#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 }