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>, eleutheroskaiwraios at googlemail.com wrote: > 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 > alt.math.undergrad 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