For the Crabs data file, fit a logistic regression model for the probability of a satellite, using

Question:

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.

d. When we treat color as quantitative instead of qualitative, state a potential advantage 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.

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