On Mon, Jan 3, 2011 at 12:15 PM, Ethan Arenson <ethan.a.aren...@gmail.com> wrote: > Hi. > > I know that R computes sums of squares based on the diagonal of > > t(Q) %*% y %*% t(y) %*% Q, > > where Q comes from the QR-decomposition of the model matrix.
So, how do you know that? When I look at the code for summary.lm I see the residual sum of squares being computed as r <- z$residuals rss <- sum(r^2) Also, your formula is not correct. I think you mean the trace of that matrix which is the squared length of Q'y and that's the same as the squared length of y. The matrix Q in a QR decomposition is orthogonal and one of the properties of orthogonal matrices is that they preserve lengths. So the length of Qy is the same as the length of Q'y is the same as the length of y. > Does anyone know where I can find a proof for this result? > > All Best and Happy New Year, > Ethan > > [[alternative HTML version deleted]] > > ______________________________________________ > 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. > ______________________________________________ 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.
