The ships dataset found in the MASS package gives the number of wave damage incidents and aggregate months of service for different types of ships broken down by year of construction and period of operation.

a. Fit a Poisson response model for the number of incidents with the predictors: log of service, type, year and period. Test whether the parameter associated with the service term can be one. Explain why we are interested in such a test.
b. Fit the Poisson rate model with all two-way interactions of the three predictors. Does this model fit the data?
c. Check the residuals. Are there any outliers? Plot residuals against the fitted values. Investigate any unusual features of this plot
d. Now fit the rate model with just the main effects and compare it to the h) interaction model. Which model is preferred?
e. Fit quasi-Poisson versions of the two previous models and repeat the comparison.
f. Interpret the coefficients of the main effects of the quasi-Poisson model. What factors are associated with higher and lower rates of damage incidents?