[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?
>
Quoting from the SysStat FAQ,
> (1) In the presence of a constant, R^2 measures variation around the
> mean of the dependent variable which is explained by the variation
around
> the mean of the independent variables.
>
> (2) Without a constant, R^2 measures variation around zero of
the
> dependent variable which is explained by the variation around zero of
the
> independent variables.
I found the following in "Applied Linear Statistical Models" 4th ed by
Neter, Kutner, Nachtscheim, and Wasserman
(Irwin publishing, 1996) p. 163:
" 3. Some statistical packages calculate r^2 for regression through the
origin to (2.72) and hence will sometimes show a negative value for r^2.
Other statistical packages calculate r^2 using the total uncorrected sum
of squares SSTOU in (2.54). This procedure avoids obtaining a negative
coefficient but lacks any meaningful interpretation."
So in essense, calculating R^2 and the F-statistic for model not
containing a y-intercept is dangerous. For the un-experienced user, the
meaning is easily misinterpreted. It appears as if the statisticians are
telling us that there is no proper way or best way to calculate these
values.
Hope that helps.
-Tony
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