Suppose y = 0 at x = 10, 20, 30, 40 and y = 1 at x = 60, 70, 80, 90. Using software, what do you get for estimates and standard errors when you fit the logistic regression model

(a) to these data?

(b) to these eight observations and two observations at x = 50, one with y = 1 and one with y = 0?

(c) to these eight observations and observations at x = 49.9 with y = 1 and at x = 50.1 with y = 0? In cases

(a) and (b), explain why actually the ML estimate ????̂ = ∞. Why does software report such a large SE for ????̂? In case (a), what is the reported maximized log-likelihood value. Why?