Access the horseshoe crab data in Table 3.2 at www.stat.ufl.edu/aa/introcda/ appendix.html. Let Y = 1 if a
Question:
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 ˆπ = 0.9968 at that point by checking that log[ ˆ π/(1− ˆπ)] = 5.74 when ˆπ= 0.9968.
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