From: Dimitrios Rizopoulos <Dimitris.Rizopoulos_at_med.kuleuven.be>

Date: Sun 17 Sep 2006 - 19:13:02 GMT

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

R-help@stat.math.ethz.ch 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 Mon Sep 18 05:17:12 2006

Date: Sun 17 Sep 2006 - 19:13:02 GMT

these standard errors and other quantities are calculated as by products of the QR decomposition used in lm.fit(). A simple way (but not efficient) to obtain them is:

exped <- c(4.2, 6.1, 3.9, 5.7, 7.3, 5.9)
sales <- c(27.1, 30.4, 25.0, 29.7, 40.1, 28.8)
S <- data.frame(exped, sales)

lmfit <- lm(sales ~ exped, data = S)

X <- model.matrix(lmfit)

sigma2 <- sum((sales - fitted(lmfit))^2) / (nrow(X) - ncol(X))

sqrt(sigma2)

sqrt(diag(solve(crossprod(X))) * sigma2)

I hope it helps.

Best,

Dimitris

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium

Tel: +32/(0)16/336899 Fax: +32/(0)16/337015 Web: http://med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm

Quoting Maciej Bliziński <m.blizinski@wit.edu.pl>:

> Hello R users,

*>
**> I have a substantial question about statistics, not about R itself, but
**> I would love to have an answer from an R user, in form of an example in
**> R syntax. I have spent whole Sunday searching in Google and browsing the
**> books. I've been really close to the answer but there are at least three
**> standard errors you can talk about in the linear regression and I'm
**> really confused. The question is:
**>
**> How exactly are standard errors of coefficients calculated in the linear
**> regression?
**>
**> Here's an example from a website I've read [1]. A company wants to know
**> if there is a relationship between its advertising expenditures and its
**> sales volume.
**>
**> ========================================================
**>> exped <- c(4.2, 6.1, 3.9, 5.7, 7.3, 5.9)
**>> sales <- c(27.1, 30.4, 25.0, 29.7, 40.1, 28.8)
**>> S <- data.frame(exped, sales)
**>> summary(lm(sales ~ exped, data = S))
**>
**> Call:
**> lm(formula = sales ~ exped, data = S)
**>
**> Residuals:
**> 1 2 3 4 5 6
**> 1.7643 -1.9310 0.7688 -1.1583 3.3509 -2.7947
**>
**> Coefficients:
**> Estimate Std. Error t value Pr(>|t|)
**> (Intercept) 9.8725 5.2394 1.884 0.1326
**> exped 3.6817 0.9295 3.961 0.0167 *
**> ---
**> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
**>
**> Residual standard error: 2.637 on 4 degrees of freedom
**> Multiple R-Squared: 0.7968, Adjusted R-squared: 0.7461
**> F-statistic: 15.69 on 1 and 4 DF, p-value: 0.01666
**> ========================================================
**>
**> I can calculate the standard error of the estimate, according to the
**> equation [2]...
**>
**>> S.m <- lm(sales ~ exped, data = S)
**>> S$pred <- predict(S.m)
**>> S$ye <- S$sales - S$pred
**>> S$ye2 <- S$ye ^ 2
**>> Se <- sqrt(sum(S$ye2)/(length(S$sales) - 1 - 1))
**>> Se
**> [1] 2.636901
**>
**> ...which matches the "Residual standard error" and I'm on the right
**> track. Next step would be to use the equation [3] to calculate the
**> standard error of the regression coefficient (here: exped). The equation
**> [3] uses two variables, meaning of which I can't really figure out. As
**> the calculated value Sb is scalar, all the parameters need also to be
**> scalars. I've already calculated Se, so I'm missing x and \bar{x}. The
**> latter could be the estimated coefficient. What is x then?
**>
**> Regards,
**> Maciej
**>
**> [1] http://www.statpac.com/statistics-calculator/correlation-regression.htm
**> [2] **http://www.answers.com/topic/standard-error-of-the-estimate
**> [3] http://www.answers.com/topic/standard-error-of-the-regression-coefficient
**>
**> --
**> Maciej Bliziński <m.blizinski@wit.edu.pl>
**> http://automatthias.wordpress.com
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch 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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