Related questions with answers

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 $4.2\$ 4.2 billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies.$

 Company  Cars (1000s) Revenue  ($millions)  U-Save Auto Rental System, Inc. 11.5118 Payless Car Rental System, Inc. 10.0135 ACE Rent A Car 9.0100 Rent-A-Wreck of America 5.537 Triangle Rent-A-Car 4.240 Affordable/Sensible 3.332\begin{array}{lcc}\text { Company } & \begin{array}{c}\text { Cars } \\ (\mathbf{1 0 0 0 s})\end{array} & \begin{array}{c}\text { Revenue } \\ \text{ (\$millions) }\end{array} \\ \text { U-Save Auto Rental System, Inc. } & 11.5 & 118 \\ \text { Payless Car Rental System, Inc. } & 10.0 & 135 \\ \text { ACE Rent A Car } & 9.0 & 100 \\ \text { Rent-A-Wreck of America } & 5.5 & 37 \\ \text { Triangle Rent-A-Car } & 4.2 & 40 \\ \text { Affordable/Sensible } & 3.3 & 32\end{array}

$

e. Fox Rent-A-Car has 11,000 cars in service. Use the estimated regression equation developed in part (c) to predict annual revenue for Fox Rent-A-Car.

Question

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

Distance to WorkNumber of Days (miles)  Absent 1835486786103125142144182\begin{array}{cc}\text{Distance to Work} & \text{Number of Days}\\\text { (miles) } & \text { Absent } \\ 1 & 8 \\ 3 & 5 \\ 4 & 8 \\ 6 & 7 \\ 8 & 6 \\ 10 & 3 \\ 12 & 5 \\ 14 & 2 \\ 14 & 4 \\ 18 & 2\end{array}

a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.

b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.

c. Predict the number of days absent for an employee that lives 5 miles from the hospital.

Solution

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a) For this exercise, we are to develop a scatter diagram for the given table.

Table 1. Given values.\small \text{Table 1. Given values.}

Distance to Work (miles) Number of Days Absent
11 88
33 55
44 88
66 77
88 66
1010 33
1212 55
1414 22
1414 44
1818 22

What are the relationships of the variables to the coordinates of a point?

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