Question
3.7 Access the horseshoe crab data in Table 3.2 at www.stat.ufl.edu/aa/introcda/ appendix.html. Let Y = 1 if a crab has at least one satellite, and
3.7 Access the horseshoe crab data in Table 3.2 at www.stat.ufl.edu/aa/introcda/
appendix.html. Let Y = 1 if a crab has at least one satellite, and let Y = 0
otherwise. Using weight as the predictor, fit the linear probability model.
a. Use ordinary least squares. Interpret the parameter estimates. Find
the predicted probability at the highest observed weight of 5.20 kg.
Comment.
b. Attempt to fit the model using ML, treating Y as binomial. What does your
software report? [The failure is due to a fitted probability falling outside
the (0, 1) range.]
c. Fit the logistic regression model. Show that the estimated 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 when = 0.9968.
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