[R] R2 always increases as variables are added?

Duncan Murdoch murdoch at stats.uwo.ca
Thu May 17 13:29:21 CEST 2007

On 17/05/2007 7:02 AM, ??? wrote:
 > Hi, everybody,
 > 3 questions about R-square:
 > ---------(1)----------- Does R2 always increase as variables are added?
 > ---------(2)----------- Does R2 always greater than 1?
 > ---------(3)----------- How is R2 in summary(lm(y~x-1))$r.squared
 > calculated? It is different from (r.square=sum((y.hat-mean
 > (y))^2)/sum((y-mean(y))^2))

You are mixing models with intercepts with models without them.  When 
you do this, it doesn't make sense to compare the variability about the 
mean.  The model y = constant + error is not a special case of the model 
y = slope*x + error.

Duncan Murdoch

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