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Generating a random variable with known correlation to an existing one

Generating a random variable with known correlation to an existing one

Generating a random variable with known correlation to an existing one

I have a vector of real-values X (computed from real data)and would like to generate a second random vector (X') that is correlated with this one to a specified extent.

For example given X, generate X' so that corr(XX')=0.60.

I thought this was a very simple problem and have tried to think though some basic regression and cholesky type solutions without success thus far. The few solutions seem to lack any elegance at all - randomly add/subtract error to each element and modify until correlation is about appropriate to account for different variances in the X. Any ideas?  This seems like a 5 minute exercise that has run amuck.

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