1

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 $R^2$.)

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Pete
  • 121
  • 3
  • @Sal You must have dropped several words from that comment: I'm having trouble finding any interpretation that is correct. – whuber Jan 14 '20 at 23:13
  • 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". – Sal Mangiafico Jan 14 '20 at 23:32
  • great answer, thanks @SalMangiafico! – Pete Jan 14 '20 at 23:56
  • Possible dups: https://stats.stackexchange.com/questions/79225/is-r2-valid-in-a-nonlinear-model, https://stats.stackexchange.com/questions/168599/should-we-report-r-squared-or-adjusted-r-squared-in-non-linear-regression, https://stats.stackexchange.com/questions/359906/is-r-squared-truly-an-invalid-metric-for-non-linear-models – kjetil b halvorsen Jan 15 '20 at 01:51
  • While I concede that this is shameful self-promotion, you might want to look at the first half of my post here: https://stats.stackexchange.com/questions/427390/neural-net-regression-sse-loss. When you expand the total sum of squares, there’s a term that drops out in linear regression but remains for nonlinear models. – Dave Jan 15 '20 at 01:57
  • @kjetilbhalvorsen I think these are all related, but not quite the same question. If they're deemed similar enough feel free to close this. – Pete Jan 15 '20 at 06:21
  • @Dave thanks for sharing, although I think also doesn't quite get at my question either – Pete Jan 15 '20 at 06:22
  • In linear regression, $R^2$ tells you how much of the variability in $y$ is explained by the model. Because that “other” term in my post is zero, that tells you how much variability remains unaccounted for. When “other” is not zero, you get no such insight. – Dave Jan 15 '20 at 10:36
  • One thing to look at is Efron's pseudo r-square. It is based on the difference between predicted *y* values and observed *y* values, so its explanation is pretty intuitive. – Sal Mangiafico Jan 18 '20 at 16:31

0 Answers0