[R] linear correlation?

dechao wang dechwang at yahoo.co.uk
Thu Mar 7 16:29:16 CET 2002

``` --- Andrew Perrin <andrew_perrin at unc.edu> wrote: > On
Thu, 7 Mar 2002, [iso-8859-1] dechao wang wrote:
>
> > Thanks Andrew,
> >
> > Consider the following 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
> >
> > You can see that as x2 changed to x3 with only
> first
> > three numbers changing, the coefficients (x1, x2)
> and
> > (x1,x3) changed little. I thought this may be
> because
> > the last three numbers were in different units.
>
> It's not because they're different units -- it's
> because they're different
> measures altogether! Can you state, in words (e.g.,
> not in mathematical
> terms) what you think a correlation would *mean*
> between these two
> vectors?  R is happily telling you, as any
> statistical package would, what
> the correlation is between two vectors of numbers.
> But that correlation
> doesn't necessarily mean anything at all; its
> meaning is based on what the
> vectors measure.
>

There are lots of examples. Let us consider the first
three numbers representing three branches of an apple
tree, the last three numbers representing the
corresponding branching angles of the branches. So x1,
x2, x3 represents three different trees. Maybe we can
ask which tree is similar to which tree?

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