On Thu, Mar 17, 2011 at 8:22 PM, Berwin A Turlach <ber...@maths.uwa.edu.au> wrote: > 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? >
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 -- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com ______________________________________________ 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.
