QUESTION 3: Life Insurance and Longevity [3+1+3+2+3+2+4+2+1+1=22 marks] 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 suspects that the longevity (age at death) of a male customer is linearly related to the age at death of his father. To verify this, he gathered data from 100 recently deceased male customers. He recorded the age at death of the customer and the age at death of his father. These data are recorded in columns 1 to 2, respectively, in file LONGEVITY.xlsx. a. Estimate a linear relationship between the longevity of a male customer and age at death of his father and interpret your results. b. Provide three measures to verify the fitness of the model. Do you think that this model is good enough to be used to estimate and predict the longevity of a male customer? Briefly explain the reasons for your answer. c. Using the estimated regression model, 1 predict the longevity of a male customer whose father lived to the age of 70. il estimate with 95% confidence the mean longevity of a male customer whose father lived to the age of 70. i1 predict with 95% confidence the longevity of a male customer whose father lived to the age of 70. Looking at the estimation results using the simple linear regression model above, the actuary wants to further investigate whether in addition to the father's age at death, other factors such as the age at death his mother and his grandparents also have some effect on his longevity. For the same 100 recently deceased male customers, he recorded the age at death of the customer plus the ages at death of his father and mother, the mean ages at death of his grandfathers and the mean ages at death of his grandmothers. These data are recorded in columns 1 to 5, respectively, in file LONGEVITY .xlsx. d. . Develop a multiple regression model and discuss the possible signs of the coefficients. Estimate the model using the recorded data. Write the estimated regression model with standard errors and p-values in the standard format. . Interpret the coefficient estimates of the independent variables. . Test to determine whether each of the independent variables is linearly related to longevity of the male customer. (o = 0.05) . Test the overall utility of the model. Is the model likely to be useful in predicting men's longevity? (a.=0.05) Discuss the required conditions for the estimation of the multiple regression model. Predict the longevity of a man whose parents lived to the age of 70, whose grandfathers averaged 75 years and whose grandmothers averaged 80