Part 1

Life insurance companies are keenly interested in predicting how long their customers will live, because their premiums and profitability depend on such numbers. Data were gathered for 100 deceased males, in order to formulate a regression that predicted longevity based on:

* Age at death of the two parents

* Mean age at death of grandfather and grandmothers

Questions

a. Perform a multiple regression analysis and show the prediction equation.

b. Is the model useful at 2.5% significance level?

c. Interpret the coefficients b1 and b2 in this model.

Part 2 (see Longevity (2)

A statistician working for the company suggeted smoking is a major determinant of a person's longevity. He added this variable as a predictor to the first group of independent variables, but also took out the insignificant variables from the previous model of Part 1.

Questions

d. Run the reduced model (that now includes only three independant variavles), and show the prediction equation.

e. Interpret the coefficient of the predictor "Smoker" in this model (that is, if say, the value of this coefficient is 4, what does it mean in this model).

f. A smoker, whose both parents passed at the age of 85 is 62 years old. How many more years is he expected to live?

g. His friend is not a smoker who lost his mother when she was 70 years old, and father when he was 60 years old. How long is he expected to live?

h. Can you determine with 90% confidence which of the two friends will die at a younger age?

Longevity 1:

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

Longevity 2:

Gmothers	Gfathers		Smoker
72	71		No
76	66		Yes
67	57		Yes
68	55		Yes
64	73		No
74	62		No
70	59		Yes
74	61		Yes
71	63		Yes
76	61		Yes
61	69		Yes
73	60		No
69	68		No
67	67		Yes
71	67		Yes
63	57		Yes
75	65		No
68	62		Yes
63	62		Yes
66	69		No
61	65		Yes
63	71		Yes
64	61		Yes
77	60		No
59	63		Yes
73	62		No
80	65		No
75	69		Yes
72	66		Yes
65	65		Yes
72	62		No
68	71		Yes
77	68		No
77	61		Yes
71	63		No
75	67		No
68	57		Yes
67	57		Yes
67	64		Yes
68	67		Yes
74	65		Yes
72	65		Yes
72	71		No
69	65		Yes
78	54		Yes
58	70		No
77	65		No
72	60		No
73	62		Yes
69	68		Yes
72	66		Yes
67	66		Yes
71	61		No
68	68		Yes
66	59		No
71	74		No
66	61		Yes
74	61		Yes
73	61		Yes
74	69		No
70	77		No
71	68		Yes
67	72		No
77	71		No
63	64		No
65	69		Yes
74	62		Yes
72	60		Yes
73	69		No
63	60		No
66	66		Yes
64	67		Yes
60	62		Yes
68	56		Yes
72	53		Yes
72	69		No
61	53		Yes
72	63		Yes
67	67		Yes
65	68		Yes
67	67		Yes
71	72		No
76	72		No
76	64		No
65	59		Yes
69	67		Yes
72	65		Yes
75	59		Yes
69	64		No
71	66		Yes
70	69		Yes
66	64		Yes
73	70		No
70	57		Yes
66	64		Yes
66	62		Yes
66	69		No
63	66		Yes
71	64		Yes
74	60		Yes