Data were collected to study a type of damage caused by waves to the forward section of certain cargo-carrying vessels. The values of the following variables were recorded: type: ship type (coded as A to E); year: year of construction (1960, 1965, 1970, 1975); period: period of operation (1960-74, 75-79); service: aggregate months of service incidents: number of damage incidents. The data were implemented using R and the results are as follows; Call: glm(formula = incidents-offset(log(service)) + type + year + period, family-poisson, data=wdships) Deviance Residuals: Min 1Q Median 3Q -1.6768 -0.8293-0.4370 0.5058 Max 2.7912 Coefficients: Estimate Std. Error z value Pr(>\zl) (Intercept) -6.40590 0.21744 -29.460 <2e-16*** typeB -0.54334 0.17759 -3.060 0.00222 ** typeC -0.68740 0.32904 -2.089 0.03670* typeD -0.07596 0.29058 -0.261 0.79377 typeE 0.32558 0.23588 1.380 0.16750 year65 0.69714 0.14964 4.659 3.18e-06*** year 70 0.81843 0.16977 4.821 1.43e-06*** year75 0.45343 0.23317 1.945 3.251 0.05182. 0.00115** period75 0.38447 0.11827 (Dispersion parameter for poisson family taken to be 1) Null deviance: 146.328 on 33 degrees of freedom Residual deviance: 38.695 on 25 degrees of freedom AIC: 154.56 (a) What is the name of the regression model above called? (4 pts) (b) Specify the model that is appropriate for this problem in mathematical notation (c) State the assumptions of the model (4 pts) (5 pts) (d) We define year60 <-(year=-1960), and rerun the above model with year60 replacing year.The residual deviance is reported as 42.329. Please construct a hypothesis test to state which of these two models is better. (7 pts)