[urgent]: random sample with predefined correlation

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2 total messages Started by Pedro Cardoso Sun, 02 Oct 2005 22:01

#59

Author: Pedro Cardoso
Date: Sun, 02 Oct 2005 22:01

17 lines
1544 bytes

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.

Re: [urgent]: random sample with predefined correlation

#60

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

23 lines
1883 bytes

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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