The Use of Partial Residual Plots in Regression Analysis

Abstract

This paper defines partial residuals in multiple linear regression. The ith partial residual vector can be thought of as the dependent variable vector corrected for all independent variables except the ith variable. A plot of the ith partial residuals vs values of the ith variable is proposed as a replacement for the usual plot displaying ordinary residuals vs the ith independent variable. This partial residual plot shows the extent and direction of linearity, while displaying deviations from linearity, such as outliers, inhomogeneity of variance, and curvilinear relationships. Some alternative definitions of partial residuals are described.