Question 1.

Annual bonuses ($1,000) of six randomly selected employees and their years of service were recorded and listed below

a. Perform a linear regression analysis to determine the equation, model validity, relation coefficient of the independent variable, t-value, and p-value of the independent variable and interpret the results.

b. Perform a correlation analysis to determine the correlation coefficient, and coefficient of determination and interpret the results.

Year (x)	1	2	3	4	5	6
Bonus (y)	6	1	9	5	17	12

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.

Question 3.

A manufacturer of outdoor copper mailboxes and lamps has received numerous complaints about premature corrosion. The manufacturer has identified the cause of the problem as the low-quality varnish used to coat the copper. You decide to replace your current varnish supplier with one of five possible alternatives. To determine which is best, use each of the five varnishes to coat 25 copper mailboxes and place the 125 mailboxes outside. Records, for each, the number of days until the first sign of corrosion is observed (Xr15-12)

a. State the null and alternate hypothesis for this scenario.

b. Is there enough evidence at the 5% significance level to allow the manufacturer to conclude that there are differences between the five varnishes?

b. What are the conditions required for the test performed in part b? Explain

c. Does it appear that the required conditions of the test in part b are met? Explain

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

Data for Q3

Varnish 1	Varnish 2	Varnish 3	Varnish 4	Varnish 5
133	173	161	160	154
171	182	115	221	180
142	214	137	208	222
154	165	173	249	147
242	168	176	148	159
147	232	138	99	175
171	217	106	182	193
155	220	238	169	209
165	184	129	162	192
156	145	163	158	173
219	126	156	240	188
159	209	140	168	147
179	152	109	121	240
189	139	128	146	183
110	237	121	191	236
198	107	149	222	186
119	266	165	176	168
177	234	121	153	169
185	158	162	238	177
206	154	166	195	128
145	199	190	196	152
81	195	214	240	213
171	133	197	152	135
175	247	130	233	165
165	185	185	138	181