On Fri, 2010-06-11 at 01:16 -0700, 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$coeff[x] * sd(x) / sd(y)
> # cd is coefficient of determination
> cd <- betax * cor(y, x)
>
> Thanks.
Sorry Sandra,
But the problem in yours script. Look this
x <- c(1,2,3,4)
y <- c(1.6,4.4,5.5,8.3)
dummy <- data.frame(x, y)
fm1 <- lm(y ~ x, data = dummy)
summary(fm1)
Call:
lm(formula = y ~ x, data = dummy)
Residuals:
1 2 3 4
-0.17 0.51 -0.51 0.17
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.3500 0.6584 -0.532 0.6481
x 2.1200 0.2404 8.818 0.0126 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.5376 on 2 degrees of freedom
Multiple R-squared: 0.9749, Adjusted R-squared: 0.9624
F-statistic: 77.76 on 1 and 2 DF, p-value: 0.01262
betax <- fm1$coeff[2] * sd(x) / sd(y)
# cd is coefficient of determination
cd <- betax * cor(y, x)
cd
x
0.974924
The formula "fm1$coeff[2] * sd(x) / sd(y)" is valid only the model have
a intercept...
--
Bernardo Rangel Tura, M.D,MPH,Ph.D
National Institute of Cardiology
Brazil
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
