[R] correlation coefficient

[Martin Maechler]

>>>>> "BN" == Benedikt Niesterok <KleinerHaifisch at gmx.net>
>>>>>     on Tue, 28 Apr 2009 15:33:02 +0200 writes:

    BN> Hello,
    BN> I would like to get a correlation coefficient (R-squared) for my model.

{{ arrrgh... how many people think they "need" an R^2 when they
   	     fit a model ?? }}

    BN> I don't know how to calculate it in R.
    BN> What I've done so far:

    BN> x<-8.5:32.5   #Vektor x
    BN> y<-c(NA ,5.88 , 6.95  , 7.2 , 7.66 , 8.02 , 8.44 , 9.06,  9.65, 10.22 ,
    BN> 10.63 ,11.06, 11.37, 11.91 ,12.28, 12.69 ,13.07 , 13.5 , 13.3 ,14.14  ,  NA  ,  NA ,   NA  ,  NA  ,  NA) #Vektor y
    BN> plot(y~x,col="green",pch=16,ylim=c(0,20),xlim=c(0,50))

    BN> (mod1<-nls(y~a+b*log(x,base=exp(1)),start=list(a=1,b=1),trace=TRUE))

This is a very *LINEAR* model.
Why don't you use  lm()?

Then you'd even get your beloved R-squared ...

    BN> xx<-seq(min(x),max(x),length=100)
    BN> yy<-6.2456*log(xx)-7.7822
    BN> lines(xx,yy,col="blue1")
    BN> summary(mod1)

    BN> This way I don't get R-squared like I do using the command "lm" for linear
    BN> models.

In general,  R^2 is *NOT* easily defined for non-linear models.
R^2 is only defined if you have a nested sub-model, aka "null-model". 
For linear models (*WITH* an intercept (!)), the sub-model is
naturally  y ~ 1.
For general nonlinear models, the only simple sub-model is  
'y ~ 0' which is often ridiculous to take as null-model, and
hence not taken by default.

More more on this, e.g. almost 7 years ago on R-help:

  https://stat.ethz.ch/pipermail/r-help/2002-July/023461.html

Martin