[R] low R square value from ANCOVA model

[peter dalgaard]

On May 8, 2012, at 08:34 , array chip wrote:

> Thank you Peter, so if I observe a significant coefficient, that significance still holds because the standard error of the coefficient has taken the residual error (which is large because large R square) into account, am I correct?

In essence, yes. One might quibble over the use of "large because", but it's not important for the main point.

-pd

> John
> From: peter dalgaard <pdalgd at gmail.com>
> To: array chip <arrayprofile at yahoo.com> 
> Cc: "r-help at r-project.org" <r-help at r-project.org> 
> Sent: Monday, May 7, 2012 11:07 PM
> Subject: Re: [R] low R square value from ANCOVA model
> 
> 
> On May 8, 2012, at 05:10 , array chip wrote:
> 
> > Hi, what does a low R-square value from an ANCOVA model mean? For example, if the R square from the model is about 0.2, does this mean the results should NOT be trusted? I checked the residuals of the model, it looked fine...
> 
> It just means that your model has low predictive power (at the individual level). I.e. the noise (error) part of the model is large relative to the signal (systematic part). Statistical inferences are not compromised by that, except of course that large error variation is reflected in large standard errors of estimated regression coefficients. 
> 
> >  
> > Thanks for any suggestion.
> >  
> > John
> >     [[alternative HTML version deleted]]
> > 
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> -- 
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
> 
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-- 
Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com