Consider the data in Table 8.4, giving the incidence of non- melanoma skin cancer among women in Minneapolis€“St. Paul by age group.
Table 8.4 Reported cases of non- melanoma skin cancer in Minneapolis€“St. Paul.

The Data set SkinCancer contains the data in Table 8.4. The age groups have been recorded to have a value near the midpoint of each group (20, 30, 40, 50, 60, 70, 80, and 90).
a. Consider age to be a continuous variable and model the non-melanoma skin cancer incidence as a function of age. Do not forget to include the population as an exposure offset in your model. Report whether you find a significant age trend in the count. Of course, check graphically that the model you propose seems reasonable, examine the residuals, and use Wald€™s test or a deviance test to make your decision.
b. How well do the observed case counts match up with the counts predicted by the model?
c. Try to improve on your model. Is the logarithm of the number of cases growing linearly with age or nonlinearly? Consider adding (age)2 or even (age)3 to your model. Try out some models and decide which one you think is best. Explain your choice.
d. Report and interpret the coefficient for age in the model. How does the risk of cancer for a woman aged 50 years relate to the risk for a woman aged 40 years?

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AgeNumber of Population Cases 15-24 25-34 35-44 45-54 55-64 65-74 75-84 85+ 16 30 71 102 130 133 40 Size 172.675 146,207 121,374 111,353 83,004 9 29,007 7,538