Re: r-Squared Question



Jerry Dallal wrote:
> Reef Fish wrote:
> >
> > Jerry Dallal wrote:
> >
> >>Reef Fish wrote:
> >>
> >>>Jerry Dallal wrote:
>
> >>Rather it is usually defined
> >>as 1-ResSS/TSS (or RegSS/TSS),
> >
> >
> > No. But it's equivalent to the usual RegSS/TotSS because
> > RegSS + SSE (your ResSS) = TotSS.
>
> Isn't that what "or" means, as in "3/6 or 1/2"?

My "no" was referring to "it is usually defined as".

I probably never read the book from which you got your
definition, because I've NEVER seen R^2 DEFINED as "1-ResSS/TSS)".

>
> >
> >>If one uses the formal definition of R^2
> >>to calculate it for this example, R^2 turns out to be -0.03, which says
> >>the problem is with the model, not R^2.
> >
> >
> > This is your ERROR, Jerry.
> >
> > The definition of Multiple R^2 CANNOT lead to a negative value!
> >
>
> I'm not sure what the issue is here. R^2 cannot lead to a negative
> value in the land of sanity and least squares.

Excuse me. Are we discussing statistics in Alice in Wonderland?

>
> The poster was getting an R^2 of 1 for his ill-fitting model, not
> obtained by any least squares procedure, by calculating it as the square
> of the correlation between observed and predicted and thought it showed
> a weakness in R^2 as a summary measure.
>
> The problem was not with R^2, but with the poster's definition of it.

Then why not tell it in Plain English that R^2 is a mathematical
quantity that CANNOT possibly take on a negative value UNLESS
someone is mangling it by introducing something improper! I mentioned
the economist's use Adjusted R^2 as another example of Quackery.


> One can calculate RegSS, ResSS, and TotalSS. The poster's model was
> worse (in terms of least squared errors) than no model at all, that is,
> ResSS was greater than TotalSS. If one blindly plugs these numbers into
> a formula for R^2 one gets -0.03. The point is that R^2 is not, in
> fact, deficient for suggesting the model is perfect. Rather, it is
> saying that something is very wrong with the model because it gives a
> negative value where such a thing should be impossible. One would hope
> that a measure of goodness-of-fit would go off the scale when assessing
> a model that(a) was derived under methods different from those the
> measure was designed to assess and (b) is worse than no model at all.

Your follow-up did not clarify or rectify the issue that whatever
the OP did, it was statistical NONSENSE.

-- Bob.

.