Simulate random data with correlation

Question

I would like to simulate some random data e.g. between 0 and 1, but with a given correlation. In other words some data where the correlation between two datasets is e.g. a constant or within a give range of correlations for example a minimum of 0.2 and a maximum of 0.8.

Any tips how to use e.g. RandomReal or another function to create such data?

thanks in advance

Answer 1

ClearAll[dist]
dist [rho_] := CopulaDistribution[{"Binormal", rho}, {UniformDistribution[{0, 1}], 
    UniformDistribution[{0, 1}]}];

data1 = RandomVariate[dist[-.9], 5000];
ListPlot[data1, Frame -> True, AspectRatio -> 1]

data2 = RandomVariate[dist[.6], 5000];
ListPlot[data2, Frame -> True, AspectRatio -> 1]

Answer 2

f[r_?NumberQ,n_Integer]:={First[#],#.{r,Sqrt[1-r^2]}}&/@RandomReal[NormalDistribution[0,1],{n,2}];

Produces n pairs of numbers with the correlation r.

Answer 3

Brute Force:

 While[! ( .9 < 
      Correlation[ a = RandomReal[{0, 1}, 10], b = RandomReal[{0, 1}, 10  ]] < .91 ) ]
 Correlation[ a, b]

0.900731

 {a, b} // MatrixForm

I expect this breaks down in a hurry for larger sets.