Bootstrap Logistic Regression

Background

The glm( )  function in R does so-called generalized linear models. 
The theory of these is usually covered in the categorical data course.
(and sometimes in sta503)

The response variable in this problem, remission or r, is categorical with 
values "0" or "1";
They are independent but not identically 
distributed Bernoulli random variables. 

Yi = Bernoulli(pi) 

where the parameter vector 
p = (p1, . . ., pn) 
is related to the so-called linear predictor vector 

eta = (eta1, . . ., etan) 

by the link function 

etai = logit(pi) = log(pi / (1 - pi))

or the inverse

p_i = exp( etai)/ [1 + exp( etai) ]

and the linear predictor vector has the usual form of a mean function 
in ordinary linear regression 

etai = Xi beta

where X is the so-called design matrix for the problem 
(the rows are cases and the columns are predictor variables) and beta
is a vector of regression coefficients. 

The predictor variables in this data set is LI. 

Now The R code

out <- glm(r ~ LI, family = "binomial", data=remission)
summary(out)

pred <- predict(out, type = "response")

n <- length(remission$LI)
nboot <- 999
a.star <- double(nboot)
b.star <- double(nboot)

for (i in 1:nboot) {
    r.star <- rbinom(n, 1, pred)
    out.star <- glm(r.star ~ LI, family = "binomial")
    a.star[i] <- coef(out.star)[1]
    b.star[i] <- coef(out.star)[2]
}