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Information for Authors: Is the Advice Regarding the Reporting of Residuals in Regression Analysis Incomplete? Should Cook’s Distance Be Included?

Department of Biochemistry, University of Western Ontario, London, Ontario, Canada

The first 20% of the full text of this article appears below.

	Introduction

 

If regression analysis is used for statistical evaluation of the data, authors must supply ... standard deviations of residuals (S_y|x, often called standard errors of estimates)... Residuals plots [e.g., Bland-Altman] are often useful.

—Extract from "Information for Authors" (2006)

The Clinical Chemistry "Information for Authors" recommends that, when regression analysis is used, SDs of residuals must be supplied. (They are not always provided.) As Cook and Weisberg note (1), this conceptual approach dates back to the early 1960s, but by the late 1970s, attention was increasingly directed to assessing the influence of individual observations on the results of regression analysis.

The concept of influence (or leverage) can be illustrated by 2 simple examples. In Fig. 1A , the regression line is shown for 4 in-line cases. When case 5 is added, the new regression line is slightly leveraged toward it (Fig. 1C ), but note that the case 5 residual is large (Fig. 1E ) and the regression lines are nearly parallel. However, when case 5 (Fig. 1B ) is added, the new regression line is much more influenced by its presence (Fig. 1D ). This case forces the regression line close to it, and its residual is correspondingly small (Fig. 1F ). What are the differences between these 2 cases? When an outlier is close to the mean value of x (as in case 5 in Fig. 1A ), its influence is small (Fig. 1C ), whereas when the outlier is a long way from the mean value of x and out of . . . [Full Text of this Article]

	leverage

 

	residuals

 

	combining leverages and residuals

 

	an example

 

	conclusion and a proposal