Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Cars Revenue Company (1,000s) ($ millions) Company A 11.5 120 Company B 10.0 135 Company C 9.0 100 Company D 5.5 39 Company E 4.2 40 Company F 3.3 34 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 160 160T 140- 160 140 140 120- 120- 120 100 100- 100- 80 80 80 60 60 60 40 .. 40 . .. 40 ... 20 20 20 2 4 6 4 6 8 10 8 10 12 14 2 4 6 8 10 12 14 12 14 Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) 160- 140- 120 100- 80 60 ... 40 20 ual Revenue ($ millions) Annual Revenue ($ millions) Annual Revenue ($ millions) Annual Revenue ($ millions)
Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Cars Revenue Company (1,000s) ($ millions) Company A 11.5 120 Company B 10.0 135 Company C 9.0 100 Company D 5.5 39 Company E 4.2 40 Company F 3.3 34 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 160 160T 140- 160 140 140 120- 120- 120 100 100- 100- 80 80 80 60 60 60 40 .. 40 . .. 40 ... 20 20 20 2 4 6 4 6 8 10 8 10 12 14 2 4 6 8 10 12 14 12 14 Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) 160- 140- 120 100- 80 60 ... 40 20 ual Revenue ($ millions) Annual Revenue ($ millions) Annual Revenue ($ millions) Annual Revenue ($ millions)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Transcribed Image Text:Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of
approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies.
Cars
Revenue
Company
(1,000s)
($ millions)
Company A
11.5
120
Company B
10.0
135
Company C
9.0
100
Company D
5.5
39
Company E
4.2
40
Company F
3.3
34
(a) Develop a scatter diagram with the number of cars in service as the independent variable.
160 T
160-
160
140
140
140
120
120
120
100
100
100
80
80
80
60
60
60
40
40
40
20
20
20
0 2
4
6 8
10
12
14
0 2
4
6 8
10
12
14
0 2 4
6 8
10
12
14
Cars in Service (1,000s)
Cars in Service (1,000s)
Cars in Service (1,000s)
160
140
120
100
80
60
40
20
nnual Revenue ($ millions)
Annual Revenue ($ millions)
Transcribed Image Text:(b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
There appears to be a negative linear relationship between cars in service (1,000s) and annual revenue ($ millions).
There appears to be a positive linear relationship between cars in service (1,000s) and annual revenue ($ millions).
There appears to be no noticeable relationship between cars in service (1,000s) and annual revenue ($ millions).
(c) Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your
numerical values to three decimal places.)
(d) For every additional car placed in service, estimate how much annual revenue will change (in dollars). (Round your answer to the nearest integer.)
Annual revenue will increase by $
for every additional car placed in service.
(e) A particular rental company has 5,000 cars in service. Use the estimated regression equation developed in part (c) to predict annual revenue (in $ millions) for this company. (Round your answer
to the nearest integer.)
million
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