# Does the appliance of R-squared to non-linear models depends on how we calculate it?

Does the appliance of R-squared to non-linear models depends on how we calculate it? $$R^2 = \frac{SS_{exp}}{SS_{tot}}$$ is going to be an inadequate measure for non-linear models since an increase of $$SS_{exp}$$ doesn't necessarily mean that the variance is decreasing, but if we calculate it as $$R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$$, then it's as much meaningful for non-linear models as it is for linear ones. I asked a similar question here where I showed that R-squared is no worse for non-linear models

So, what is the particular reason to say that in the case of non-linear models $$\mathbf{R^2}$$ loses its interpretation of proportion of variance explained? In both cases (I mean linear and non-linear models) we learn by how much your model's variance decreased with respect to its initial (total) variance. If $$R^2 = 0.86 \text %$$ then your model's variance decreased by $$0.86 \text %$$ (no matter whether it's linear or not).

EDIT:

1. $$SS_{tot} = \|y - \bar y\|^2$$
2. $$SS_{exp} = \|\hat y - \bar y\|^2$$
3. $$SS_{res} = \|y - \hat y\|^2$$.

Where:

1. $$y$$ is a vector of true answers;
2. $$\bar y$$ is a vector whose elements are mean of $$y$$;
3. $$\hat y$$ is a vector with our model's predictions.
• What is $SS_{exp}?$
– Dave
Oct 11, 2021 at 23:48
• @Dave, Hello! I've edited. Oct 12, 2021 at 0:33
• In a linear model, is $SS_{tot}=SS_{res}+SS_{exp}?$ What about in a nonlinear model? stats.stackexchange.com/q/427390/247274 stats.stackexchange.com/questions/494274/…
– Dave
Oct 12, 2021 at 0:38
• @Dave, Yes, I see that. But do you actually calculate $SS_{exp}$ when you use $R^2$? No. The formula you use is $R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$ which doesn't care about $SS_{exp}$ at all. It just calculate the difference $SS_{tot} - SS_{res}$ in the nominator and after that divides it by $SS_{tot}$. Why is it worse for nonlinear models, then? We still learn by how much your model's variance decreased with respect to its initial (total) variance. Oct 12, 2021 at 0:47
• Doesn’t the “exp” mean “explained”?
– Dave
Oct 12, 2021 at 0:48