## Paul Johnson ## 2014-02-05 ## Distributions: Visualize Covariance = 0 x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) plot(-3:3, -3:3, type = "n") abline(h = 0, lty = 4) abline(v = 0, lty = 4) points(x1, x2) x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) points(x1, x2) x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) text(x1, x2, "3") x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) text(x1, x2, "4") x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) text(x1, x2, "5") for (i in 6:100){ x1 <- rnorm(1, m = 0, s = 1) x2 <- rnorm(1, m = 0, s = 1) text(x1, x2, i) } ## Now, lets manufacture 2 variables that have a positive covariance. ## This is a fairly common way to do it. ## First, collect 100 values for x1 x1 <- rnorm(100, m = 0, s = 1) ## Second, collect some "noise" data. Call it e1. It is truly uncorrelated with x1 e1 <- rnorm(100, m = 0, s = 1) ## Create x2 that is partly a reflection of x1 and partly of e1 x2 <- x1 + e1 plot(-3:3, -3:3, type = "n") abline(h = 0, lty = 4) abline(v = 0, lty = 4) points(x1, x2) cov(x1, x2) legend("topleft", legend = c("'True' Covariance = 1.0")) x2 <- - x1 + e1 plot(-3:3, -3:3, type = "n") abline(h = 0, lty = 4) abline(v = 0, lty = 4) points(x1, x2) cov(x1, x2) legend("topleft", legend = c("'True' Covariance = 11.0"))