For Table 4.3, let Y = 1 if a crab has at least one satellite, and Y = 0 otherwise. Using x = weight, fit the linear probability model.

a. Use ordinary least squares. Interpret the parameter estimates. Find the estimated probability at the highest observed weight (5.20 kg). Comment.

b. Fit the logistic regression model. Show that the fitted probability at a weight of 5.20 kg equals 0.9968.

c. Fit the probit model. Find the fitted probability at 5.20 kg.

Table 4.3:

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Number of Crab Satellites by Female's Characteristics" Sa Cs w Wt Sa CS w Sa CS W Sa Wt Wt Wt 2 3 28.3 3.05 8 3 3 22.5 1.55 3 3 26.0 2.60 3 3 25.6 2.15 4 2 21.0 1.85 2 3 29.0 3.00 1 2 25.0 2.30 4 3 26.2 1.30 2 3 24.9 2.10 2 1 25.7 2.00 2 3 27.5 3.15 1 1 26.1 2.80 3 3 28.9 2.80 2 1 30.3 3.60 2 3 22.9 1.60 3 3 26.2 2.30 3 3 24.5 2.05 2 3 30.0 3.05 2 3 26.2 2.40 2 3 25.4 2.25 2 3 25.4 2.25 4 3 27.5 2.90 01 1 26.0 2.30 03 2 24.7 1.90 02 3 25.8 2.65 2 1 26.0 2.30 14 1 1 27.1 2.95 0 |2 3 27.4 2.70 3 3 26.7 2.60 3 2 1 26.8 2.70 4 |1 3 25.8 2.60 4 3 23.7 1.85 02 3 27.9 2.80 6 2 1 30.0 3.30 6 |2 3 25.0 2.10 5 2 3 27.7 2.90 5 2 3 28.3 3.00 15 2.25 3 3 24.8 2.10 2 1 23.7 1.95 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 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 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 4 2 3 23.8 2.10 3 3 24.3 2.15 11 8. 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 4 3 23.4 1.90 1 1 27.7 2.50 2 3 28.2 2.60 4 4 4 3 24.7 2.10 6. 2 1 25.7 2.00 0 14 3 25 2.55 27.8 2.75 3 1 27.0 2.45 2 3 29.0 3.20 10 3 3 25.6 2.80 3 3 24.2 1.90 3 3 25.7 1.20 33 23.1 1.б5 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 3 3 26.2 2.22 3 3 28.4 3.20 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 |2 3 26.0 2.15 2 3 26.2 2.40 7|3 3 23.0 1.65 02 2 22.9 1.60 02 3 25.1 2.10 3 1 25.9 2.55 0 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 12 2 24.7 2.55 1 2 3 29.0 3.10 3 2 3 27.0 2.50 2 4 3 23.7 1.80 5 3 3 27.0 2.50 02 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 2 3 26.2 2.30 02 3 24.7 1.95 03 2 29.8 3.50 8 4 3 25.7 2.15 0 |3 3 26.2 2.17 0 4 3 27.0 2.63 4 4 4 3 27.0 2.25 2 2 24.0 1.70 2 1 28.7 3.20 3 3 26.5 1.97 2 3 24.5 1.60 3 3 27.3 2.90 2 3 26.5 2.30 2 3 25.0 2.10 3 3 22.0 1.40 1 1 30.2 3.28 2 2 25.4 2.30 2 1 24.9 2.30 4 3 25.8 2.25 10 3 3 27.2 2.40 2 3 30.5 3.32 4 3 25.0 2.10 4 3 3 25.7 2.10 4 3 29.3 3.23 4 6. 12 3 3 23.8 1.80 2 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 3 24.0 1.90 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 2 2 24.5 2.00 6. 6. 4 6. 10 2 3 30.0 3.00 2 1 22.9 1.60 2 3 23.9 1.85 2 3 26.0 2.28 2 3 25.8 2.20 3 3 29.0 3.28 4 1 1 26.5 2.35 0 4 3 3 23.8 1.80 2 3 28.2 3.05 3 3 24.1 1.80 1 1 28.0 2.62 4 "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.