[R] Strange R squared, possible error
Berwin A Turlach
berwin at maths.uwa.edu.au
Fri Mar 18 02:05:16 CET 2011
G'day Gabor,
On Thu, 17 Mar 2011 20:38:21 -0400
Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> > Or am I missing something?
O.k., because the residuals don't add to zero, there may be a non-zero
correlation between residuals and fitted values, which messes up the
equation at the variance level.
> Try it on an example to convince yourself:
>
> > fm <- lm(demand ~ Time, BOD)
> > var(fitted(fm)) + var(resid(fm)) - var(BOD$demand)
> [1] 3.552714e-15
> >
> > fm0 <- lm(demand ~ Time - 1, BOD)
> > var(fitted(fm0)) + var(resid(fm0)) - var(BOD$demand)
> [1] 59.28969
But, and this is of course the geometry of least squares:
R> sum(fitted(fm)^2) + sum(resid(fm)^2) - sum(BOD$demand^2)
[1] 0
R> sum(fitted(fm0)^2) + sum(resid(fm0)^2) - sum(BOD$demand^2)
[1] 2.273737e-13
and the reason why the formula changes if there is no (explicit)
intercept term in the model.
Cheers,
Berwin
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