For the Crabs data file, fit a logistic regression model for the probability of a satellite, using color alone as the predictor. a. Treat color as a nominal-scale factor. Report the prediction equation and explain how to use it to compare the first and fourth colors. 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 (scores 1, 2, 3, 4), obtain a prediction equation. Interpret the coefficient of color and test the hypothesis that color has no effect. 116 4. LOGISTIC REGRESSION d. When we treat color as quantitative instead of qualitative, state a potential advan- tage relating to power and a potential disadvantage relating to model lack of fit. e. Using weight and quantitative color as explanatory variables, find standardized coefficients, and interpret