# [R] linear correlation?

Liu.Chunhua@epamail.epa.gov Liu.Chunhua at epamail.epa.gov
Fri Mar 8 18:02:45 CET 2002

```What about if we measure the height (x1 in cm) and weight (x2 in kg) of
a sample of people from some population. It seems it makes sense to me
to get the correlation between x1 and x2.

Charlie Liu,
Intern at ECO/EPA.

"Scott, Uriel"
<uriel.scott at mirant.        To:     "Scott, Uriel" <uriel.scott at mirant.com>, 'dechao
com>                        wang' <dechwang at yahoo.co.uk>, r-help at stat.math.ethz.ch
Sent by:                    cc:
owner-r-help at stat.ma        Subject:     RE: [R] linear correlation?
th.ethz.ch

03/07/02 12:28 PM

Sorry, I also misread your original question and thought x1 was in cm
and x2
in kg.

I don't think it makes any sense for some values of x1 (or x2) to be in
cm
and others in kg.  How can they represent samples from the same
population?
It would be okay if, say, some were in cm and others in km as they are
equivalent units, and you could simply convert to the same unit, but
otherwise I don't see how some members of a population are in cm and
others
in kg.

> -----Original Message-----
> From:         Scott, Uriel [SMTP:uriel.scott at mirant.com]
> Sent:         Thursday, March 07, 2002 10:12 AM
> To:           'dechao wang'; r-help at stat.math.ethz.ch
> Subject:           RE: [R] linear correlation?
>
>
> 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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