Answered: Company Cars (1,000s) Revenue ($…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.

Company	Cars (1,000s)	Revenue ($ millions)
Company A	11.5	118
Company B	10.0	133
Company C	9.0	98
Company D	5.5	37
Company E	4.2	40
Company F	3.3	30

(a)

Develop a scatter diagram with the number of cars in service as the independent variable.

A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on the horizontal axis and between 30 to 140 on the vertical axis. Each consecutive point is higher on the diagram than the previous point. The 3 leftmost points and the 3 rightmost points have a large amount of space between them.

A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on the horizontal axis and between 30 to 140 on the vertical axis. The fifth point from the left is noticeably higher on the diagram than both the fourth and sixth points from the left. The 3 leftmost points and the 3 rightmost points have a large amount of space between them.

A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on the horizontal axis and between 40 to 150 on the vertical axis. The fifth point from the left is noticeably higher on the diagram than both the fourth and sixth points from the left. The 3 leftmost points and the 3 rightmost points have a large amount of space between them.

A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram and are between 3 to 12 on the horizontal axis and between 30 to 140 on the vertical axis. The second point from the left is noticeably higher on the diagram than both the first and third points from the left. The 3 leftmost points and the 3 rightmost points have a large amount of space between them.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

There appears to be no noticeable 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 a negative linear 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.)

ŷ = ??

(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 7,000 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?

Expert Solution

Step 1

ANSWER:

(b) According to the scatter diagram developed in part (a), there appears to be a positive linear relationship between the number of cars in service and annual revenue. The points on a scatter diagram generally increase as the number of cars in service increases, indicating that there may be a correlation between the two variables.

(c) To develop an estimated regression equation using the least squares method, we need to calculate the slope and intercept of the regression line. Using formulas:

scss

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Slope = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2)

Intercept = ȳ - Slope * x̄

Where N is the number of data points, x and y are the data points, x̄ and ȳ are the sample means of x and y, we get:

Makefile

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N = 6

Σx = 43.5

Σy = 456

Σxy = 5077

Σx^2 = 329.7