A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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The given text provides an exercise involving regression analysis using baseball pitching data. The data includes the number of wins (x) and the earned run averages (ERA, y) for eight pitchers in a season. The task is to find the equation of the regression line, create a scatter plot, and use the regression equation to make predictions for different values of x.

### Predict the ERA (Earned Run Average)

Given the values:
- (a) x = 5 wins
- (b) x = 10 wins
- (c) x = 19 wins

#### Instructions:
1. **Predict the ERA for 5 wins**:
   - Choose the best option:
     - A. \( \hat{y} = \) [Round to two decimal places.]
     - B. Not meaningful: x = 5 is not in the data.
     - C. Not meaningful: x = 5 is outside the data range.

2. **Predict the ERA for 10 wins**:
   - Choose the best option:
     - A. \( \hat{y} = \) [Round to two decimal places.]
     - B. Not meaningful: x = 10 is not in the data.
     - C. Not meaningful: x = 10 is within the data range.

3. **Predict the ERA for 19 wins**:
   - Choose the best option:
     - A. \( \hat{y} = \) [Round to two decimal places.]
     - B. Not meaningful: x = 19 is not in the data.

#### Data Table:
The right side shows a data table with:
- Wins, x
- Earned Run Average (ERA), y

| Wins (x) | ERA (y) |
|----------|---------|
| 20       | 2.82    |
| 18       | 3.34    |
| 17       | 2.59    |
| 16       | 3.72    |
| 14       | 3.85    |
| 12       | 4.31    |
| 11       | 3.81    |
| 9        | 5.05    |

This regression analysis exercise helps understand how to predict outcomes using statistical methods based on given data, by identifying relationships between variables.
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Transcribed Image Text:The given text provides an exercise involving regression analysis using baseball pitching data. The data includes the number of wins (x) and the earned run averages (ERA, y) for eight pitchers in a season. The task is to find the equation of the regression line, create a scatter plot, and use the regression equation to make predictions for different values of x. ### Predict the ERA (Earned Run Average) Given the values: - (a) x = 5 wins - (b) x = 10 wins - (c) x = 19 wins #### Instructions: 1. **Predict the ERA for 5 wins**: - Choose the best option: - A. \( \hat{y} = \) [Round to two decimal places.] - B. Not meaningful: x = 5 is not in the data. - C. Not meaningful: x = 5 is outside the data range. 2. **Predict the ERA for 10 wins**: - Choose the best option: - A. \( \hat{y} = \) [Round to two decimal places.] - B. Not meaningful: x = 10 is not in the data. - C. Not meaningful: x = 10 is within the data range. 3. **Predict the ERA for 19 wins**: - Choose the best option: - A. \( \hat{y} = \) [Round to two decimal places.] - B. Not meaningful: x = 19 is not in the data. #### Data Table: The right side shows a data table with: - Wins, x - Earned Run Average (ERA), y | Wins (x) | ERA (y) | |----------|---------| | 20 | 2.82 | | 18 | 3.34 | | 17 | 2.59 | | 16 | 3.72 | | 14 | 3.85 | | 12 | 4.31 | | 11 | 3.81 | | 9 | 5.05 | This regression analysis exercise helps understand how to predict outcomes using statistical methods based on given data, by identifying relationships between variables.
The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in the recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not.

- (a) x = 5 wins
- (b) x = 10 wins
- (c) x = 19 wins
- (d) x = 15 wins

*Click the icon to view the table of numbers of wins and earned run average.*

(a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. \( \hat{y} = \) __________ (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x = 5 is not an x-value in the original data.

C. It is not meaningful to predict this value of y because x = 5 is well outside the range of the original data.

(b) Predict the ERA for 10 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. \( \hat{y} = \) __________ (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x = 10 is not an x-value in the original data.

C. It is not meaningful to predict this value of y because x = 10 is inside the range of the original data.

(c) Predict the ERA for 19 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. \( \hat{y} = \) __________ (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x = 19 is not an x-value in the original data.

**Wins and ERA Table**:

- Wins, x | Earned run average, y
  - 20 | 2.82
  - 18 | 3.34
  - 17 | 2.59
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Transcribed Image Text:The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in the recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. - (a) x = 5 wins - (b) x = 10 wins - (c) x = 19 wins - (d) x = 15 wins *Click the icon to view the table of numbers of wins and earned run average.* (a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. \( \hat{y} = \) __________ (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x = 5 is not an x-value in the original data. C. It is not meaningful to predict this value of y because x = 5 is well outside the range of the original data. (b) Predict the ERA for 10 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. \( \hat{y} = \) __________ (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x = 10 is not an x-value in the original data. C. It is not meaningful to predict this value of y because x = 10 is inside the range of the original data. (c) Predict the ERA for 19 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. \( \hat{y} = \) __________ (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because x = 19 is not an x-value in the original data. **Wins and ERA Table**: - Wins, x | Earned run average, y - 20 | 2.82 - 18 | 3.34 - 17 | 2.59
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