tooth {bootstrap}

Tooth Strength Data

Description

Thirteen accident victims have had the strength of their teeth measured, It is desired to predict teeth strength from measurements not requiring destructive testing. Four such bvariables have been obtained for each subject, (D1,D2) are difficult to obtain, (E1,E2) are easy to obtain.

Usage

data(tooth)

Format

A data frame with 13 observations on the following 6 variables.

patient

a numeric vector

D1

a numeric vector

D2

a numeric vector

E1

a numeric vector

E2

a numeric vector

strength

a numeric vector

Details

Do the easy to obtain variables give as good prediction as the difficult to obtain ones?

Source

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

Examples

str(tooth)
mod.easy <-  lm(strength ~ E1+E2, data=tooth)
mod.diffi <- lm(strength ~ D1+D2, data=tooth)
summary(mod.easy)
summary(mod.diffi)
if(interactive())par(ask=TRUE)
theta <- function(ind) {
    easy <- lm(strength ~ E1+E2, data=tooth, subset=ind)
    diffi<- lm(strength ~ D1+D2, data=tooth, subset=ind)
    (sum(resid(easy)^2) - sum(resid(diffi)^2))/13   }
tooth.boot <- bootstrap(1:13, 2000, theta)
hist(tooth.boot$thetastar)
abline(v=0, col="red2") 
qqnorm(tooth.boot$thetastar)
qqline(tooth.boot$thetastar, col="red2")