From: Maciej Bliziński <m.blizinski_at_wit.edu.pl>

Date: Sun 17 Sep 2006 - 18:22:28 GMT

*> 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))

Date: Sun 17 Sep 2006 - 18:22:28 GMT

How exactly are standard errors of coefficients calculated in the linear regression?

> 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]...Received on Mon Sep 18 04:24:23 2006

> 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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