The form for the distribution shown in Equation (8.5) was discovered and published by Simon-Denis Poisson (17811840). One of the first applications of the Poisson

The form for the distribution shown in Equation (8.5) was discovered and published by Siméon-Denis Poisson (1781–1840). One of the first applications of the Poisson distribution was in the 19th century, to model the number of deaths by horse or mule kicks in 10 corps of the Prussian army. 14 Preece, Ross, and Kirby have a nice description of the data in their paper, which uses Poisson regression. 15 In fact, there were 14 corps, but 4 are typically deleted. The horsekick Data set contains the total number of deaths by horse kicks per year for 10 corps of the Prussian army over a 20-year time period. Perform a Poisson regression analysis using deaths per corp as the response and year as the covariate, and address the following questions.
a. Conduct Wald’s test to determine if there is significant evidence that the number of deaths by horse kick depends on time.
b. Use the deviance and Pearson statistics to investigate goodness of fit of the model.
c. Examine the Pearson residuals to check for overdispersion.