linear correlation?
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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