Refer to Table 4.2. Let Y = 1 if a crab has at least one satellite, and Y = 0 otherwise. Using weight as the predictor, fit the linear probability model.

a. Use ordinary least squares. Interpret the parameter estimates. Find the pre- dicted probability at the highest observed weight of 5.20 kg. Comment.

b. Attempt to fit the model using ML, treating Y as binomial. (The failure is due to a fitted probability falling outside the (0, 1) range. In (a), least squares corresponds to ML for a normal random component, for which fitted values outside this range are permissible.)

c. Fit the logistic regression model. Show that the predicted logit at a weight of 5.20 kg equals 5.74. Show that = 0.9968 at that point by checking that log[/(1)] = 5.74.

d. Fit the probit model. Interpret the parameter estimates using characteristics of the normal cdf that describes the response curve. Find the predicted probability at weight = 5.20 kg.