Question: For Table 4.3, Table 4.7 shows SAS output for a Poisson loglinear model fit using X = weight and Y = number of satellites. a.

For Table 4.3, Table 4.7 shows SAS output for a Poisson loglinear model fit using X = weight and Y = number of satellites.

a. Estimate E(Y) for female crabs of average weight, 2.44 kg.

b. Use Î²Ì‚ to describe the weight effect. Show how to construct the reported confidence interval.

c. Construct a Wald test that Y is independent of X. Interpret.

d. Can you conduct a likelihood-ratio test of this hypothesis? If not, what else do you need?

e. Is there evidence of overdispersion? If necessary, adjust standard errors and interpret.

Table 4.3:

Table 4.7:

Criterion Deviance Pearson Chi- Square Log Likelihood DF 171 171 Value 560.8664 535.8957 71.9524 Parameter Estimate Std

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 1.5 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. Criterion Deviance Pearson Chi- Square Log Likelihood DF 171 171 Value 560.8664 535.8957 71.9524 Parameter Estimate Std Error Wald 95% Conf Limits Chi- Sq Pr > Chisq -0.7791 0.4619 Intercept -0.4284 weight 0.1789 0.0650 -0.0777 0.7167 5.73 82.15 0.5893 0.0167

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