# [R] linear correlation?

Scott, Uriel uriel.scott at mirant.com
Thu Mar 7 16:12:01 CET 2002

```Whether the two variables have the same units does not matter.  Moreover,
even if there were some way of converting cm to kg the correlation would
still be the same because the correlation is invariant under unit conversion
as it is invariant under multiplication of its arguments by a constant.

As for your second question, the correlation estimator is a continuous
function of each of the individual data points, so perturbing the values of
any of them by a sufficiently small amount will only perturb the correlation
by a small amount.

> -----Original Message-----
> From:	dechao wang [SMTP:dechwang at yahoo.co.uk]
> Sent:	Thursday, March 07, 2002 5:34 AM
> To:	r-help at stat.math.ethz.ch
> Subject:	[R] linear correlation?
>
> Hi, I have checked statistic textbooks about
> correlations, but I am still not sure the correlation
> analysis with different units, for example,
>
> x1<-c(1,  2,  3,   100, 200, 300)
> x2<-c(1.1,2.8,3.3, 108, 209, 303)
> the unit of the first 3 numbers is cm
> the unit of the last 3 numbers is kg
>
> cor(x1,x2)=0.999655
>
> Can I explain the correlation coefficient as normal in
> which all numbers have the same unit?
>
> Secondly, if keep the three large numbers unchanged,
> just change the three small numbers, the coefficient
> changes little, this means that the variation of three
> small numbers is hidden by the three larger numbers.
> Is there any solution in R to solve this issue?
>
> Thanks,
>
> Dechao
>
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