Bootstrap with regression model. Resample the residuals.


library(bootstrap)
data(cell)
plot(cell)

ffit <-  lm( log.surv ~  dose + I(dose^2), data=cell )

#### curve(predict(ffit, data.frame(dose = x)), add = TRUE)

coefficients(ffit)
resid <- residuals(ffit)
pred <- predict(ffit)
alpha.hat <- coefficients(ffit)[1]
beta1.hat <- coefficients(ffit)[2]
beta2.hat <- coefficients(ffit)[3]


x <- dose
n <- nrow(cell)
nboot <- 1000
alpha.star <- double(nboot)
beta1.star <- double(nboot)            ### place holder for results
beta2.star <- double(nboot)            ### place holder for results


for (i in 1:nboot) {
    e.star <- sample(x = resid, size = n, replace = TRUE)
    y.star <- pred + e.star
    bfit  <- lm(y.star ~ x + I(x^2))
    alpha.star[i] <- coef(bfit)[1]
    beta1.star[i] <- coef(bfit)[2]
    beta2.star[i] <- coef(bfit)[3]
}

beta1.hat
sd(beta1.star)
beta2.hat
sd(beta2.star)
beta2.hat / sd(beta2.star)
summary(ffit)