[R] Strange R squared, possible error

[Berwin A Turlach]

G'day Gabor,

On Thu, 17 Mar 2011 11:36:38 -0400
Gabor Grothendieck <ggrothendieck at gmail.com> wrote:

> The idea is that if you have a positive quantity that can be broken
> down into two nonnegative quantities: X = X1 + X2 then it makes sense
> to ask what proportion X1 is of X.   For example: 10 = 6 + 4 and 6 is
> .6 of the total.
> 
> Now, in the case of a model with an intercept its a mathematical fact
> that the variance of the response equals the variance of the fitted
> model plus the variance of the residuals.  Thus it makes sense to ask
> what fraction of the variance of the response is represented by the
> variance of the fitted model (this fraction is R^2).
> 
> But if there is no intercept then that mathematical fact breaks down.
> That is, its no longer true that the variance of the response equals
> the variance of the fitted model plus the variance of the residuals.
[...]

Do you have any reference to back this up, as I am somewhat surprised.

I know that if there is no intercept in the model, then the residuals
may not add to zero, but we are still doing least-squares, i.e. the
fitted values are orthogonal to the residual vector and the variance of
the response is the sum of the variance of the fitted model plus the
variance of the residuals.

Or am I missing something?

Cheers,

	Berwin

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