[R] R-squared value for linear regression passing through origin using lm()
S Ellison
S.Ellison at lgc.co.uk
Thu Oct 18 15:00:49 CEST 2007
>I think there is reason to be surprised, I am, too. ...
>What am I missing?
Read the formula and ?summary.lm more closely. The denominator,
Sum((y[i]- y*)^2)
is very large if the mean value of y is substantially nonzero and y*
set to 0 as the calculation implies for a forced zero intercept. In
effect, the calculation provides the fraction of sum of squared
deviations from the mean for the case with intercept, but the fraction
of sum of squared y ('about' zero) for the non-intercept case.
This is surprising if you automatically assume that better R^2 means
better fit. I guess that explains why statisticians tell you not to use
R^2 as a goodness-of-fit indicator.
>>> Ralf Goertz <R_Goertz at web.de> 18/10/2007 13:11:55 >>>
>> 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.
Ralf
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