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Title: Some Misconceptions about R²
Authors: James A. Colton and Keith M. Bower
Publication Source: International Society of Six Sigma Professionals, EXTRAOrdinary Sense, Vol. 3 No. 2 August 2002, pp. 20-22

Abstract

This article addresses two frequently encountered mistakes when assessing the multiple coefficient of determination (a.k.a. R²), namely:

(1) R² is very large, so the model is useful for predicting new observations, and
(2) R² is small, therefore no meaningful relationships exist in the data.

Notes

This paper was written to provide counterexamples to dispel some widely held misconceptions. The first scenario was an attempt to promote the usefulness of the predicted-R² statistic. Typically, practitioners in quality improvement are instructed to assess R² alone for model assessment, though the interpretation may be misleading when there is a small ratio of data to regression coefficients, as illustrated in the example.

The second scenario was deliberately constructed to illustrate the fact that very low R² values may still result in statistically significant effects being detected. This is appropriate for studies where there may be a large amount of noise present in the system. Examples include screening designs in experimentation, as well as economic data and other “noisy” systems.

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