For the horseshoe crab data, fit a logistic regression model for the probability of a satellite, using color alone as the predictor.

a. Treat color as nominal scale (qualitative). Report the prediction equation, and explain how to interpret the coefficient of the first indicator variable.

b. For the model in (a), conduct a likelihood-ratio test of the hypothesis that color has no effect. Interpret.

c. Treating color in a quantitative manner, obtain a prediction equation.

Interpret the coefficient of color.

d. For the model in (c), test the hypothesis that color has no effect. Interpret.

e. When we treat color as quantitative instead of qualitative, state an advantage relating to power and a potential disadvantage relating to model lack of fit.