From: Bernardo Rangel Tura <tura_at_centroin.com.br>

Date: Fri, 11 Jun 2010 07:25:35 -0300

Date: Fri, 11 Jun 2010 07:25:35 -0300

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_at_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.Received on Fri 11 Jun 2010 - 10:29:11 GMT

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