> ### Generate Bivariate Normal Data
> 
> #######################################################################
> 
> # help(rmvnorm)
> # rmvnorm(n, mean=rep(0,d), cov=diag(d), sd, rho, d=2)
> 
> n <- 30
> 
> rho <- 0.90
> 
> X <- rmvnorm(n, rho=0.90, d=2)
> 
> z1 <- X[,1]
> z2 <- X[,2]
> 
> r.samp <- cor(z1,z2)
> r.samp
[1] 0.877
> 
> plot(z1,z2)
> 
> # Fisher's z-transformation
> 
> zrho <- c(-1,0,1)*1.96*(1/sqrt(n-3)) + 0.50*log((1+r.samp)/(1-r.samp))
> zrho
[1] 0.984 1.361 1.738
> 
> # 95% Fisher's CI centered at the sample correlation, r.samp
> 
> (exp(2*zrho)-1)/(exp(2*zrho)+1)
[1] 0.755 0.877 0.940
> 
> # Nonparametric Bootstrap
> 
> B <- 1000
> 
> r.boot <- numeric(B)
> 
> for(i in 1:B){
+ 	index <- seq(1:n)	
+ 	index.boot <- sample(index, n, replace = T)
+ 	r.boot[i] <- cor(z1[index.boot],z2[index.boot])
+ }
> 
> summary(r.boot)
 Min. 1st Qu. Median  Mean 3rd Qu.  Max. 
 0.65   0.846  0.882 0.873   0.911 0.965
> r.boot.ci <- quantile(r.boot,c(0.025,0.975))
> r.boot.ci
  2.5% 97.5% 
 0.757 0.942
> hist(r.boot)
> 
> r.boot.ztran <- 0.50*log((1+r.boot)/(1-r.boot))
> hist(r.boot.ztran)
>