meaning of sigma from LM, is it the same as RMSE

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meaning of sigma from LM, is it the same as RMSE

John Sorkin
Please forgive my re-sending this question. I did not see any replies from my prior post. My apologies if I missed something.

Is the sigma from a lm, i.e.

fit1 <- lm(y~x)
summary(fit1)
summary(fit1)$sigma

the RMSE (root mean square error)

Thanks,
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
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Re: meaning of sigma from LM, is it the same as RMSE

Roy Mendelssohn - NOAA Federal
?summary.lm

-Roy

On Apr 4, 2012, at 4:47 PM, John Sorkin wrote:

> Please forgive my re-sending this question. I did not see any replies from my prior post. My apologies if I missed something.
>
> Is the sigma from a lm, i.e.
>
> fit1 <- lm(y~x)
> summary(fit1)
> summary(fit1)$sigma
>
> the RMSE (root mean square error)
>
> Thanks,
> John
>
> John David Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> University of Maryland School of Medicine Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>
> Confidentiality Statement:
> This email message, including any attachments, is for th...{{dropped:6}}
>
> ______________________________________________
> [hidden email] 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.

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Roy Mendelssohn
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NOAA/NMFS
Environmental Research Division
Southwest Fisheries Science Center
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Pacific Grove, CA 93950-2097

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Re: meaning of sigma from LM, is it the same as RMSE

Mark Difford
In reply to this post by John Sorkin
On Apr 05, 2012; 1:47am John Sorkin wrote:

> Is the sigma from a lm...the RMSE (root mean square error)

John,

RMSE is usually calculated using the number of observations/cases, whereas summary.lm()$sigma is calculated using the residual degrees of freedom. See below:

## Helps to study the output of anova()
set.seed(231)
x <- rnorm(20, 2, .5)
y <- rnorm(20, 2, .7)
T.lm <- lm(y ~ x)
> summary(T.lm)$sigma
[1] 0.7403162
> anova(T.lm)
Analysis of Variance Table

Response: y
          Df Sum Sq Mean Sq F value Pr(>F)
x          1 0.0036 0.00360  0.0066 0.9363
Residuals 18 9.8652 0.54807

> sum(resid(T.lm)^2)
[1] 9.865225
> sqrt(sum(resid(T.lm)^2)/18)
[1] 0.7403162
> sqrt(sum(resid(T.lm)^2)/20)  ## RMSE (y = 20)
[1] 0.7023256
## OR
> sqrt(mean((y-fitted(T.lm))^2))
[1] 0.7023256

Regards, Mark.
Mark Difford (Ph.D.)
Research Associate
Botany Department
Nelson Mandela Metropolitan University
Port Elizabeth, South Africa