In Question 15, you found that the estimated Poisson regression model was log(/t = €“8.67 + 0.049 (age), which can be re-expressed in terms of the estimated cancer rate:
/t = e€“8067 + 0.049(age)(8.14)
Then for the BGA location, we can estimate the cancer rate, (/t), for a given value of median age.
a. Estimate the mean number of cancer cases in BGA when the median age is 62. Use this model to estimate the cancer rate in BGA when the median age is 62. Find the estimated cancer incidence rate (recall that the cancer incidence rate is equal to the rate × 100,000). For median age equal to 62 years, t = 1682 for the BGA data.
b. Calculate the difference between the observed cancer incidence rate from Table 8.1 and your estimated cancer incidence rate. How do they compare?
Table 8.1 Cancer cases and cancer incidence rates (CIR) by age group for the Bartlett€“Green Acres neighborhood of Randolph (BGA), 1964€“1984, and similar data from the Connecticut Tumor Registry (CTR), 1980€“1984.

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Location BGA BGA BGA BGA BGA Overall Cases Person-Years CIR Age Group Median Age 14,489 5,431 1,682 3,398 27.6 17-43 460.31 44-59 60-64 353.265-79 30.0 51.5 62.0 72.0 475.7 49 752 2,422 1,612 5,465 25,000 19.6 17-43 467.91 44-59 156,670 1028.9 60-64 285,798 1912.2 65-79 839,007.5 89.6 517,613 30.0 51.5 62.0 72.0 CTR Over 10,251,799,088.5 569.8