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 11.5 118 Company B 10.0 137 Company C 9.0 102 Company D 5.5 39 Company E 4.2 40 Company F 3.3 32 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 160 T 160- 140 140 120 120- 100 100- te ($ millions) ne ($ millions)

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**Car Rental Market Analysis for Six Smaller Car Rental Companies**

In the highly competitive U.S. car rental market, companies greatly vary in terms of fleet size, facility locations, and annual revenue. Hertz, the market leader as of 2011, operates a fleet of 320,000 cars and achieves annual revenue of approximately $4.2 billion. Below is an analysis of six smaller car rental companies, highlighting the relationship between the number of cars in service (in thousands) and their respective annual revenues (in millions of dollars).

| Company | Cars in Service (1,000s) | Revenue ($ millions) |
|---------|--------------------------|----------------------|
| Company A | 11.5 | 118 |
| Company B | 10.0 | 137 |
| Company C | 9.0 | 102 |
| Company D | 5.5 | 39 |
| Company E | 4.2 | 40 |
| Company F | 3.3 | 32 |

### (a) Scatter Diagram Analysis

The scatter diagram below uses the number of cars in service as the independent variable (X-axis) and the annual revenue as the dependent variable (Y-axis). This visual representation helps identify any potential correlation between the two variables.

- **Graph Analysis**:
  - Horizontal Axis (X): Cars in Service (1,000s)
  - Vertical Axis (Y): Annual Revenue ($ millions)

Below are different scatter diagrams that were assessed to determine the most accurate representation:

1. Incorrect scatter diagram
2. Incorrect scatter diagram
3. Correct scatter diagram: A positive linear relationship is observed.
4. Incorrect scatter diagram

![Scatter Diagram](scatter-diagram.png)

### (b) Interpretation of Scatter Diagram

The correct scatter diagram indicates that **there appears to be a positive linear relationship between cars in service (1,000s) and annual revenue ($ millions)**. As the number of cars in service increases, the annual revenue tends to increase as well.

### (c) Estimated Regression Equation

Using the least squares method, the following estimated regression equation is derived to predict annual revenue ($ millions) based on the number of cars in service (1,000s):

\[ \hat{y} = -16.71 + 13.0x \]

This regression equation can be used to estimate how changes in the number of cars in service will affect the annual revenue.

### Conclusion

By analyzing these variables, smaller car
Transcribed Image Text:**Car Rental Market Analysis for Six Smaller Car Rental Companies** In the highly competitive U.S. car rental market, companies greatly vary in terms of fleet size, facility locations, and annual revenue. Hertz, the market leader as of 2011, operates a fleet of 320,000 cars and achieves annual revenue of approximately $4.2 billion. Below is an analysis of six smaller car rental companies, highlighting the relationship between the number of cars in service (in thousands) and their respective annual revenues (in millions of dollars). | Company | Cars in Service (1,000s) | Revenue ($ millions) | |---------|--------------------------|----------------------| | Company A | 11.5 | 118 | | Company B | 10.0 | 137 | | Company C | 9.0 | 102 | | Company D | 5.5 | 39 | | Company E | 4.2 | 40 | | Company F | 3.3 | 32 | ### (a) Scatter Diagram Analysis The scatter diagram below uses the number of cars in service as the independent variable (X-axis) and the annual revenue as the dependent variable (Y-axis). This visual representation helps identify any potential correlation between the two variables. - **Graph Analysis**: - Horizontal Axis (X): Cars in Service (1,000s) - Vertical Axis (Y): Annual Revenue ($ millions) Below are different scatter diagrams that were assessed to determine the most accurate representation: 1. Incorrect scatter diagram 2. Incorrect scatter diagram 3. Correct scatter diagram: A positive linear relationship is observed. 4. Incorrect scatter diagram ![Scatter Diagram](scatter-diagram.png) ### (b) Interpretation of Scatter Diagram The correct scatter diagram indicates that **there appears to be a positive linear relationship between cars in service (1,000s) and annual revenue ($ millions)**. As the number of cars in service increases, the annual revenue tends to increase as well. ### (c) Estimated Regression Equation Using the least squares method, the following estimated regression equation is derived to predict annual revenue ($ millions) based on the number of cars in service (1,000s): \[ \hat{y} = -16.71 + 13.0x \] This regression equation can be used to estimate how changes in the number of cars in service will affect the annual revenue. ### Conclusion By analyzing these variables, smaller car
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