and Velleman (1981) on interactive regression modelling. The authors rightly emphasize the value of graphical inspection of the data, but they seem to have overlooked some of the information in their plots. Figure 1 in their paper suggests a hyperbolic relation between MPG and DISPlacement, and their Fig. 2 is clearly nonlinear, with increasing variability in GPM as DISP increases. This suggests that MPG and DISP should be re-expressed on a log scale. Figure 1 of the present note shows log MPG plotted against log DISP. The plot looks linear with constant variance, and the same pattern appears in plots of log MPG against log WT and log HP. Plots of log MPG against the remaining variables do not show anything unusual, and there are no marked outliers. Fitting a normal multiple regression of logMPG on all explanatory variables, with weight, displacement and horsepower replaced by their logs, gives an R2 of .896. Residual plots against explanatory variables show no peculiarities, and a normal plot is closely linear, as shown in our Fig. 2. A Bos-Ccox plot also supports the log transformation. The two largest negative residuals are slightly separated from the others, but do not look too far out of line. They correspond to the Cadillac and Continental.