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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

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.

  1. Perform a multiple regression analysis on these data.
  2. Interpret the coefficient estimates and their signs.
  3. Test for the significance of all the independent variable coefficients. (a = 0.05)
  4. Is the model likely to be useful in predicting men's longevity?
  5. Are the required conditions satisfied? Justify your answer.

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

Longevity Mother Father Gmothers Gfathers
80 85 78 72 71
73 88 63 76 66
70 66 75 67 57
72 72 67 68 55
79 88 73 64 73
83 90 72 74 62
70 67 65 70 59
72 76 71 74 61
72 66 75 71 63
71 78 64 76 61
67 69 66 61 69
74 71 76 73 60
80 74 77 69 68
63 68 66 67 67
71 70 70 71 67
66 64 66 63 57
74 82 71 75 65
71 71 71 68 62
65 75 60 63 62
74 76 66 66 69
66 69 68 61 65
71 76 67 63 71
73 69 80 64 61
74 79 70 77 60
68 74 62 59 63
77 81 78 73 62
77 85 69 80 65
74 77 69 75 69
68 72 71 72 66
68 75 63 65 65
74 82 66 72 62
71 73 72 68 71
80 84 73 77 68
72 75 61 77 61
77 82 76 71 63
76 88 69 75 67
62 65 57 68 57
70 75 57 67 57
71 72 67 67 64
69 72 63 68 67
73 79 71 74 65
72 77 69 72 65
84 80 90 72 71
73 76 74 69 65
70 78 70 78 54
78 75 74 58 70
82 83 78 77 65
77 75 66 72 60
67 68 69 73 62
72 69 72 69 68
67 67 67 72 66
72 78 64 67 66
75 73 69 71 61
72 71 66 68 68
75 73 73 66 59
80 84 75 71 74
72 78 64 66 61
71 76 61 74 61
71 77 70 73 61
89 86 77 74 69
74 79 71 70 77
72 72 77 71 68
74 78 68 67 72
77 85 77 77 71
77 72 72 63 64
73 67 71 65 69
72 74 64 74 62
65 66 63 72 60
81 82 77 73 69
76 80 70 63 60
64 71 67 66 66
72 73 69 64 67
69 75 67 60 62
59 59 62 68 56
69 73 69 72 53
76 82 65 72 69
63 71 56 61 53
66 74 64 72 63
72 85 60 67 67
68 72 66 65 68
73 80 75 67 67
78 82 72 71 72
83 82 82 76 72
78 82 70 76 64
67 73 62 65 59
70 77 60 69 67
68 74 79 72 65
66 80 63 75 59
75 76 72 69 64
71 71 60 71 66
72 77 64 70 69
71 76 67 66 64
77 79 74 73 70
67 68 68 70 57
68 71 61 66 64
67 76 62 66 62
74 77 64 66 69
70 66 68 63 66
72 78 70 71 64
69 73 60 74 60

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