Refer to Table 4.2.

a. Fit a Poisson loglinear model using both weight and color to predict the number of satellites. Assigning dummy variables, treat color as a nominal factor. Interpret the parameter estimates.

b. Estimate the mean number of satellites for female crabs of average weight (2.44 kg) that are (i) medium light, (ii) dark.

c. Test whether color is needed in the model. (Hint: From Section 4.5.3, the likelihood-ratio statistic for comparing two models is the difference in their G goodness-of-fit statistics.)

d. Note that the estimated color effects are monotone across the four categories. Fit a simpler model that treats color as quantitative by assuming a linear color effect. Interpret the color effect in this model, and repeat the analyses of

(b) and (c). Compare the fit to the model in (a). Interpret.

e. Add width to the model. Note the effect of the strong positive correlation between width and weight. Are both width and weight needed?