On 2010-06-11 2:16, Sandra Hawthorne wrote:
Hi,
I'm trying to verify the calculation of coefficient of determination (r
squared) for linear regression. I've done the calculation manually with a
simple test case and using the definition of r squared outlined in summary(lm)
help. There seems to be a discrepancy between the what R produced and the
manual calculation. Does anyone know why this is so? What does the multiple r
squared reported in summary(lm) represent?
# The test case:
x<- c(1,2,3,4)
y<- c(1.6,4.4,5.5,8.3)
dummy<- data.frame(x, y)
fm1<- lm(y ~ x-1, data = dummy)
summary(fm1)
betax<- fm1$coeff[x] * sd(x) / sd(y)
# cd is coefficient of determination
cd<- betax * cor(y, x)
The discrepancy is due to incorrect manual calculation.
You're using (incorrectly, at that) formulas for simple
regression _with an intercept term_ whereas you model
has _no_ intercept term.
What summary.lm reports is clearly described on the
help page. See r.squared in the Value section.
-Peter Ehlers
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