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 $4.2 billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies (Auto Rental News website, August 7, 2012).

Company	Cars (1000s)	Revenue ($millions)
U-Save Auto Rental System, Inc.	11.5	118
Payless Car Rental System, Inc.	10	135
ACE Rent A Car	9	100
Rent-A-Wreck of America	5.5	37
Triangle Rent-A-Car	4.2	40
Affordable/Sensible	3.3	32

1. Develop a scatter diagram with the number of cars in service as the independent variable. See page 208 of the course packet.
2. What does the scatter diagram developed in part a indicate about the relationship between the two variables?
3. Calculate the intercept and the slope for the estimated regression equation. Show your work with a table as on page 175 of the course packet. You may use Excel to construct the table and calculate the values in the table. Don’t use Excel’s statistical functions or Data Analysis.
4. Write the regression model and the estimated regression equation.
5. Explain the meaning of the estimated intercept and slope in part c.
6. Fox Rent-A-Car has 11,000 cars in service. Use the estimated regression equation developed in part d to predict annual revenue for Fox Rent-A-Car.
7. Calculate SST, SSR, and SSE. Show your work with a table as on page 182 of the course packet. You may use Excel to construct the table and calculate the values in the table.
8. Using part g, calculate the coefficient of the determination and explain its meaning.
9. Enter the data in Excel and use Data Analysis to get the regression results. See pages 208 – 209 of the course packet and pages 680 – 681 of the textbook.
10. Use the regression printout from Excel in part i to find the values of b0, b1, SST, SSR, SSE, and R2.
11. Calculate the sample covariance and the sample correlation. Show your work with a table as on page 25 of the course packet. You may add one more column to the table in part c to get this table.
12. Based on the sample correlation in part k, what does it tell you about the relationship between the two variables?
13. Show the relationship between the sample correlation and the coefficient of determination.

Answer 1

A)

Scatter plot between Cars and Revenue is given below.

B)

Here as we can see that if number of cars increase then Revenue also increases. So we can say that there is a strong linear relationship between Number of cars and Revenue.

C)

Here let us denote No of cars by X and Revenue be denoted by Y.

Then slope and intercept are given by:

where

and Intercept is given by:

Slope = 12.97

Intercept = -17.00

D)

Here the fitted regression line is given by:

E)

Here Value of slope is 12.97

Interpretation :

It implies that if we increase Number of cars by 1000 then Revenue will increase by 12.97 million dollars.

Value of intercept is -17.00

Here it means that if no of cars is 0 then revenuue is -17 million dollars. Which does not have any significance since revenue can not be negative.

F)

Here Fox Rent-A-Car has 11,000 cars in service

So value of x = 11000/1000 = 11

Since cars is in 1000s in our model.

So the revenure according the equation in D is given by:

So there will be 125.67 million dollars revenue from 11000 cars.