I don't disagree, Bob gives a useful elaboration. But I do think
the "multiple correlation coefficient" should at least be a correlation
coefficient, i.e. corr(Xb,y) maximized over b. In this case, that's
1.0. If you compute something else, call it something else.
At 1:03 PM -0600 2/24/00, Bob Parks wrote:
> >
> >The multiple correlation between X and Y does not depend on if there
> >is a constant term in the regression or not. The residual sum of
> >squares does. R2 is simply 1.0.
> >
> >Basically, the answer is: both are quite incorrect, or: only two decimals
> >are correct.
>
>Although I hate to pretend to correct Jan in anyway, I will:
>
>YEP both are incorrect but the correlation squared between X and Y
>is not necessarily the answer one wants for R2, is it?
>
>There are two interpretations for R2 -
>1. The correlation squared between the predicted and actual;
>2. The percentage explained variance.
>
>With a constant term in least squares the two are identical.
>
>Without a constant term the two can and in this case do differ.
>
>The correlation between the actual and fitted values of
>regressing Y on X is 1.0000000000000, so an answer to 1.
>produces the same answer as the correlation between Y and X.
>
>But the residuals are not identically 0 so one might not like
>to argue that R2 should be 1.000000000000 since one would expect
>(at least I would) that the residuals should be 0 for R2 = 1.0000000
>(up to numerical accuracy anyway).
>
>The residuals are:
>
> 5.537190
> 4.462810
> 3.388430
> 2.314050
> 1.239669
> 0.165289
>-0.909091
>-1.983471
>-3.057851
>-4.132231
>-5.206612
>
>with a mean of .165289.
>
>The problem, without the constant term, is that the decomposition
>of sums of squares is not the usual ssqc(Y) = ssqc(X) + ssq(res)
>(ssqc = sum of corrected squares) from which most programmers
>make their calculation of R2 (many packages will report
>R2 = -0.157025 in this particular case).
>
>We are left with a lot of different answers
>
>R2 = ssqc(X)/ssqc(Y) = 1.00000 (because this is the
>correlation between Y and X)
> = ssq (X)/ssq (Y) = .232246
> = 1 - (ssqc(res)/ssqc(Y)) = -.154293
> = 1 - (ssq (res)/ssq (Y)) = .999365 which is what SYSTAT and
>SPSS report
>
>(assuming that I did my calculations correctly)
>Maybe some others on the list can point to theoretical pieces on R2
>of which I am unaware to single out one of these. I tend to like
>the second one.
>
>In the end, IMHO, NEVER do regression without a constant term.
>
>Bob
> >
> >
> >At 12:45 PM +0000 2/24/00, [EMAIL PROTECTED] wrote:
> >>I have found a difference between the results produced by SPSS and
> >>SYSTAT in linear regression with no constant term. Below are the
> >>results from the programs. As you can see the adjusted R2 given by the
> >>2 programs is different. Which one is correct?
> >>
> >>Data (from NIST line origin dataset):
> >>Y X
> >>130 60
> >>131 61
> >>132 62
> >>133 63
> >>134 64
> >>135 65
> >>136 66
> >>137 67
> >>138 68
> >>139 69
> >>140 70
> >>
> >>Linear regression Y on X with no constant term.
> >>
> >>SYSTAT:
> >>R2 = 0.999365492
> >>adj R2 = 0.999365492
> >>
> >>SPSS:
> >>R2 = 0.9993654922987
> >>adj R2 = 0.9993020415285
> >>
> >>I would appreciate some help.
> >>
> >>Many thanks,
> >>Dr L Green.
> >>
> >>
> >>Sent via Deja.com http://www.deja.com/
> >>Before you buy.
> >>
> >>
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Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550; fax (310)-206-5658; email: [EMAIL PROTECTED]
http://www.stat.ucla.edu/~deleeuw and http://home1.gte.net/datamine/
============================================================================
No matter where you go, there you are. --- Buckaroo Banzai
============================================================================
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
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