[R] Calculation of r squared from a linear regression

[Sandra Hawthorne]

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)

Thanks.