[R] wrong calculation of R-squared in summary.lm

From: Stefan Schlager <stefan.schlager_at_uniklinik-freiburg.de>
Date: Wed, 30 Mar 2011 14:17:42 +0200

Dear all,

I just stumbled upon the fact, that when I perform a regression on multivariate responses, that are not centred, I get a ricilulously high R-squared value. After reading the code of summary.lm, I found a bug in the function summary.lm:

mss is calculated by:
  mss <-sum((f - mean(f))^2) - where f are the fitted values.

This works only for a single response variable, because otherwise the matrix containing the fitted values is scaled by a scalar. replacing this with:
mss <- scale(f,scale=FALSE) solved the problem for me.

Example for bug:
response<-cbind(rnorm(500)+1000,rnorm(500)+300) predictor<-rnorm(500)
fit<-lm(response ~ predictor)
summary.lm(fit) now reports a R^2 value of 1!!!

Please correct me, if I'm wrong


Stefan Schlager M.A.
Medizinische Fakult├Ąt der der Albert Ludwigs- Universit├Ąt Freiburg Hebelstr. 29

79104 Freiburg

Faculty of Medicine, Albert-Ludwigs-University Freiburg Hebelstr. 29
D- 79104 Freiburg

phone +49 (0)761 203-5522
fax +49 (0)761 203-6898

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