library(boot)

LSAT <- c(576,635,558,578,666,580,555,661,651,605,653,575,545,572,594)
GPA <- c(3.39,3.30,2.81,3.03,3.44,3.07,3.00,3.43,3.36,3.13,3.12,2.74,
2.76,2.88,2.96)

n = length(LSAT)
Brep = 10000

xy <- data.frame(cbind(LSAT,GPA))
xy

# Bootstrap the Pearson correlation coefficient

pearson <- function(d,i=c(1:n)){
        d2 <- d[i,]
        return(cor(d2$LSAT,d2$GPA))
     }
bootcorr <- boot(data=xy,statistic=pearson,R=Brep)
bootcorr  
boot.ci(bootcorr,conf=.95)

windows()
par(mfrow=c(2,1))
hist(bootcorr$t,main="Bootstrap Pearson Sample Correlation Coefficients")
plot(ecdf(bootcorr$t),main="ECDF of Bootstrap Correlation Coefficients")


# Bootstrap the transformed Pearson correlation coefficient

xihat <- function(dd,i=c(1:n)){
        dd2 <- dd[i,]
        return(.5*log((1+cor(dd2$LSAT,dd2$GPA))/(1-cor(dd2$LSAT,dd2$GPA))))
     }
bootxi <- boot(data=xy,statistic=xihat,R=Brep)
bootxi  
boot.ci(bootxi,conf=.95)

windows()
par(mfrow=c(2,1))
hist(bootxi$t,main="Bootstrap Transformed Correlation Coefficients")
plot(ecdf(bootxi$t),main="ECDF of Bootstrap Transformed Correlation
Coefficients")