Doctors data (stored under the name "doctors") is concerned with the number of deaths by heart disease in a sample of doctors from different age groups and with different smoking status (smokeron-smoker).

V1=observation number/V2=age (1=35-44yo/2=45-54yo/3=55-64yo/4=65-74yo/5=75-84yo)/V3=number of deaths/V4=aggregate years of risk/V5=smoking status(1=smoker/2=non-smoker)

a) Fit a suitable set of Poisson regression models to the data and select what you think is the best model, using AIC to inform your selection. Please bear the following points in mind:

- Treat log(V4) as a covariate (as opposed to an offset)

- Investigate interactions as well as main effects

b) Focusing on the model you selected in part (a), perform a change of deviance test to assess whether it would be better to treat log(V4) as an offset or as a covariate.

c) Repeat parts (a) and (b) using negative binomial regression models,

d) Returning to the best Poisson regression model that you identified in part (a), estimate the scale parameter and provide a Wald test of the null hypothesis that = 1, presenting your answer in the form of a p-value.

All of the calculations are performed in R software. I need help with these questions urgently.

> doctors V1 V2 V3 V4 V5 1 1 1 32 52407 1 2 2 2 104 43248 1 3 3 3 206 28612 3 1 4 4 4 4 186 12663 1 5 5 5 102 5317 1 6 6 1 2 18790 2 7 7 2 12 10673 2 8 8 3 28 5710 2 9 9 9 4 28 2585 2 10 10 5 31 1462 2 > doctors V1 V2 V3 V4 V5 1 1 1 32 52407 1 2 2 2 104 43248 1 3 3 3 206 28612 3 1 4 4 4 4 186 12663 1 5 5 5 102 5317 1 6 6 1 2 18790 2 7 7 2 12 10673 2 8 8 3 28 5710 2 9 9 9 4 28 2585 2 10 10 5 31 1462 2