Diagnostic Value of Residual and Partial Residual Plots

Abstract

Abstract This article illustrates why partial residual plots in addition to the usual residual plots are useful in a multiple regression analysis. The expected values of the vector of residuals and the vector of partial residuals are presented and examined for the situation when a regressor variable is misspecified in the model. If curvature exists in a predictor variable, the plot of residuals versus the variable displays the points scattered around a line that is a linear transformation of the correct functional form of the variable. Hence a nonrandom pattern may appear in the plot, but the appropriate transformation may not be evident. For a partial residual plot, the underlying signal displays the correct functional form of the predictor variables across the relevant range of interest, except in instances when severe collinearity exists.