From: Andres Legarra <alegarra_at_neiker.net>

Date: Mon 12 Sep 2005 - 16:53:02 EST

Date: Mon 12 Sep 2005 - 16:53:02 EST

[R] Backtransforming regression coefficient for scaled covariate

Your

covariate in the second part of the polynomial is x^2 and not x. Therefore
the transformation should be applied to x^2.
Like this:

(lm2 <- lm(y ~ scale(x) + I(scale(x^2)) )
then you would use

coef(lm2)[3]/sd(x^2)

Andres

-- Andres Legarra NEIKER Apdo. 46 Vitoria-Gasteiz 01080 Spain -- ----- Original Message ----- From: Gorjanc Gregor To: r-help@stat.math.ethz.ch Sent: Sunday, September 11, 2005 10:25 PM Subject: [R] Backtransforming regression coefficient for scaled covariate Hello! Scaling i.e. (x - mean(x)) / sd(x) of covariates in the model can improve the efficiency of estimation. That is nice, but sometimes one needs to report estimates for original scale. I was able to backtransform estimates of linear regression quite easily but I stumped on higher polynomials. Is there a general rule that I am not aware of or is my algebra so bad? I appologize for not pure R question but I hope others will also benefit. I attached the R code for example bellow.Received on Mon Sep 12 17:04:07 2005

## --- Generate data for linear regression ---

e <- rnorm(n = 100, sd = 10) x <- rnorm(n = 100, mean = 100, sd = 10) b <- 3 mu <- 2 y <- mu + b * x + e plot(y = y, x = x)

## Fit linear regression

(lm1 <- lm(y ~ x))

## Fit linear regression with transformed i.e. standardized covariate

(lm2 <- lm(y ~ scale(x)))

## Backtransform estimate of regression coefficient

coef(lm2)[2] / sd(x)

## --- Generate data for quadratic regression ---

e <- rnorm(n = 100, sd = 10) x <- runif(n = 100, min = 1, max = 100) b1 <- 2 b2 <- -0.01 mu <- 2 y <- mu + b1 * x + b2 * x^2 + e plot(y = y, x = x)

## Fit regression

(lm1 <- lm(y ~ x + I(x^2)))

## Fit regression with transformed i.e. standardized covariate

(lm2 <- lm(y ~ scale(x) + I(scale(x)^2)))

## Backtransform estimates of regression coefficients

## ??

Lep pozdrav / With regards, Gregor Gorjanc ---------------------------------------------------------------------- University of Ljubljana Biotechnical Faculty URI: http://www.bfro.uni-lj.si/MR/ggorjan Zootechnical Department mail: gregor.gorjanc <at> bfro.uni-lj.si Groblje 3 tel: +386 (0)1 72 17 861 SI-1230 Domzale fax: +386 (0)1 72 17 888 Slovenia, Europe ---------------------------------------------------------------------- "One must learn by doing the thing; for though you think you know it, you have no certainty until you try." Sophocles ~ 450 B.C. ______________________________________________ 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 ______________________________________________ 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

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