#This first script is what I run in class
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)
plot(LSAT,GPA)
School=as.data.frame(cbind(LSAT,GPA),row.names=NULL)
# You should try the command below without stype (the default)
lsat.boot=boot(School,corr,R=999,stype="w")
lsat.boot
boot.ci(lsat.boot,conf=.95,type=c("norm","basic","perc","bca"))
#
# An alternative approach using a different stype
#
corrlsat=function(d,w) {
data=d[w,]
return(corr(data))
}
lsat.boot=boot(School,corrlsat,R=999,stype="i")
boot.ci(lsat.boot,conf=.95,type=c("norm","basic","perc","bca"))
#
# After loading the data and re-running lsat.boot and corrlsat, 
# here are commands to accompany the bootstrap exercise.
#
# The following command generates CIs for the transformation atanh
# This command won't produce percentile t (studentized) CIs because
# no variance function is provided.
boot.ci(lsat.boot,type="all",h=atanh)
# Change corrlsat to provide a variance function for the percentile t 
# method.
corrlsat=function(d,w) {
data=d[w,]
nd=dim(data)[1]
return(c(corr(data),((1-corr(data)^2)^2)/(nd-3)))
}
lsat.boot=boot(School,corrlsat,R=999,stype="i")
boot.ci(lsat.boot,type="all",h=atanh,hdot=function(x) 1/(1-x)^2)
# Now provide the inverse function to obtain CIs on the original metric
lsat.boot=boot(School,corrlsat,R=999,stype="i")
boot.ci(lsat.boot,type="all",h=atanh,hinv=tanh,hdot=function(x) 1/(1-x)^2)