# [R] Calculation of r squared from a linear regression

From: Sandra Hawthorne <sandra_d_hawthorne_at_yahoo.com.au>
Date: Fri, 11 Jun 2010 01:16:31 -0700 (PDT)

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.

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