       Re: Computing a covariance matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg73653] Re: Computing a covariance matrix
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 24 Feb 2007 02:08:30 -0500 (EST)
• Organization: The University of Western Australia
• References: <erme5t\$i8b\$1@smc.vnet.net>

```In article <erme5t\$i8b\$1 at smc.vnet.net>,

> I was looking on how to compute a covariance matrix given a set of
> measurements and I was utterly frustrated having to jump from one
> discussion group to another and harvesting the web through maths
> websites having to cope with all sorts of notations.

I would have thought that you would find the required
derivation/computation in _many_ places.

> I managed to find a nice example on how to derive a covariance matrix and decided to
> share it with you :)
>
> Go to:
>
>
> "How the stat packages compute a correlation matrix"
>
> http://luna.cas.usf.edu/~mbrannic/files/pmet/vcv2.htm
>
> It should be quite easy to understand how it is done. It even shows
> you how to standardise the matrix at the end.
>
> NOTE: this is cross-posted at:
>
> sci.math
> sci.stat.math
> comp.soft-sys.math.mathematica

As far as I can see, you have only posted this message to MathGroup
(comp.soft-sys.math.mathematica), not to the other groups.

Also, I'm not sure what this has to do with Mathematica specificially? I
note that CovarianceMatrix, which computes VCV in your notation, is in
the package

<< Statistics`MultiDescriptiveStatistics`

Here is a direct Mathematica implementation of your example:

X = {{1, 2, 3}, {2, 3, 4}, {1, 2, 3}, {5, 4, 3}, {4, 4, 4}}

x = Transpose[X] - Mean[X]

SSCP = x . Transpose[x]

VCV = SSCP/(Length[X] - 1)

s = Sqrt[Variance /@ x]

correlationmatrix = VCV/Outer[Times, s, s]

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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