RE: [R] linear regression: evaluating the result Q
It looks just like the classical F-test for lack-of-fit, using estimate of
`pure errors' from replicates, doesn't it? This should be in most applied
regression books. The power (i.e., probability of finding lack-of-fit when
it exists) of such tests will depend on the data.
Andy
> From: RenE J.V. Bertin
>
> Hello,
>
> I'd like to come back to this question I obtained some
> valuable help with a while ago.
>
> I just came across a paper applying a seemingly rather
> clever/elegant technique to assess the extent to which a
> linear fit is appropriate, given once data. These authors
> apply an ANOVA to the residuals, and take a NS result as an
> indication that the fitted relationship is indeed
> (sufficiently) linear.
>
> But is this a clever/elegant technique, and is it good and robust?
> A rather pathological example where it fails (I think):
>
> ##> kk<-data.frame( ordered(factor( rep( 1:25, each=11))),
> ordered(factor(rep( 0:10, 25))), sin( pi*jitter(rep(0:10,25))) )
> ##> names(kk)<-c("s","x","y")
> ##> summary( aov(y~x+Error(s), data=kk) )
>
> Error: s
> Df Sum Sq Mean Sq F value Pr(>F)
> Residuals 24 2.592 0.108
>
> Error: Within
>Df Sum Sq Mean Sq F value Pr(>F)
> x 10 1.174 0.117 0.974 0.467
> Residuals 240 28.924 0.121
>
> (it doesn't fail when using a cosine instead of a sine, of course).
>
> And if so, before I reinvent the wheel in implementing it
> myself: is anyone here aware of an existing implementation of
> a test that does just that?
>
> Thanks,
> RenE Bertin
>
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Re: [R] linear regression: evaluating the result Q
On Thu, 16 Sep 2004, RenE J.V. Bertin wrote: > On Thu, 16 Sep 2004 17:03:09 +0100 (BST), Prof Brian Ripley <[EMAIL PROTECTED]> > wrote regarding > "Re: [R] linear regression: evaluating the result Q" > > Thank you, that should get me going into the right direction! > > 8-) Well, for rlm no, as it is not least-squares fitting and R^2 is very > 8-) suseptible to outliers. For glm, not really unless it is a Gaussian > 8-) model. > > This is what I feared. How then would one evaluate the goodness of > an rlm fit, on a comparable 0-1 scale? Via the estimated robust scales. > 8-) > Aside from question 2), what is the best way to compare > 8-) > the calculated slope with another slope (say of the unity line)? > 8-) > 8-) Use offset, as in y ~ x + offset(x) and test for the coefficient of x to > 8-) be zero. (That's R only, BTW.) > > offset seems to be ignored by rlm(), is that correct? (Which isn't too > much of a problem as long as confint operates correctly on rlm objects.) Yes -- rlm was written before R existed. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] linear regression: evaluating the result Q
On Thu, 16 Sep 2004, RenE J.V. Bertin wrote: > Dear all, > > A few quick questions about interpreting and evaluating the results of > linear regressions, to which I hope equally quick answers are possible. > > 1) The summary.lm method prints the R and R^2 correlation coefficients > (something reviewers like to see). It works on glm objects and (after > tweaking it to initialise z$df.residual with rdf) also on rlm objects. > Are the R, R^2 and also the p values reported reliable for these fit > results? If not, how do I calculate them best? Well, for rlm no, as it is not least-squares fitting and R^2 is very suseptible to outliers. For glm, not really unless it is a Gaussian model. > 2) For a simple 1st order linear fit, what is the best way to calculate > the (95%) confidence interval on/of the slope? Use confint. (MASS chapter 7 has examples.) > 3) The p values reported for the calculated coefficients and intercept > indicate to what extent these values are significantly different from > zero (right?). Yes. > Aside from question 2), what is the best way to compare > the calculated slope with another slope (say of the unity line)? Use offset, as in y ~ x + offset(x) and test for the coefficient of x to be zero. (That's R only, BTW.) -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
