Re: Covariance matrix

saneman wrote:
I have this matrix:

A =

1 1000
2 1010
3 1020
4 1030
5 1040
6 1050
7 1060
8 1070
9 1080
10 1090

If the first column is the variable X and the second column is the variable
Y I would like to see how correlated the data is. Computing the covariance
matrix gives:


C =

9.1667 91.6667
91.6667 916.6667

I have read that if an element in C is 0 there is no covariance between the
corresponding variables, if its positive there is a covariance between the
two variables and if its negative there is a covariance between X and -Y.

In C the covariance between X and Y is 91.6667. But how should that number
be interpretated and does the magnitude have anything to say?

If I plot the above data X and Y does not seem very correlated (close to
each other).

But you can fit a straight line through them -- with no error.


I think you want 'correlation', i.e. eqn. (7) of:

http://mathworld.wolfram.com/Covariance.html

That will leave you with:

C =

9.1667/Sx.Sx 91.6667/Sx.Sy
91.6667/Sx.Sy 916.6667/Sy.Sy

where Sx = sqrt(9.1667) = 3.03
Sy = sqrt(916.6...) = 30.3

So the diagonal terms are 1. and the off diagonal terms are approx. 1 (maybe exactly).

Best regards,

Jon C.
.

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