File:Correlation examples.png

 Description See below. Date 2007-12-08 (first version); 2007-12-08 (last version) Source Transferred from en.wikipedia; Transfer was stated to be made by User:jtneill. Author Original uploader was Imagecreator at en.wikipedia Permission( Reusing this file) Released into the public domain (by the author).

Summary

An example of the correlation of x and y for various distributions of (x,y) pairs. It was created by this Mathematica 6 code, which I wrote and release into the public domain (needs makePlot!):

```n = 2000;
GraphicsArray[{
Table[makePlot[
Table[{RandomReal[NormalDistribution[0, 1]], (1 - Abs[w])*
RandomReal[NormalDistribution[0, 1]]} .
RotationMatrix[-Sign[w]*Pi/4], {i, -1, 1, 2./n}], 1000], {w,
1, -1, -1/3}],
Table[makePlot[Table[{x, slope*x}, {x, -1, 1, 2./n}], 100], {slope,
1, -1, -1/3}],
{
makePlot[
Table[{x + RandomReal[]/3,
4 (x^2 - 1/2)^2 + RandomReal[]/500} , {x, -1, 1, 2./n}], 2000],
makePlot[
Table[{RandomReal[{-1, 1}], RandomReal[{-1, 1}]} .
RotationMatrix[-Pi/8], {x, -1, 1, 2./n}], 1400],
makePlot[
Table[{RandomReal[{-1, 1}], RandomReal[{-1, 1}]} .
RotationMatrix[-Pi/4], {x, -1, 1, 2./n}], 1400],
makePlot[Table[{x, x^2 + RandomReal[]}/2, {x, -1, 1, 2./n}],
1400],
makePlot[
Table[{x, x^2 + RandomReal[]/2}*(RandomInteger[1]*2 - 1), {x, -1,
1, 2./n}], 1000],
makePlot[
Table[{Sin[x*Pi] + RandomReal[NormalDistribution[0, 1/8]],
Cos[x*Pi] + RandomReal[NormalDistribution[0, 1/8]]}, {x, -1, 1,
2./n}], 1400],
makePlot[
Table[{RandomReal[NormalDistribution[0, 1/3]],
RandomReal[
NormalDistribution[0, 1/3]]} + {RandomInteger[1]*2 - 1,
RandomInteger[1]*2 - 1}, {x, -1, 1, 2./n}], 1400]
}
}]
```

Licensing

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