# Correlation Bands

**Purpose**

Correlation Bands have to be present for any correl metric

Let’s say I simulate data from a bivariate norm

> set.seed(1977) > n <- 100 > rho <- 0.1 > sample.mean <- c(0, 0) > sample.cov <- matrix(data = c(1, rho, rho, 1), nrow = 2, ncol = 2) > x <- rmnorm(n = n, mean = sample.mean, varcov = sample.cov) > temp <- cbind(runif(400), runif(400)) > y <- rbind(x, temp) > r <- cor(y)[1, 2] |

**In the above sample there are 400 obs from a uniform dist**

while 100 obs from a bivariate norm. Ideally the correl should be 0 but above is showing 0.114

Hence Fischer transformation is needed

> w <- 0.5 * log((1 + r)/(1 - r)) > z <- w/sqrt(500 - 3) > pnorm(z) [1] 0.5020618 |

Hence one rejects the alternate …Correl Band between the 2 series has 0 and hence one cannot be certain about the sample correlation. In any case, it measures linear dependence only.