This page discusses why Minitab does not compute $R^2$ for nonlinear regression. I understand that calculating $R^2$ between the response and the predictor ($y$ vs $x$) is not justified. However, is there any reason why calculating $R^2$ between the response and the predicted response ($y$ vs $\hat{y}$) is invalid?

(I know there are other goodness-of-fit metrics that may be better suited for nonlinear regression, but in this case I'm interested in $R^2$.)

  • $\begingroup$ @Sal You must have dropped several words from that comment: I'm having trouble finding any interpretation that is correct. $\endgroup$ – whuber Jan 14 '20 at 23:13
  • $\begingroup$ Yikes. Thanks. That comment wasn't meant to be published yet. :) . Anyway, my intended point was: If you calculate an r-squared between y and y-hat, that may indicate that e.g. the linear relationship between y and y-hat is strong, but doesn't necessarily indicate that the y and y-hat values are similar in value. You might look at measures of "accuracy". $\endgroup$ – Sal Mangiafico Jan 14 '20 at 23:32
  • $\begingroup$ great answer, thanks @SalMangiafico! $\endgroup$ – Pete Jan 14 '20 at 23:56
  • $\begingroup$ While I concede that this is shameful self-promotion, you might want to look at the first half of my post here: stats.stackexchange.com/questions/427390/…. When you expand the total sum of squares, there’s a term that drops out in linear regression but remains for nonlinear models. $\endgroup$ – Dave Jan 15 '20 at 1:57

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