For model (4.3) for the horseshoe crabs with color and width predictors, add three terms to permit interaction between color and width.

a. Report the prediction equations relating width to the probability of a satellite, for each color. Plot or sketch them, and interpret.

b. Test whether the interaction model fits better than the simpler model without interaction terms. Interpret. Compare their predictive power by finding the correlation R between the observed and fitted values for each model.