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Inspired by the comments here https://stackoverflow.com/questions/27288483/python-multiple-curve-fitting-models

In matlab, why is the R squared value displayed if it is meaningless for non-linear equations?

Is there a different use for it than those comments suggest?

This is the comment:

R.sq is meaningless for non-linear models. For linear models, R.sq is the fraction of variability explained by the model. For non-linear models this is not the case. Within a family (say, polynomials), models with more parameters will always produce larger R.sq, so this metric is useless to assess goodness of fit

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$R^2$ is a good measure of explained variance in both linear and nonlinear models. It has its issues, such as not being between 0 and 1, but it's still useful.

A minor problem can arise in evaluating the fit of the regression in that the familiar measure, $R^2 = 1 − \frac{\sum_{i=1}^ne^2_i}{\sum_{i=1}^n(y_i-\bar{y})^2}$ , (7-17) is no longer guaranteed to be in the range of 0 to 1. It does, however, provide a useful descriptive measure.

Greene,William H., Econometric analysis, 7th ed., 2012

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    $\begingroup$ In fitting very nonlinear models, such as those with strange attractors, I can even think of an example where optimizing $R^2$ was the objective function. Courtney Brown, Serpents in the Sand, 1995. I believe it's the ecology and policy section, but I can't recall precisely. $\endgroup$
    – Sycorax ♦
    Dec 10, 2014 at 2:14
  • $\begingroup$ $R^2$ works just fine in your example, as they've been optimizing the parameters, and not selecting the models. $\endgroup$
    – Aksakal
    Dec 10, 2014 at 2:24

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