For Table 4.3, fit a logistic regression model for the probability of a satellite, using color alone as the predictor.

a. Treat color as nominal. Explain why this model is saturated. Express its parameter estimates in terms of the sample logits for each color.

b. Conduct a likelihood-ratio test that color has no effect.

c. Fit a model that treats color as quantitative. Interpret the fit, and test that color has no effect.

d. Test the goodness of fit of the model in part (c). Interpret.

Table 4.3:

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Number of Crab Satellites by Female's Characteristics" Sa cs w Sa CS Wt Sa Wt Wt Wt Sa 2 3 28.3 3 3 26.0 3 3 25.6 1.85 3 3 22.5 1.55 2 3 23.8 2.10 3 3 24.3 2.15 2 1 26.0 2.30 3.05 26.0 2.30 9 3 3 24.8 2.10 03 2 24.7 1.90 02 3 25.8 2.65 14 1 1 27.1 2.95 02 3 27.4 2.70 3 3 26.7 2.60 2 1 26.8 2.70 2 1 23.7 2 3 28.2 3.05 2 3 25.2 2.00 2 2 23.2 1.95 4 3 25.8 2.00 4 3 27.5 2.60 2 2 25.7 2.00 2 3 26.8 2.65 3 3 27.5 3.10 3 1 28.5 3.25 2 3 28.5 3.00 1 1 27.4 2.70 2 3 27.2 2.70 3 3 27.1 2.55 2 3 28.0 2.80 2 1 26.5 1.30 3 3 23.0 1.80 3 2 26.0 2.20 3 2 24.5 2.25 2 3 25.8 2.30 2.60 1.95 2.15 11 4 2 21.0 2 3 29.0 1 2 25.0 4 3 26.2 3.00 4 3 24.7 2.20 2 1 22.5 1.60 2 3 28.7 3.15 1 1 29.3 3.20 2 1 26.7 2.70 6. 2.30 1.30 2 3 24.9 2.10 4 1 3 25.8 2.60 2 1 25.7 5 4 3 23.7 1.85 2 3 27.9 2.80 6 2 1 30.0 3.30 6 2 3 25.0 2.10 2 3 27.7 2.90 5 2 3 28.3 3.00 15 0 4 3 25.5 2.25 2 3 26.0 2.15 2 3 26.2 2.40 7 |3 3 23.0 1.65 2 2 22.9 1.60 0 |2 3 25.1 2.10 03 1 25.9 2.55 4 1 25.5 2.75 5 2 1 26.8 2.55 02 1 29.0 2.80 3 3 28.5 3.00 1|2 2 24.7 2.55 1 |2 3 29.0 3.10 2 3 27.0 2.50 2 |4 3 23.7 1.80 5 3 3 27.0 2.50 0 12 3 24.2 1.65 4 3 22.5 1.47 6 2 3 25.1 1.80 72 3 24.9 2.20 6 |2 3 27.5 2.63 3 |2 1 24.3 2.00 4 2 3 29.5 3.02 4 2 3 26.2 2.30 02 3 24.7 1.95 03 2 29.8 3.50 4 3 25.7 2.15 03 3 26.2 2.17 0 4 3 27.0 2.63 0 2 2 24.5 2.00 2.00 2 3 27.5 3.15 4 3 23.4 1.90 6. 1 1 26.1 3 3 28.9 2 1 30.3 2 3 22.9 3 3 26.2 3 3 24.5 3.05 1 1 27.7 2.50 2 3 28.2 2.60 4 3 24.7 2.10 2 1 25.7 2.00 2 1 27.8 2.75 3 1 27.0 2.45 2 3 29.0 3.20 3 3 25.6 2.80 3 3 24.2 1.90 2.80 2.80 4 4 3.60 6. 1.60 4 2.30 2.05 2 3 30.0 2 3 26.2 2 3 25.4 2 3 25.4 4 3 27.5 10 2.40 2.25 2.25 3 3 25.7 1.20 4 2.90 3 3 23.1 1.65 4 2 3 28.5 3.05 2 1 29.7 3.85 3 3 23.1 1.55 3 3 24.5 2.20 2 3 27.5 2.55 2 3 26.3 2.40 2 3 27.8 3.25 2 3 31.9 3.33 2 3 25.0 2.40 4 3 27.0 2.25 4 3 23.5 1.90 4 3 26.7 2.45 3 3 25.5 2.25 2 3 28.2 2.87 2 1 25.2 2.00 2 3 25.3 1.90 3 3 25.7 2.10 2 2 24.0 2 1 28.7 1.70 3.20 3 3 26.5 1.97 2 3 24.5 1.60 4 1 3 3 27.3 2.90 2 3 26.5 2.30 2 3 25.0 1.40 2.10 4 3 29.3 3.23 12 3 3 22.0 1 1 30.2 2 2 25.4 2 1 24.9 4 3 25.8 6. 3 3 23.8 1.80 2 3 27.4 2.90 2 3 26.2 2.02 2 1 28.0 2.90 2 1 28.4 3.10 2 1 33.5 5.20 2 3 25.8 2.40 3.28 3 3 26.2 2.22 2.30 3 3 28.4 3.20 4 1 2 24.5 1.95 2 3 27.9 3.05 2 2 25.0 2.25 3 3 29.0 2.92 2 1 31.7 3.73 2 3 27.6 2.85 4 3 24.5 1.90 3 3 23.8 1.80 2 3 28.2 3.05 2.30 2.25 10 3 3 27.2 2 3 30.5 4 3 25.0 2 3 30.0 2 1 22.9 2 3 23.9 2 3 26.0 2 3 25.8 2.40 6. 3.32 3 3 3 24.0 1.90 2.10 10 4 2 1 23.1 2.00 2 3 28.3 3.20 2 3 26.5 2.35 2 3 26.5 2.75 3 3 26.1 2.75 3.00 1.60 1.85 2.28 2.20 3 3 24.1 1.80 3 3 29.0 3.28 1 1 28.0 2.62 1 1 26.5 2.35 "C, color (1, light medium; 2, medium; 3, dark medium; 4, dark); S, spine condition (1, both good; 2, one worn or broken; 3, both worn or broken); W, carapace width (cm); Wt, weight (kg); Sa, number of satellites. 114 202 60n 3o9d 2304