The coefficient of determination: is it the R-squared or r-squared?

Published at November 26, 2022 · 9 min read

We often use the coefficient of determination as a swift ‘measure’ of goodness of fit for our regression models. Unfortunately, there is no unique symbol for such a coefficient and both \(R^2\) and \(r^2\) are used in literature, almost interchangeably. Such an interchangeability is also endorsed by the Wikipedia (see at: https://en.wikipedia.org/wiki/Coefficient_of_determination ), where both symbols are reported as the abbreviations for this statistical index. As an editor of several International Journals, I should not agree with such an approach; indeed, the two symbols \(R^2\) and \(r^2\) mean two different things, and they are not necessarily interchangeable, because, depending on the setting, either of the two may be wrong or ambiguous....