Binary Regression

Neter, problem 14.9

In an experiment testing the effect of a toxic substance, 
1500 experimental insects were divided at random into 6
groups of 250 each. The insects in each group we exposed to
a fixed dose of the toxic substance. A day later, each insect
was observed. Death from exposure was scored 1, and survival
was scored 0. The results are shown below; X_j denotes the
dose level (on a logarithmic scale) received by the insects 
in group j and R_j denotes the number of insects that died
out of the 250 (n_j) in the group.

X_j n_j R_j
1 250 28
2 250 53
3 250 93
4 250 126
5 250 172
6 250 197

a) Fit a logistic regression model to the above data,
and give the maximum likelihood estimates of B0 and B1.
b) Plot the fitted response function and the estimated
proportions p_j on the same graph. Does the fit look ok?
c) What is the estimated probability that an insect dies
when the dose level is X = 3.5?
d) What is the estimated median lethal dose -- that is, 
the dose for which 50 percent of the experimental insects
are expected to die?