x <-c(8.26, 6.33, 10.4, 5.27, 5.35, 5.61, 6.12, 6.19, 5.2,7.01, 8.74, 7.78, 7.02, 6, 6.5, 5.8, 5.12, 7.41, 6.52, 6.21,12.28, 5.6, 5.38, 6.6, 8.74)
CV<-function(x) {sqrt(var(x))/mean(x)}
CV(x)

jack <- numeric(length(x)-1)
pseudo <- numeric(length(x))
for (i in 1:length(x))
{
 jack<-x[-i]
 pseudo[i]<-length(x)*CV(x)-(length(x)-1)*CV(jack)
}
jack.estim<-mean(pseudo)
jack.estim
jack.se<-sqrt(var(pseudo)/length(x))
jack.se

jack.estim+qt(0.975,length(x)-1)*jack.se
jack.estim-qt(0.975,length(x)-1)*jack.se

hist(pseudo)

library(bootstrap)
x1<-runif(6)
x1
jack1<-jackknife(x1,max)
jack1

estim.jack<-mean(jack1$jack.values)
estim.jack
bias<-jack1$jack.bias
quantile(jack1$jack.values,c(0.025,0.05,0.95,0.975))
estim.jack+qt(0.975,length(x)-1)*jack1$jack.se
estim.jack-qt(0.975,length(x)-1)*jack1$jack.se

boot1 <-numeric(1000)
for (i in 1:1000)
{
 boot1[i] <- CV(sample(x,replace=T))
}

boot.estim<-mean(boot1)
boot.se<-sqrt(var(boot1))
hist(boot1)
quantile(boot1,0.975)
quantile(boot1,0.025)
bias <- mean(boot1) - CV(x)
CV(x) - bias
CV(x) - bias - 1.96*boot.se
CV(x) - bias + 1.96*boot.se

library("boot")
school<-1:15
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)
law.data <- data.frame(School=school, LSAT=lsat, GPA=gpa)
correl<-function(data,indices)
{
 data<-law.data[indices,]
 cor(data[,2],data[,3])
}
boot.obj1 <- boot(law.data, correl, 1000)
boot.obj1

boot.ci(boot.obj1,type=c("norm","perc","bca"),conf=c(0.90,0.95))
plot(boot.obj1)

regcoef<-function(data,indices)
{
  data<-law.data[indices,]
  mod<-lm(LSAT~GPA,data)
  coef(mod)
}

boot.obj2 <- boot(law.data,regcoef,1000)
boot.obj2
boot.ci(boot.obj2,index=1,type=c("norm","perc","bca"),conf=c(0.90,0.95))
boot.ci(boot.obj2,index=2,type=c("norm","perc","bca"),conf=c(0.90,0.95))

plot(boot.obj2,index=1)
plot(boot.obj2,index=2)