A Note on Residual Analysis

In this note some aspects of residual analysis are considered critically. The relation between residual analysis in the sense of Freund, Vail, and Clunies-Ross and the analysis of covariance is clearly exhibited. The note establishes exact expressions for the difference between the “true” additional regression sum of squares obtained by simultaneous regression analysis and the regression sum of squares due to additional variables by residual analysis. The difference is given some simple interpretations. It is shown that a residual analysis test statistic considered by Freund, et al. is subject to certain serious defects.