[R] r2 for lm() with zero intercept

Berwin A Turlach berwin at maths.uwa.edu.au
Tue Dec 2 06:17:05 CET 2008

G'day Glenn,

On Tue, 2 Dec 2008 12:53:44 +1100
<Glenn.Newnham at csiro.au> wrote:

> I'm a little confused about the R2 and adjusted R2 values reported by
> lm() when I try to fix an intercept. When using +0 or -1 in the
> formula I have found that the standard error generally increases (as
> I would expect) but the R2 also increases (which seems counter
> intuitive). 


In particular the part:

r.squared: R^2, the 'fraction of variance explained by the model',

              R^2 = 1 - Sum(R[i]^2) / Sum((y[i]- y*)^2),

          where y* is the mean of y[i] if there is an intercept and
          zero otherwise.

> I do realise that many will say I shouldn't be fixing the intercept
> anyway 

Quite true; accept if there are very good reasons.  I have seen
intercept through the origin being misused to obtain a large R^2 and
significant coefficient when there were none.



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