# [R] linear correlation?

Andrew Perrin andrew_perrin at unc.edu
Thu Mar 7 15:07:57 CET 2002

```On Thu, 7 Mar 2002, [iso-8859-1] dechao wang wrote:

> 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?

I don't think the correlation depends on the units; it's a ratio, not an
absolute. Consider the case of making the centimeters into meters:

> x1m<-x1 * 100
> cor(x1m,x2)
[1] 0.999655

The correlation doesn't change.

>
> 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?
>

I'm not sure what you mean by "hidden"; in your case, the correlations
between the vectors are similar for both first and second halves:
> cor(x1[4:6],x2[4:6])
[1] 0.9997853
> cor(x1[1:3],x2[1:3])
[1] 0.953821

so removing either half isn't going to change the result much.

----------------------------------------------------------------------
Andrew J Perrin - andrew_perrin at unc.edu - http://www.unc.edu/~aperrin
Assistant Professor of Sociology, U of North Carolina, Chapel Hill
269 Hamilton Hall, CB#3210, Chapel Hill, NC 27599-3210 USA

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```