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?

John
 

________________________________
 From: peter dalgaard <pdalgd@gmail.com>

Cc: "r-help@r-project.org" <r-help@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
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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