Re: [urgent]: random sample with predefined correlation

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Article #60

#60

From: Ray Koopman
Date: Mon, 03 Oct 2005 07:41

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Pedro Cardoso wrote:
> Hello all, I have this problem:
>
>     I have a vector x of values and I would like "randomly" produce other
> vector y,
>     such that correlation(x,y) is equal to some predefined value.
>
>     example:
>         x=(1, 2, 1, 2, 3, 4, 5, 1, 8)
>         y=(?, ?; ?, ?, ?, ?, ?, ?, ?)
>         correlation(x,y)=0.7
>
>
>     Can anyone help?
>
> best regards,
> Pedro.

I assume you would like Mathematica code again. This should do it:

  y = {0,r,Sqrt[1-r^2]}.First@QRDecomposition[{1.,#,Random[]}&/@x]

where r is the desired correlation[x,y].  Tr@y == 0. && y.y == 1.

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Subject: Re: [urgent]: random sample with predefined correlation
Date: 3 Oct 2005 00:41:29 -0700
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