Re: [R] Calculation of r squared from a linear regression

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

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

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