For the horseshoe crab data with color and width as predictors (Section 5.5.1), fit the logistic regression model permitting interaction.

a. Report the prediction equations relating width to the probability of a satel- lite, for each of the four colors. Plot them, and interpret.

b. Test for a difference between the slope parameters for medium-dark and dark crabs.

c. Test whether the interaction model gives a better fit than the simpler model lacking the interaction terms.