If you have two uncorrelated normally distributed random numbers, given by x, you can use the following to determine Y, which will be correlated with x(:,1)....
x=randn(1e3,2);
R0 = 0.75;
corr(x(:,1), x(:,2))
Y=R0*x(:,1)+(sqrt(1-R0)*x(:,2));
corr(x(:,1), Y)
It also appears to work well if x is from a uniform distribution, but the returned results are no longer uniformly distributed.
x=rand(1e3,2);
R0 = 0.75;
corr(x(:,1), x(:,2))
Y=R0*x(:,1)+(sqrt(1-R0)*x(:,2));
corr(x(:,1), Y)
It should be noted that the real correlation between x(:,1) and Y can vary significantly from R0 if N is small, also it works less well if x(:,1) and x(:,2) are coincidently correlated.
There are ways of doing this with Cholesky and eignevector decomposition, but I can't remember them off the top of my head.
UPDATED:
As John pointed out, the about solution does not maintain the uniformity of the random numbers after adjusted for correlations. I have attached a function that I sometimes use for this purpose, which does return uniform results
This is based on an example script provided here http://comisef.wikidot.com/tutorial:correlateduniformvariates
