[R] Fitting exponential curve to data points

Karl Ove Hufthammer Karl.Hufthammer at math.uib.no
Tue Jul 24 16:06:34 CEST 2007

Andrew Clegg:

> Great, thanks. If I want to demonstrate that a non-linear curve fits
> better than an exponential, what's the best measure for that? Given
> that neither of nls() or optim() provide R-squared.

You really need to *very* careful when trying to interprete R² (which can
be defined in many nonequivalent ways) in the nonlinear case. Recommended
(and, dare I say, *required* reading):

Anderson-Sprecher R. (1994). ‘Model comparisons and R²’. The American
  Statistician, volume 48, no. 2, pages 113–117. DOI: 10.2307/2684259

Kvålseth T.O. (1985). ‘Cautionary note about R²’. The American Statistician,
  volume 39, no. 4, pages 279–285. DOI: 10.2307/2683704

Scott A. and Wild C. (1991). ‘Transformations and R²’. The American
  Statistician, volume 45, no. 2, pages 127–129. ISSN 0003-1305.
  DOI: 10.2307/2684375

The Scott & Wild paper has an example that looks very similar to yours, and
that may be instructive.

FYI, in case you’re not used to DOIs: you can resolve the above DOIs to
fulltext URLs using http://dx.doi.org/

Karl Ove Hufthammer

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