Checked content

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

PD-icon.svg This work has been released into the public domain by its author, Imagecreator at the wikipedia project. This applies worldwide.

In case this is not legally possible:
Imagecreator grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Converted to SVG.svg This graph image could be recreated using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is already available, please upload it. After uploading an SVG, replace this template with {{ vector version available|new image name.svg}}.
The following pages on Schools Wikipedia link to this image (list may be incomplete):

A background to Schools Wikipedia

Wikipedia for Schools was collected by SOS Childrens Villages. In 133 nations around the world, SOS Children's Villages works to bring better education and healthcare to families in desperate need of support. Find out more about sponsoring a child.