For Table 4.2, fit a logistic regression model for the probability of a satellite, using color alone as the predictor.

a. Treat color as qualitative (nominal). Conduct a likelihood-ratio test of the hypothesis that color has no effect. Compare the result to the test for color conducted in Section 5.5.2 for the model that also contains width. Explain how the relation between the tests is analogous to that for a continuous response between a test for a factor in one-way ANOVA and in analysis of covariance.

b. Treating color in a quantitative manner, obtain a prediction equation. Inter- pret the fit, and test the hypothesis that color has no effect.

c. Test goodness of fit of the model in (b). Interpret, and use Pearson or adjusted residuals to describe any lack of fit.

d. The data are binomial responses at four color levels. Explain why the model in

(a) is saturated. Express its parameter estimates in terms of the sample logits for each color.