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Summary[edit]

Description
English: redesign File:Correlation_examples.png using vector graphics (SVG file)
Date
Source Own work, original uploader was Imagecreator
Author DenisBoigelot, original uploader was Imagecreator
Permission
(Reusing this file)

Released into the public domain (by the authors).
Other versions

Derivative works of this file: CovrarianceCorrelation.svg

 File:Correlation_examples.png

#Title: An example of the correlation of x and y for various distributions of (x,y) pairs
#Tags: Mathematics; Statistics; Correlation
#Author: Denis Boigelot
#Packets needed : mvtnorm (rmvnorm), RSVGTipsDevice (devSVGTips)
#How to use: output()
#
#This is an translated version in R of an Matematica 6 code by Imagecreator.

library(mvtnorm)
library(RSVGTipsDevice)

MyPlot <- function(xy, xlim = c(-4, 4), ylim = c(-4, 4), eps = 1e-15) {
   title = round(cor(xy[,1], xy[,2]), 1)
   if (sd(xy[,2]) < eps) title = "" # corr. coeff. is undefined
   plot(xy, main = title, xlab = "", ylab = "",
        col = "darkblue", pch = 16, cex = 0.2,
        xaxt = "n", yaxt = "n", bty = "n",
        xlim = xlim, ylim = ylim)
}

MvNormal <- function(n = 1000, cor = 0.8) {
   for (i in cor) {
      sd = matrix(c(1, i, i, 1), ncol = 2)
      x = rmvnorm(n, c(0, 0), sd)
      MyPlot(x)
   }
}

rotation <- function(t, X) return(X %*% matrix(c(cos(t), sin(t), -sin(t), cos(t)), ncol = 2))

RotNormal <- function(n = 1000, t = pi/2) {
   sd = matrix(c(1, 1, 1, 1), ncol = 2)
   x = rmvnorm(n, c(0, 0), sd)
   for (i in t)
      MyPlot(rotation(i, x))
}

Others <- function(n = 1000) {
   x = runif(n, -1, 1)
   y = 4 * (x^2 - 1/2)^2 + runif(n, -1, 1)/3
   MyPlot(cbind(x,y), xlim = c(-1, 1), ylim = c(-1/3, 1+1/3))

   y = runif(n, -1, 1)
   xy = rotation(-pi/8, cbind(x,y))
   lim = sqrt(2+sqrt(2)) / sqrt(2)
   MyPlot(xy, xlim = c(-lim, lim), ylim = c(-lim, lim))

   xy = rotation(-pi/8, xy)
   MyPlot(xy, xlim = c(-sqrt(2), sqrt(2)), ylim = c(-sqrt(2), sqrt(2)))
   
   y = 2*x^2 + runif(n, -1, 1)
   MyPlot(cbind(x,y), xlim = c(-1, 1), ylim = c(-1, 3))

   y = (x^2 + runif(n, 0, 1/2)) * sample(seq(-1, 1, 2), n, replace = TRUE)
   MyPlot(cbind(x,y), xlim = c(-1.5, 1.5), ylim = c(-1.5, 1.5))

   y = cos(x*pi) + rnorm(n, 0, 1/8)
   x = sin(x*pi) + rnorm(n, 0, 1/8)
   MyPlot(cbind(x,y), xlim = c(-1.5, 1.5), ylim = c(-1.5, 1.5))

   xy1 = rmvnorm(n/4, c( 3,  3))
   xy2 = rmvnorm(n/4, c(-3,  3))
   xy3 = rmvnorm(n/4, c(-3, -3))
   xy4 = rmvnorm(n/4, c( 3, -3))
   MyPlot(rbind(xy1, xy2, xy3, xy4), xlim = c(-3-4, 3+4), ylim = c(-3-4, 3+4))
}

output <- function() {
   devSVGTips(width = 7, height = 3.2) # remove first and last line for no svg exporting
   par(mfrow = c(3, 7), oma = c(0,0,0,0), mar=c(2,2,2,0))
   MvNormal(800, c(1.0, 0.8, 0.4, 0.0, -0.4, -0.8, -1.0));
   RotNormal(200, c(0, pi/12, pi/6, pi/4, pi/2-pi/6, pi/2-pi/12, pi/2));
   Others(800)
   dev.off() # remove first and last line for no svg exporting
}

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
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Date/TimeThumbnailDimensionsUserComment
current06:00, 10 May 2011Thumbnail for version as of 06:00, 10 May 2011506 × 231 (2.18 MB)DenisBoigelot{{Information |Description ={{en|1=fd}} |Source ={{own}} |Author =DenisBoigelot |Date = |Permission = |other_versions = }} fjdk
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Short title R SVG Plot
Image title R SVG Plot with tooltips! (mode=1)
Retrieved from "https://en.wikipedia.org/wiki/File:Correlation_examples2.svg"