[R] linear correlation?

[Michaell Taylor]

Uh???

A good deal of this thread leaves me perplexed.  

Of course you can correlate vectors of differing units.  Correlations
are covariances expressed in a standardized unit.  I.e. differing units
is the reason for correlation coefficients in the first place.

Of course you can correlate measures of different phenomenon - i.e.
economic growth is correlated with percentage of voters voting for the
incumbent in the next election.  Correlation of two different measures
of the same phenomenon is called a test of reliability. 

Of course you can correlate cm and kg.  I would be perfectly confortable
stating that an person's weight in kg is correlated to their height in
cm.  Anyone disagree?

Obviously one has to be careful in extracting substantive meaning from
correlations - just like every statistic that I can think of.

In term of the big number small number thing.  The major source of your
observed correlations is coming from their being a set of small numbers
and a set of big numbers.  Think of these things as points on a graph.
In your example,

> x1<-c(1,  2,  3,   100, 200, 300)
> > > > x2<-c(1.1,2.8,3.3, 108, 209, 303)
> > > > x3<-c(2.8,3.8,5.3, 108, 209, 303)
> > > > cor(x1,x2)
> > > [1] 0.999655
> > > > cor(x1,x3)
> > > [1] 0.9997286

The minor fluctions in these series between observations 1, 2,3  and
4,5,6 is totally dwarfed by the difference between 3-4  It is this jump
between (3,3.3) and (100,108) which drives your correlations. 
Comparatively, the other changes are a wash.


============
Michaell Taylor
Senior Economist, Reis, New York, USA
Associate Professor, NTNU, Norway
Adjunct Professor, UD, South Africa



On Thu, 2002-03-07 at 10:16, Setzer.Woodrow at epamail.epa.gov wrote:
> 
> Perhaps I've led a sheltered life, but my own experience leads me to
> question the logic behind an analysis that leads me to want to compute
> correlations between vectors in which the elements have different units;
> cm and kg are not generally interconvertible!
> 
> R. Woodrow Setzer, Jr.                                            Phone:
> (919) 541-0128
> Experimental Toxicology Division                       Fax:  (919)
> 541-5394
> Pharmacokinetics Branch
> NHEERL MD-74; US EPA; RTP, NC 27711
> 
> 
>                                                                                                                                     
>                     dechao wang                                                                                                     
>                     <dechwang at yahoo.co.u        To:     r-help at stat.math.ethz.ch                                                    
>                     k>                          cc:                                                                                 
>                     Sent by:                    Subject:     [R] linear correlation?                                                
>                     owner-r-help at stat.ma                                                                                            
>                     th.ethz.ch                                                                                                      
>                                                                                                                                     
>                                                                                                                                     
>                     03/07/02 05:33 AM                                                                                               
>                                                                                                                                     
>                                                                                                                                     
> 
> 
> 
> 
> 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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