# Commands for the car data.  The variable speed is car speed,
# while dist is stopping distance (in feet).
data(cars)
attach(cars)
plot(cars,xlab="Speed (mph)",ylab="Stopping distance (ft)")
cl=loess(dist~speed)
lines(speed,cl$fitted)
lines(lowess(cars$speed,cars$dist,f=2/3,iter=3),col="red")
lboot=function(x,B=20){
nl=dim(x)[1]
cl=NULL
plot(x[,3],x[,4],xlab="Speed (mph)",ylab="Stopping distance (ft)")
lines(x[,3],x[,1],type="l",col="red")
for(i in 1:B){
bsamp=x[,1]+sample(x[,2],nl,replace=TRUE)
cfit=loess(bsamp~x[,3])$fitted
cl=cbind(cl,cfit)
lines(x[,3],cfit)
}
return(cl)
}
py=lboot(cbind(cl$fitted,cl$residuals,speed,dist))
# Repeat with larger bootstrap sample to get confidence bands
py=lboot(cbind(cl$fitted,cl$residuals,speed,dist),B=100)
plot(cars,xlab="Speed (mph)",ylab="Stopping distance (ft)")
cband=apply(py,1,quantile,probs=c(.05,.95))
lines(speed,cband[1,],col="red")
lines(speed,cband[2,],col="blue")
title("Car data with 90% empirical confidence bands")