QUESTION A4: Life Insurance and Longevity

Life insurance companies are keenly interested in predicting how long their customers will live, because their premiums and profitability depend on such numbers. An actuary for one insurance company gathered data from 100 recently deceased male customers. He recorded the age at death of the customer plus the ages at death of his mother and father, the mean ages at death of his grandmothers and the mean ages at death of his grandfathers. These data are recorded in columns 1 to 5 respectively, in file LONGEVITY.xlsx.

a Perform a multiple regression analysis on these data.

b Interpret the coefficient estimates and their signs.

c Test for the significance of all the independent variable coefficients. (a = 0.05)

d Is the model likely to be useful in predicting men’s longevity?

e Are the required conditions satisfied? Justify your answer.

f Predict the longevity of a man whose parents lived to the age of 70, whose grandmothers averaged 80 years and whose grandfathers averaged 75.

Suppose that in addition to these data, the actuary also recorded whether the man was a smoker (1 = yes, and 0 = no). These data are recorded in column 6 of the same file.

g. Perform a multiple regression analysis on these data.

h. Compare the estimation results produced in part g with those in part a. Describe the differences.

i. Does smoking affect length of life (a = 0.05)? Explain

LONGEVITY