atical program is recommer A study of emergency service facilities investigated the relationship betveen the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number of Facilities Average Distance (miles) 1.67 11 1.11 16 0.84 21 0.63 27 0.52 30 0.48 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. 35 1.8 1.8 1.8 1.6 1.6 1.6 30- 1.4 1.2 1. 1.4 1.4 1.2 25 1.2 1. 1. 20 0.8 0.8 0.8 15 0.6 0.6- 0.6 0.4 0.4 0.4 10 .. 0.2 0.2 0.2 0. 0. 0. 0. 0.2 04 0.6 0.8 1. 1.2 1.4 1.6 1.8 10 15 20 25 30 35 10 15 20 25 30 35 10 15 20 25 30 35 Distance Number Number Number (b) Does a simple linear regression model appear to be appropriate? Explain. O No, the scatter diagram suggests that there is no relationship. O No, the scatter diagram suggests that there is a curvilinear relationship. O Yes, the scatter diagram suggests that there is a linear relationship.

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**A statistical program is recommended.**

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected.

| Number of Facilities | Average Distance (miles) |
|----------------------|--------------------------|
| 9                    | 1.67                     |
| 11                   | 1.11                     |
| 16                   | 0.84                     |
| 21                   | 0.63                     |
| 27                   | 0.52                     |
| 30                   | 0.48                     |

**(a)** Develop a scatter diagram for these data, treating average distance traveled as the dependent variable.

There are three scatter plots provided. Each has a horizontal axis (x-axis) and a vertical axis (y-axis):

1. **Scatter Plot 1:** X-axis represents "Distance," ranging from 0.2 to 1.8 miles. Y-axis represents "Number," ranging from 0 to 35 facilities. The points show a downward trend.
   
2. **Scatter Plot 2:** X-axis represents "Number," ranging from 5 to 35 facilities. Y-axis represents "Distance," ranging from 0.2 to 1.8 miles. The points show a downward trend.
   
3. **Scatter Plot 3:** X-axis represents "Number," ranging from 5 to 35 facilities. Y-axis represents "Distance," ranging from 0.2 to 1.8 miles. The points show an upward trend.

**(b)** Does a simple linear regression model appear to be appropriate? Explain.

- ☐ No, the scatter diagram suggests that there is no relationship.
- ☐ No, the scatter diagram suggests that there is a curvilinear relationship.
- ☑ Yes, the scatter diagram suggests that there is a linear relationship.

**(c)** Develop an estimated regression equation for the data of the form \( y = \beta_0 + \beta_1x + \beta_2x^2 \), a second-order model with one predictor variable. (Round your numerical values to four decimal places.)

\( y = \) ____
Transcribed Image Text:**A statistical program is recommended.** A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. | Number of Facilities | Average Distance (miles) | |----------------------|--------------------------| | 9 | 1.67 | | 11 | 1.11 | | 16 | 0.84 | | 21 | 0.63 | | 27 | 0.52 | | 30 | 0.48 | **(a)** Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. There are three scatter plots provided. Each has a horizontal axis (x-axis) and a vertical axis (y-axis): 1. **Scatter Plot 1:** X-axis represents "Distance," ranging from 0.2 to 1.8 miles. Y-axis represents "Number," ranging from 0 to 35 facilities. The points show a downward trend. 2. **Scatter Plot 2:** X-axis represents "Number," ranging from 5 to 35 facilities. Y-axis represents "Distance," ranging from 0.2 to 1.8 miles. The points show a downward trend. 3. **Scatter Plot 3:** X-axis represents "Number," ranging from 5 to 35 facilities. Y-axis represents "Distance," ranging from 0.2 to 1.8 miles. The points show an upward trend. **(b)** Does a simple linear regression model appear to be appropriate? Explain. - ☐ No, the scatter diagram suggests that there is no relationship. - ☐ No, the scatter diagram suggests that there is a curvilinear relationship. - ☑ Yes, the scatter diagram suggests that there is a linear relationship. **(c)** Develop an estimated regression equation for the data of the form \( y = \beta_0 + \beta_1x + \beta_2x^2 \), a second-order model with one predictor variable. (Round your numerical values to four decimal places.) \( y = \) ____
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