> 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
----------------------------------------------------------------------------
I see the problem very simply. You have two independent pieces of
information, one the location of the means of each of the variables in n
space, and two the correlation of the variables between each other.
The problem is when you force the regression to only have one parameter,
which of the two pieces of independent information do you use to compute the
coefficient from? All the above methods are arbitrary methods to resolve
this problem. There is no final answer.
DAHeiser
>
>
>
>
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