Re: how to create dataset with given correlation coefficient


Start with X and Z iid N(0,1).

If W = aX + bZ, then cov(W,X) = a var(X).

E(W) = aE(X)+bE(Z) = 0
var(W) = a^2 + b^2.
cov(W,X) = cov(aX+bZ,X) = a var(X)+0 = a

If |a|<1 and you choose b to make W have variance 1, then
corr(W,X) = a

You can then choose Y to be a linear function of W to achieve the
desired population std dev. and mean.

Glen

.

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