G'day Gabor, On Thu, 17 Mar 2011 11:36:38 -0400 Gabor Grothendieck <ggrothendi...@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 ========================== Full address ============================ A/Prof Berwin A Turlach Tel.: +61 (8) 6488 3338 (secr) School of Maths and Stats (M019) +61 (8) 6488 3383 (self) The University of Western Australia FAX : +61 (8) 6488 1028 35 Stirling Highway Crawley WA 6009 e-mail: ber...@maths.uwa.edu.au Australia http://www.maths.uwa.edu.au/~berwin ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.