Why does linearizing a logarithmic plot slightly increase the $R^2$ of the line of best fit? My graphs are shown below...
2026-04-04 16:56:20.1775321780
Why does linearizing a logarithmic plot slightly increase the $R^2$ of the line of best fit?
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Your $R^2$ is the Pearson correlation coefficient. It quantifies linear correlation. It can be misleadingly low when the relationship between variables is nonlinear. Spearman's rank correlation coefficient is a slight variant on the same idea, where we compute the ranks of each coordinate, then take Pearson's $R^2$ for those. An invertible order-preserving transformation of one or both variables doesn't change Spearman's coefficient, so it's equal to the Pearson coefficient you obtained from a transformation that makes the relationship linear, i.e. $0.9276$ as opposed to $0.9227$.
But the values are close together, because over sufficiently small ranges linearization is a good approximation of a more complex relationship. (This follows from calculus.) By "small range", in the case of $y$ exponential in $x$ I mean $y$ doesn't vary too much in relative terms (i.e. over too many orders of magnitude), nor $x$ too much in absolute terms.