Re: Simple Linear Regression question

On Sep 4, 5:26 pm, Rich Ulrich <rich.ulr...@xxxxxxxxxxx> wrote:


There is a second version of R^2  that can be conventional
for regression through the origin, using the deviations around
zero instead of deviations around the mean for Total-SS.

I agree, but I don't know that it's ever taught and I don't know which
stat packages contain it. I've never seen it in a text book (not that
I read statistics textbooks in my spare time, mind you). In my
doctoral seminar, I warn the students about the pitfalls of using the
standard R^2 (and adjusted R^2) with regression through the origin,
but I've been hesitant to expound on the alternate formula because I
don't know what they'll get from their software (most, but not all,
will use SPSS), and it seems safest to ignore it.



Interpreting R^2 is a bit tricky when the intercept is forced to zero,
and in fact Minitab flat out won't print an R^2 in that case.

I don't see where Mintab comes into it....

I had a conversation with one of the developers (I think) a long, long
time ago. I wondered why Minitab simply refused to cough up an R^2
when you forced the intercept to zero. The response was that the
developers thought it would be misleading, or prone to
misinterpretation, so they bagged it. I intended this as support for
the assertion of trickiness.

Of course, there's nothing all that tricky about it if you get the
alternate version of R^2 -- you just have to remember SSTO is around
zero and not around the sample mean -- but again I'm not sure when
you'll get the alternate version (and whether you will know it if you
don't).

I think that SPSS does present both versions of R^2, generally,
when the regression is forced through the origin.  The "usual"
version can happen to come out as negative, since the SS-Residual
is compared to the SS around the mean, which *can* be
smaller than SSR -- so that the SS-accounted-for is negative.

I just checked, and R produces the alternate version (only, at least
in summary output). If SPSS gives both, that's better than I'd hoped
for -- I had the impression that SPSS only gave the standard version.

/Paul
.

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