5.10 For the horseshoe crab data, fit the logistic regression model with x = weight as the sole predictor of the presence of satellites.

a. For a classification table using the sample proportion of 0.642 as the cutoff, report the sensitivity and specificity. Interpret.

b. Form a ROC curve, and report and interpret the area under it.

c. Investigate the model goodness-of-fit using the Hosmer–Lemeshowstatistic or some other model-checking approach. Interpret.

d. Inferentially compare the model to the model with x and x2 as predictors.

Interpret.

e. Compare the models in

(d) using the AIC. Interpret.