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?