Table 3.4 showed data on accidents involving trains.

a. Is it plausible that the collision counts are independent Poisson variates with constant rate over the 29 years? Respond by comparing a Poisson GLM for collision rates that contains only an intercept term to a Poisson GLM that contains also a time trend. The deviances of the two models are 35.1 and 23.5.

b. Section 3.3.6 fitted a negative binomial model. The estimated collision rate x years after 1975 was e−4.20(e−0.0337)x = (0.015)(0.967)x . The ML estimate ˆ β = −0.0337 has SE = 0.0130. Conduct the Wald test of H0: β = 0 against Ha: β = 0.

c. The likelihood-ratio 95% confidence interval for β is (−0.060,−0.008).

Find the interval for the multiplicative annual effect on the accident rate, and interpret.