Access the horseshoe crab data file (shown partly in Table 3.2) at www.stat

.ufl.edu/~aa/cat/data. In the data file, y = 1 if a crab has at least one satellite and y = 0 otherwise.

a. Using weight as the predictor, fit the linear probability model to P(Y = 1). If your software cannot use the identity link with the binomial or fails to converge, use ordinary least squares by treating Y as normally distributed. Interpret the parameter estimates. Find Pˆ(Y = 1) at the highest observed weight of 5.20 kg. Comment.

b. Fit the logistic regression model. Show that at a weight of 5.20 kg, Pˆ(Y = 1) =

0.9968.