How to (efficiently) generate and catch some data-set that has similar correlation?

Question

run:=Module[
    {cor1,cor2,x1,x2,y1,y2},
    cor1=0.5;cor2=0.4;

    While[
        cor1!=cor2, 
        cor1 =Round[Correlation[x1 = RandomReal[10, 10], y1 = RandomReal[10, 10]],0.001]; 
        cor2 =Round[Correlation[x2 = RandomReal[10, 20], y2 = RandomReal[10, 20]],0.001]; 
    ];

    (*Print[{cor1,cor2}];*)

    Show[
        ListPlot[Thread[{x1, y1}], Frame -> True,PlotStyle->Red] ,
        ListPlot[Thread[{x2, y2}], Frame -> True]
    ]
]

I have started with some basic lines, which will generate some random points. Call the {x1,y1} dataset 1 and {x2,y2} the dataset 2.

I then want to Catch the two set when they have similar Correlation, for example, both are 0.43 to 2 decimal places, then plot them side by side.

Or -0.453 to 3 decimal places, then plot them side by side.

What's the best way to do it?

Thanks.

Answer 1

With[
 {
  decimals = 3,
  length = 10,
  range = 10
  },
 Block[
  {
   rcor = Round[Correlation[#[[All, 1]], #[[All, 2]]], Power[10, -decimals]] &,
   ds1 = RandomReal[range, {length, 2}],
   ds2 = RandomReal[range, {length, 2}],
   corr
   },
  corr = rcor[ds1];
  While[
   corr =!= rcor[ds2],
   ds2 = RandomReal[range, {length, 2}]
   ];
  {ds1, ds2}
  ]]