# Using R^2 in nonlinear regression

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 $$R^2$$.)

• @Sal You must have dropped several words from that comment: I'm having trouble finding any interpretation that is correct. – whuber Jan 14 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 at 23:32
• great answer, thanks @SalMangiafico! – Pete Jan 14 at 23:56
• – kjetil b halvorsen Jan 15 at 1:51
• 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. – Dave Jan 15 at 1:57