Reference no: EM133034079
(1) Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales = β0 + β1Population + β2Income + ε, where Sales refers to the sales of StrongBones (in $ millions), Population is the number of women over the age of 60 (in millions), and Income is the average income of women over the age of 60 (in $1,000s). She collects data on 28 cities across the United States and obtains the following regression results:
|
|
Coefficients
|
Standard Error
|
t Stat
|
p-Value
|
|
Intercept
|
10.07
|
3.79
|
2.66
|
0.0208
|
|
Population
|
8.08
|
1.28
|
6.31
|
0.0080
|
|
Income
|
7.21
|
6.51
|
1.11
|
0.3826
|
a. What is the sample regression equation? (Enter your answers in millions rounded to 2 decimal places.)
b-1. Interpret the coefficient of population.
(a)As the number of women over the age of 60 increases by 1 million, sales of StrongBones is predicted to increase by $8.08 million.
(b)As the number of women over the age of 60 increases by 1 million, sales of StrongBones is predicted to increase by $7.21 million.
(c)As the number of women over the age of 60 increases by 1 million, sales of StrongBones is predicted to increase by $8.08 million, holding income constant.
(d)As the number of women over the age of 60 increases by 1 million, sales of StrongBones is predicted to increase by $7.21 million, holding income constant.
b-2. Interpret the coefficient of income.
(a)As the average income of women over the age of 60 increases by $1,000, sales of StrongBones is predicted to increase by $8.08 million.
(b)As the average income of women over the age of 60 increases by $1,000, sales of StrongBones is predicted to increase by $7.21 million.
(c)As the average income of women over the age of 60 increases by $1,000, sales of StrongBones is predicted to increase by $8.08 million, holding population constant.
(d)As the average income of women over the age of 60 increases by $1,000, sales of StrongBones is predicted to increase by $7.21 million, holding population constant.
c. Predict Sales if a city has 1.0 million women over the age of 60 and their average income is $40,000. (Enter your answer in millions rounded to 2 decimal places.)
(2)The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four predictor variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.
|
Time
|
Miles
|
Weight
|
Speed
|
Oil
|
|
7.9
|
42.5
|
20
|
49
|
12
|
|
0.8
|
98.2
|
24
|
41
|
24
|
|
8.5
|
43.1
|
23
|
66
|
13
|
|
1.5
|
110.2
|
29
|
58
|
29
|
|
1.2
|
102.1
|
32
|
51
|
21
|
|
2.2
|
96.7
|
23
|
58
|
15
|
|
2.6
|
92.5
|
19
|
58
|
18
|
|
7.2
|
53.7
|
22
|
63
|
15
|
|
8.1
|
51.3
|
18
|
52
|
17
|
|
4.2
|
84.4
|
29
|
58
|
29
|
|
0.7
|
120.7
|
33
|
57
|
22
|
|
5.0
|
77.9
|
23
|
50
|
32
|
|
4.9
|
69.1
|
25
|
45
|
23
|
|
4.9
|
54.7
|
22
|
58
|
18
|
|
5.7
|
66.5
|
22
|
63
|
31
|
|
8.5
|
39.8
|
21
|
55
|
20
|
|
5.7
|
52.8
|
16
|
60
|
25
|
|
6.3
|
53.8
|
16
|
51
|
19
|
|
4.7
|
74.3
|
25
|
68
|
25
|
|
6.5
|
59
|
21
|
59
|
17
|
|
6.4
|
52.3
|
20
|
55
|
21
|
|
7.0
|
69.1
|
20
|
56
|
24
|
|
4.2
|
94.1
|
20
|
55
|
24
|
|
7.4
|
45.3
|
15
|
53
|
13
|
|
6.0
|
60.9
|
22
|
54
|
20
|
b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
d. What is the predicted time before the first engine overhaul for a particular truck driven 61,000 miles per year with an average load of 21 tons, an average driving speed of 55 mph, and 19,000 miles between oil changes. (Do not round intermediate calculations. Round final answer to 2 decimal places.)