Re: r-Squared Question

This should be the final round. :-)

Jerry Dallal wrote:
> Reef Fish wrote:

< big snip >

> > Never said THAT was a typo. Read what I wrote again. I said you
> > chose to show (7.71) FIRST, instead of the definition (7.35).
>
> But it's not 7.71. It's 3.71!

You are right! I stand corrected on the order of the equations.

So the resolution of this mystery is that Neter et al did NOT
introduce R^2 until Chapter 7 (multiple regression), but made
some observations about r^2 to the simple regression ANOVA
quantities in Chapter 3.
>
>
> >
> >>>"It measures the proportion of total variation fitted by the
> >>>regression".
> >
> >
> > I've been using that for DECADES in my Lecture Notes.
> >
> >>That's why I like your suggestion of "variation fitted". No text that
> >>I've read has an equally suitable replacement for "explained by". It's
> >>all mumbo-jumbo.
> >
> >
> > I am quite sure others have used much less misleading terms than
> > "percent variation explained". My co-author Harry Roberts did use
> > the word "explain" but immediately explained at length that it
> > must NOT be taken to mean causal or other meaning of "explain".
> > In retrospect, I should have suggested the simple, unambiguous
> > wording of "variation fitted" because that's all it is, no more,
> > no less.
>
>
> Less misleading, yes. Concise, no. The language is often so tortured
> as to be unintelligible to a naive audience, hence my descriptor
> "mumbo-jumbo".

Agreed.


> >>>JD> Kleinbaum et al,, latest: (RegSS-ResSS)/TotSS
> >>>
> >>>RF> IMPOSSIBLE! It's WRONG. That's not R^2 at all. I assume it's
> >>>RF> your copying error.
> >
> >
> > which you posted for the first time. So, what was ACTUALLY in
> > Kleinbaum's book?
>
>
> As I posted in my earlier correction, (TotSS-ResSS)/TotSS

Ok. The appearance of that post was delayed by google. So, that
definition is like the rest of them.


> > The "careless" was referring to
> >
> > RF> > or how YOU and the others got the R^2 = -.03 ?
> >
> > In Google, you made THREE consecutive posts, at 8:08 pm, 8:16 pm and
> > 8:27 om of July 12.
> >
> > Your correction of your own post (8:27 pm) was this:
> >
> > JD> I've canceled my earlier post, but given the way cancels
> > JD> propagate, some copies of the original will survive. So, for the
> > JD> record, keep this post and the one with R^2= -0.03, and ignore the
> > one
> > JD> with R^2=0.
> >
> > You KEPT the R^2 = -.03,
> >
> > which certainly did not follow from any of the definitions you cited.
>
> I gave the data!
>
> > X Y YHat Y-Yhat
> > 1 101 97 4
> > 2 102 99 3
> > 3 103 101 2
> > 4 104 103 1
> > 5 105 105 0
> > 6 106 107 -1
> > 7 107 109 -2
> > 8 108 111 -3
> > 9 109 113 -4
> > 10 110 115 -5
>
> X and Y are the data. Yhat is the fit of the model proposed by the
> poster. The values were given by him. They have a correlation
> coefficient of 1 with Y. Hence, the square of the correlation between
> observed and expected values is 1, even thought the fit is far from
> perfect. This is why he was asking whether it was a "defect" in R^2.
>
> *I* calculated the residuals: Y-Yhat
>
> ResSS is the sum of their (residuals) squares = 85. However, TSS =
> Sum[(Y-105.5)^2] is only 82.5.
>
> I plug those numbers into 1-ResSS/TotSS and get -0.03. Do you get
> something different?

No, I didn't even look at your data! :-) I was looking ONLY
at the definitions you gave, and saw that:

(a) all had RegSS/TotSS which cannot be negative,

(b) even Searle's def. had the "square" of a correlation,
so that can't be negative either.

>
> One might also "argue" that since the model does worse than no model at
> all, that the RegSS is negative (the net amount it accounts for is
> negative) and get at it that way.

But the RegSS is SUM OF SQUSRES which can't be negative either!

>
> Given these Ys and Yhats, -0.03 is what you get when you plug the
> numbers into the formula! It's like assigning code numbers to subjects'
> ethnicity and calculating the mean. It's *worse* than meaningless
> (because the result is ennobled by having gone through a statistics
> program), but a number pops out nonetheless.
>
> Hey, this *is* Alice in Wonderland! The whole point is that the result
> is nonsensical. But it *is* -0.03. :-)

This is Alice's nightmare in not-so-Wonderland. It's past my bed time,
so I'll settle for

"the result is nonsensical"

which was what I had STARTED with (in my FIRST post in this thread)
WITHOUT going through any of the nonsensical calculations you did! :-)

-- Bob.

.