I know. Did anyone see the r^2 for the correlation?

Shamiq · on May 7, 2009

I was taught by an econometrician that r^2 values don't mean much, but I cannot remember his logic as to why. Maybe something about malleability?

tel · on May 7, 2009

That Anscombe example sheds light on the misuse of r^2. All of those examples have the same r^2 value.

joeyo · on May 8, 2009

Those are some very nice examples.

However, is there a better/more respected metric for comparing how two datasets are related? Mutual Information perhaps?

tel · on May 8, 2009

I'm not an expert -- more of a hobbyist who is actively trying to improve my statistical chops -- but I don't think there's ever a general metric for this sort of thing. For any statistic it's important to demonstrate that it's being used as intended so that its lay translation means what it seems to mean.

I mean, r^2 isn't all that misleading if your relation really is linear. R^2 plus a graph of the regression would be sufficient. Just taking a look at the residuals of the Anscombe sets easily shows that linear fitting (thus r^2) is inappropriate for sets 2-4.

(btw: if you fit the second Anscombe data set with a 2nd order polynomial, r^2 = 1. Of course, it's pretty clear that there's hardly any error in that set.)