Question 2.

Life insurance companies are very interested in predicting how long their client will live, because their premiums and profitability depend on this variable. An actuary for an individual insurance company gathered data from 100 recently deceased male clients. Recorded the age of death of the client, the ages at the death of his mother and father, the ages at the death of his grandmother and grandfather and the smoking or non-smoking habit of the client (Xr18-10)

a. Perform a regression analysis of this data.

b. Comment on the validity of the regression model

c. Determine which were the independent variables that had a linear relationship with customer longevity at 95% confidence.

d. Interpret each coefficient of the regression.

e. Predict with 95% a level of confidence that the longevity of a man whose parents lived 70 years, his grandmother lived 80 years, his grandfather lived 75 and is not a smoker.

Data for Q2

Longevity	Mother	Father	Grandma	Grandpa	Smoke
80	85	78	72	71	0
73	88	63	76	66	1
70	66	75	67	57	1
72	72	67	68	55	1
79	88	73	64	73	0
83	90	72	74	62	0
70	67	65	70	59	1
72	76	71	74	61	1
72	66	75	71	63	1
71	78	64	76	61	1
67	69	66	61	69	1
74	71	76	73	60	0
80	74	77	69	68	0
63	68	66	67	67	1
71	70	70	71	67	1
66	64	66	63	57	1
74	82	71	75	65	0
71	71	71	68	62	1
65	75	60	63	62	1
74	76	66	66	69	0
66	69	68	61	65	1
71	76	67	63	71	1
73	69	80	64	61	1
74	79	70	77	60	0
68	74	62	59	63	1
77	81	78	73	62	0
77	85	69	80	65	0
74	77	69	75	69	1
68	72	71	72	66	1
68	75	63	65	65	1
74	82	66	72	62	0
71	73	72	68	71	1
80	84	73	77	68	0
72	75	61	77	61	1
77	82	76	71	63	0
76	88	69	75	67	0
62	65	57	68	57	1
70	75	57	67	57	1
71	72	67	67	64	1
69	72	63	68	67	1
73	79	71	74	65	1
72	77	69	72	65	1
84	80	90	72	71	0
73	76	74	69	65	1
70	78	70	78	54	1
78	75	74	58	70	0
82	83	78	77	65	0
77	75	66	72	60	0
67	68	69	73	62	1
72	69	72	69	68	1
67	67	67	72	66	1
72	78	64	67	66	1
75	73	69	71	61	0
72	71	66	68	68	1
75	73	73	66	59	0
80	84	75	71	74	0
72	78	64	66	61	1
71	76	61	74	61	1
71	77	70	73	61	1
89	86	77	74	69	0
74	79	71	70	77	0
72	72	77	71	68	1
74	78	68	67	72	0
77	85	77	77	71	0
77	72	72	63	64	0
73	67	71	65	69	1
72	74	64	74	62	1
65	66	63	72	60	1
81	82	77	73	69	0
76	80	70	63	60	0
64	71	67	66	66	1
72	73	69	64	67	1
69	75	67	60	62	1
59	59	62	68	56	1
69	73	69	72	53	1
76	82	65	72	69	0
63	71	56	61	53	1
66	74	64	72	63	1
72	85	60	67	67	1
68	72	66	65	68	1
73	80	75	67	67	1
78	82	72	71	72	0
83	82	82	76	72	0
78	82	70	76	64	0
67	73	62	65	59	1
70	77	60	69	67	1
68	74	79	72	65	1
66	80	63	75	59	1
75	76	72	69	64	0
71	71	60	71	66	1
72	77	64	70	69	1
71	76	67	66	64	1
77	79	74	73	70	0
67	68	68	70	57	1
68	71	61	66	64	1
67	76	62	66	62	1
74	77	64	66	69	0
70	66	68	63	66	1
72	78	70	71	64	1
69	73	60	74	60	1