Re: r-Squared Question



Jerry Dallal wrote:
> Reef Fish wrote:
> >
> > 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)".
> >
>
> I'm willing to concede the point, but for the fun of it I pulled four
> texts from my shelf:
>
> Draper & Smith, 2nd: RegSS/TotSS, as "Percentage Variation Explained"

So THEY contributed to the misconception and TWO ERRORS ("Percentage"
and "Explained") I wrote about.

> Netter et al., latest ed: R^2 = RegSS/TSS = 1-ResSS/TSS

I've taught from Neter et al (several editions) and R^2 was
always DEFINED as RegSS/TotSS. Yours must've been some "Netter". :-)

> Kleinbaum et al,, latest: (RegSS-ResSS)/TotSS

IMPOSSIBLE! It's WRONG. That's not R^2 at all. I assume it's
your copying error.
>
> Searle: the square of the cc between observed and predicted!

That's a baddy, as a definition.

>
> >>>>If one uses the formal definition of R^2

What formal definition, Jerry? Now that you've listed three (and
one typo) from statistics textbooks?

> >>>>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?
>
> In this instance, yes!

Actually Beyond Alice in Wonderland! :-) See above references to
Kleinbaum, your "formal definition of R^2" and R^2 = -.03.

>
> > 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.
>
> >
> > Your follow-up did not clarify or rectify the issue that whatever
> > the OP did, it was statistical NONSENSE.
>
> You might look at it that way.

There's no other valid way to look at it, Jerry.

> You might also look at it as answering
> the question, "How does this measure work if applied to arbitrary
> models?" and leaving it to the reader to draw his/her own inference
> about R^2=-0.03.

How does WHAT measure work? There is some weak excuse for using
the Searle-like "definition" to get some correlation, but even
Searle's definition would NOT yield a NEGAGIVE number, unless
Searle can get an complex number i*sqrt(-0.3) as a correlation.

-- Bob.

.

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