R help - Sep 2005 - correlation question

Dear R-helpers,

First, double apologies because the question is not
directly related to R, and also probably quite simple.

I have observed (with many data) that given 2 series X and Y
cor(X,Y) and cor(log(X), log(Y)) differs only very slightly.
I suspect this is because log(x) is monotonous,
... but I am unable to demonstrate it.
(perhaps it is also wrong ?).

Would somebody here be able and kind enough to put me on
the rigth track (a piece of clue or a link would be nice).

Thanks
Vincent

First: The question is really not related to R.

What you can find very easly in books or in the internet:
The correlation coefficient is invariant under a linear transformation
(and the proof) 
#E.g. 
library(rrcov)
data(brain)
cor(brain)
cor(scale(brain))  #Is the same, BUT
cor(log(brain))    #Is VERY different.

Best,
Matthias


> Dear R-helpers,
> 
> First, double apologies because the question is not
> directly related to R, and also probably quite simple.
> 
> I have observed (with many data) that given 2 series X and Y
> cor(X,Y) and cor(log(X), log(Y)) differs only very slightly.
> I suspect this is because log(x) is monotonous,
> ... but I am unable to demonstrate it.
> (perhaps it is also wrong ?).
> 
> Would somebody here be able and kind enough to put me on
> the rigth track (a piece of clue or a link would be nice).
> 
> Thanks
> Vincent
> 
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>

TEMPL Matthias a ??crit :
> First: The question is really not related to R.
> What you can find very easly in books or in the internet:
> The correlation coefficient is invariant under a linear transformation
> (and the proof) 
yes.
> #E.g. 
> library(rrcov)
> data(brain)
> cor(brain)
> cor(scale(brain))  #Is the same,
ok
> cor(log(brain))    # BUT Is VERY different.
Ah, thank you very much for this example.
So it seems cor(X,Y) ~ cor(log(X), log(Y)) is in fact
only a particular feature of my data (prices series)
(perhaps/probably because they are quite continuous ?).

Nothing general. I was completely off the track. Sorry.
> Best,
> Matthias
Thanks again for this counter-example and the enlightenment.
Vincent