From: 李俊杰 <klijunjie_at_gmail.com>

Date: Mon, 21 May 2007 08:23:56 +0800

Date: Mon, 21 May 2007 08:23:56 +0800

Hi, Mark

What I want to do exactly is that I want to make a comparison between a model with intercept and one without intercept on adjusted r2 term, since we know that minimizing adjusted r-square is a variable selection strategy. I know there are other alternatives to conduct a variable selection, but I really have to try this one.

Thanks.

2007/5/21, Leeds, Mark (IED) <Mark.Leeds_at_morganstanley.com>:

*>
**> Hi : You can put in the -1 and then create your own vector of 1's which
**> which will be a "variable" but I'm not sure if I undersrand what you want
**> and I don't think others do either because
**> I didn't see other responses. I don't mnean to be offensive or rude but
**> can you explain what you want to do more clearly. If you do that, I'm sure
**> you willg et more responses.
**>
**>
**>
*

> -----Original Message-----

*> From: r-help-bounces_at_stat.math.ethz.ch [mailto:
**> r-help-bounces_at_stat.math.ethz.ch] On Behalf Of ???
**> Sent: Saturday, May 19, 2007 2:54 AM
**> To: Paul Lynch
**> Cc: r-help_at_stat.math.ethz.ch
**> Subject: Re: [R] R2 always increases as variables are added?
**>
**> I know that "-1" indicates to remove the intercept term. But my question
**> is why intercept term CAN NOT be treated as a variable term as we place a
**> column consited of 1 in the predictor matrix.
**>
**> If I stick to make a comparison between a model with intercept and one
**> without intercept on adjusted r2 term, now I think the strategy is always to
**> use another definition of r-square or adjusted r-square, in which
**> r-square=sum((y.hat)^2)/sum((y)^2).
**>
**> Am I in the right way?
**>
**> Thanks
**>
**> Li Junjie
**>
**>
**> 2007/5/19, Paul Lynch <plynchnlm_at_gmail.com>:
**> >
**> > In case you weren't aware, the meaning of the "-1" in y ~ x - 1 is to
**> > remove the intercept term that would otherwise be implied.
**> > --Paul
**> >
**> > On 5/17/07, 李俊杰 <klijunjie_at_gmail.com> 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))$r.squared
**> > > calculated? It is different from (r.square=sum((y.hat-mean
**> > > (y))^2)/sum((y-mean(y))^2))
**> > >
**> > > I will illustrate these problems by the following codes:
**> > > ---------(1)----------- R2 doesn't always increase as variables
**> > > are
**> > added
**> > >
**> > > > x=matrix(rnorm(20),ncol=2)
**> > > > y=rnorm(10)
**> > > >
**> > > > lm=lm(y~1)
**> > > > y.hat=rep(1*lm$coefficients,length(y))
**> > > > (r.square=sum((y.hat-mean(y))^2)/sum((y-mean(y))^2))
**> > > [1] 2.646815e-33
**> > > >
**> > > > lm=lm(y~x-1)
**> > > > y.hat=x%*%lm$coefficients
**> > > > (r.square=sum((y.hat-mean(y))^2)/sum((y-mean(y))^2))
**> > > [1] 0.4443356
**> > > >
**> > > > ################ This is the biggest model, but its R2 is not the
**> > biggest,
**> > > why?
**> > > > lm=lm(y~x)
**> > > > y.hat=cbind(rep(1,length(y)),x)%*%lm$coefficients
**> > > > (r.square=sum((y.hat-mean(y))^2)/sum((y-mean(y))^2))
**> > > [1] 0.2704789
**> > >
**> > >
**> > > ---------(2)----------- R2 can greater than 1
**> > >
**> > > > x=rnorm(10)
**> > > > y=runif(10)
**> > > > lm=lm(y~x-1)
**> > > > y.hat=x*lm$coefficients
**> > > > (r.square=sum((y.hat-mean(y))^2)/sum((y-mean(y))^2))
**> > > [1] 3.513865
**> > >
**> > >
**> > > ---------(3)----------- How is R2 in summary(lm(y~x-1))$r.squared
**> > > calculated? It is different from (r.square=sum((y.hat-mean
**> > > (y))^2)/sum((y-mean(y))^2))
**> > > > x=matrix(rnorm(20),ncol=2)
**> > > > xx=cbind(rep(1,10),x)
**> > > > y=x%*%c(1,2)+rnorm(10)
**> > > > ### r2 calculated by lm(y~x)
**> > > > lm=lm(y~x)
**> > > > summary(lm)$r.squared
**> > > [1] 0.9231062
**> > > > ### r2 calculated by lm(y~xx-1)
**> > > > lm=lm(y~xx-1)
**> > > > summary(lm)$r.squared
**> > > [1] 0.9365253
**> > > > ### r2 calculated by me
**> > > > y.hat=xx%*%lm$coefficients
**> > > > (r.square=sum((y.hat-mean(y))^2)/sum((y-mean(y))^2))
**> > > [1] 0.9231062
**> > >
**> > >
**> > > Thanks a lot for any cue:)
**> > >
**> > >
**> > >
**> > >
**> > > --
**> > > Junjie Li, klijunjie_at_gmail.com
**> > > Undergranduate in DEP of Tsinghua University,
**> > >
**> > > [[alternative HTML version deleted]]
**> > >
**> > > ______________________________________________
**> > > R-help_at_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.
**> > >
**> >
**> >
**> > --
**> > Paul Lynch
**> > Aquilent, Inc.
**> > National Library of Medicine (Contractor)
**> >
**>
**>
**>
**> --
**> Junjie Li, klijunjie_at_gmail.com
**> Undergranduate in DEP of Tsinghua University,
**>
**> [[alternative HTML version deleted]]
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-- Junjie Li, klijunjie_at_gmail.com Undergranduate in DEP of Tsinghua University, [[alternative HTML version deleted]]Received on Mon 21 May 2007 - 00:33:33 GMT______________________________________________ R-help_at_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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