Suppose i want to use weight as the predictor variable for the Horseshoe crab data set in order to predict Y, the number of Satellites the female crab has. Use the following SAS produces the following parameter estimates for the Poisson regression model with a log link:

a) Estimate the mean of Y for female crabs of weight 2.25 kg.

b) Conduct a 95% confidence interval for the average number of satellites around a female weighting 2.25 kg.

c)Conduct a Wald Test of the hypothesis that the mean of Y is independent of weight. Please state the null and alternative hypothesis.

d)Conduct a likelihood-ratio test about the weight effect.
 

Parameter DF Intercept 1 Weight 1 Scale 0 Estimate Standard Error -3.3458 0.5411 0.1635 0.0199 1.0000 0.0000 Likelihood Ratio 95% Confidence Limits -4.2569 -2.2307 0.1250 0.2025 1.0000 1.0000 Wald Chi- Square 37.11 67.49 Pr> chi Square