[R] linear correlation?

Thu Mar 7 17:01:57 CET 2002

To follow up, consider the vector x3 <- c(3,2,1,108, 209, 303) with the
same units as before.
> cor(x1,x3)
[1] 0.9995864

Now express the first three values as microns instead of cm:
x4 <- x3
x4[1:3] <- 10000 * x4[1:3]

> cor(x1,x4)
[1] -0.7461934

Just changing the units changes the whole sense of the correlation.

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                    Andrew Perrin                                                                                                   
                    <andrew_perrin at unc.e        To:     Joerg Maeder <maeder at atmos.umnw.ethz.ch>                                    
                    du>                         cc:     dechao wang <dechwang at yahoo.co.uk>, "'R-help at lists.R-project.org'"          
                    Sent by:                    <R-help at stat.math.ethz.ch>                                                          
                    owner-r-help at stat.ma        Subject:     Re: [R] linear correlation?                                            
                    th.ethz.ch                                                                                                      

                    03/07/02 09:45 AM                                                                                               
                    Please respond to                                                                                               
                    andrew_perrin                                                                                                   

On Thu, 7 Mar 2002, Joerg Maeder wrote:

> Hello
>
> 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?
>
> No, that will give different results. The unit must be the same for
all
> values. Which unit isn't important, but it must be the same

OOPS - I apologize, I misread the question, I understood the OP to be
saying that x1 was in cm and x2 was in kg.

What on earth would a correlation mean between two vectors, each of
which
is made up of two entirely different measures? (These aren't just
different units, they're measures of entirely different phenomena.)

----------------------------------------------------------------------
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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