10.8 Bootstrap with regression

An alternative to estimating confidence intervals on the regression parameters from the pooled error variance
in the ANOVA table (p. 459) is to use bootstrapping. There are two ways of doing this:
sample cases with replacement, so that some points are left off the graph while others appear more than
once in the dataframe;
calculate the residuals from the fitted regression model, and randomize which fitted y values get which

residuals

regdat <- read.table("c:\\temp\\regdat.txt",header=T)
attach(regdat)

names(regdat)

plot(explanatory,response,pch=21,col="green",bg="red")
model <- lm(response~explanatory)

abline(model,col="blue")

model

b.boot <- numeric(10000)
for (i in 1:10000){
indices <- sample(1:35,replace=T)
xv <- explanatory[indices]
yv <- response[indices]
model <- lm(yv~xv)
b.boot[i] <- coef(model)[2]
}

hist(b.boot,main="",col="green")

quantile(b.boot,c(0.025,0.975))

library(boot)

reg.boot <- function(regdat, index){
xv <- explanatory[index]
yv <- response[index]
model <- lm(yv~xv)
coef(model)

}

reg.model <- boot(regdat,reg.boot,R=10000)

boot.ci(reg.model,index=2)

model <- lm(response~explanatory)
fit <- fitted(model)

res <- resid(model)

residual.boot <- function(res, index){
y <- fit+res[index]
model <- lm(y~explanatory)

coef(model) }

res.model <- boot(res,residual.boot,R=10000)

boot.ci(res.model,index=2)