From: Gabor Grothendieck <ggrothendieck_at_gmail.com>

Date: Thu, 17 Mar 2011 20:38:21 -0400

Date: Thu, 17 Mar 2011 20:38:21 -0400

On Thu, Mar 17, 2011 at 8:22 PM, Berwin A Turlach
<berwin_at_maths.uwa.edu.au> wrote:

> 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?
**>
*

Try it on an example to convince yourself:

-- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com ______________________________________________ R-help_at_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.Received on Fri 18 Mar 2011 - 00:44:01 GMT

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