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 for 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, of file . .Perform a multiple regression analysis on these data. Is the model likely to be useful in predicting men's longevity? Are the required conditions satisfied? Interpret and test the coefficients. Use " = .05.  Predict with 95% confidence the longevity of a man whose parents lived to the age of 70, whose grandmothers averaged 80 years, and whose grandfathers averaged 75. Estimate with 95% confidence the mean longevity of men whose mothers lived to 75, whose fathers lived to 65, whose grandmothers averaged 85 years, and whose grandfathers averaged 75.

       y = 3.224 + .451(x₁) + .411(x₂) + .01655(x₃) + .08686(x₄)

                    y = 3.224 + .08236(Mother) + .01092(Father) + .09275(GMothers) + .09275(GFathers)

        y = 3.224 + .451(70) + .411(70) + .01655(80) + .08686(75)

        y = 3.224 + 31.51 + 28.77 + 1.324 + 6.5145

        y = 71.3425 years

        y = 3.224 + .451(75) + .411(65) + .01655(85) + .08686(75)

        y = 3.224 + 33.825 + 26.715 + 1.40675 + 6.5145

        y = 71.68525 years