File:CovrarianceCorrelation.svg
From Wikipedia, the free encyclopedia
![File:CovarianceCorrelation.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/CovarianceCorrelation.svg/800px-CovarianceCorrelation.svg.png)
Size of this PNG preview of this SVG file: 800 × 365 pixels. Other resolutions: 320 × 146 pixels | 640 × 292 pixels | 1,024 × 467 pixels | 1,280 × 584 pixels | 2,560 × 1,168 pixels | 1,260 × 575 pixels.
Original file (SVG file, nominally 1,260 × 575 pixels, file size: 3.03 MB)
![]() | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
DescriptionCovarianceCorrelation.svg |
English: added covariance values to the plot of File:Correlation_examples.png using vector graphics (SVG file) |
Date | (UTC) |
Source | |
Author |
|
This is a retouched picture, which means that it has been digitally altered from its original version. The original can be viewed here: Correlation examples2.svg: ![]()
|
#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
}
I, the copyright holder of this work, hereby publish it under the following license:
![]() ![]() |
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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Original upload log
This image is a derivative work of the following images:
- File:Correlation_examples2.svg licensed with Cc-zero
- 2011-05-10T06:00:35Z DenisBoigelot 506x231 (2285771 Bytes) {{Information |Description ={{en|1=fd}} |Source ={{own}} |Author =[[User:DenisBoigelot|DenisBoigelot]] |Date = |Permission = |other_versions = }} fjdk
Uploaded with derivativeFX
Captions
Add a one-line explanation of what this file represents
Items portrayed in this file
depicts
27 August 2011
image/svg+xml
93e247f79949884233d4ef5337a46e69a4d5ceaa
3,175,815 byte
575 pixel
1,260 pixel
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 08:42, 27 August 2011 | ![]() | 1,260 × 575 (3.03 MB) | Sigbert | {{Information |Description={{en|1= added covariance values to the plot of File:Correlation_examples.png using vector graphics (SVG file)}} |Source=*File:Correlation_examples2.svg |Date=2011-08-27 08:39 (UTC) |Author=*[[:File:Correlation_example |
File usage
No pages on the English Wikipedia use this file (pages on other projects are not listed).
Global file usage
The following other wikis use this file:
- Usage on de.wikipedia.org
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Width | 1008pt |
---|---|
Height | 460pt |
Retrieved from "https://en.wikipedia.org/wiki/File:CovarianceCorrelation.svg"