File:Correlation examples2.svg

From Department of Mathematics at UTSA
Jump to navigation Jump to search

Original file(SVG file, nominally 506 × 231 pixels, file size: 2.18 MB)

This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.

Summary

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
}

Licensing

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.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Captions

OVRHEAD AN D REVENUE

Items portrayed in this file

depicts

9 May 2011

image/svg+xml

31cfb22bd2b6ebd79849d3d8a0f44e93c16c64af

2,285,771 byte

231 pixel

506 pixel

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current00:00, 10 May 2011Thumbnail for version as of 00:00, 10 May 2011506 × 231 (2.18 MB)DenisBoigelot{{Information |Description ={{en|1=fd}} |Source ={{own}} |Author =DenisBoigelot |Date = |Permission = |other_versions = }} fjdk

The following page uses this file:

Metadata