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?

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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