On Mon, 29 Jun 2009, John Hunter wrote:
But my question was more numerical: in particular, the R^2 of the
model should be equal to the square of the correlation between the fit
values and the actual values.
No.
It is with the intercept and is not w/o
it, as my code example shows. Am I correct in assuming these should
always be the same, and if they are not, does it reflect a bug in R or
perhaps a numerical instability?
No.
The R^2 is based on dividing the sum of squared errors in the model by the sum
of squared errors in the null model ('proportion of variation explained')
For a model with no intercept, the null model is mu=0, so the R^2 is the sum of
squared residuals divided by the sum of squared y values.
One could define the R^2 as you expected, and arguments could be made either
way. The definition that lm uses keeps the connection to the likelihood that
your definition loses in the no-intercept case.
-thomas
Thomas Lumley Assoc. Professor, Biostatistics
tlum...@u.washington.edu University of Washington, Seattle
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