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 a 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. The equation of the regression line is ŷ = x + Wins and ERA (Round to two decimal places as needed.) Wins, x 20 A 9 Print Earned run average, y 2.76 3.35 2.72 3.77 3.89 4.32 3.74 5.04 Done
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 a 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. The equation of the regression line is ŷ = x + Wins and ERA (Round to two decimal places as needed.) Wins, x 20 A 9 Print Earned run average, y 2.76 3.35 2.72 3.77 3.89 4.32 3.74 5.04 Done
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Analysis of Wins and Earned Run Average (ERA) for Baseball Pitchers
**Objective:**
The objective of this analysis is to explore the relationship between the number of wins and the earned run averages (ERA) of eight baseball pitchers during a recent season. We will construct a scatter plot of the data, draw a regression line, and utilize the regression equation to predict ERA values based on the number of wins.
**Data Table:**
The data presented below includes the number of wins (x) and the corresponding earned run averages (y) for the pitchers:
| Wins (x) | Earned Run Average (y) |
|----------|------------------------|
| 20 | 2.76 |
| 18 | 3.35 |
| 17 | 2.72 |
| 16 | 3.77 |
| 14 | 3.89 |
| 12 | 4.32 |
| 11 | 3.74 |
| 9 | 5.04 |
**Steps for Analysis:**
1. **Scatter Plot Construction:**
- Plot the given data points on a graph with the number of wins on the x-axis and the earned run average on the y-axis.
2. **Regression Line:**
- Draw the best-fit line through the scatter plot to visually represent the trend in the data.
3. **Regression Equation:**
- The regression line can be expressed with the equation \( \hat{y} = bx + a \), where \( \hat{y} \) is the predicted ERA, \( b \) is the slope of the line, and \( a \) is the y-intercept.
**Equation of the Regression Line:**
The equation of the regression line, rounding to two decimal places, is:
\[ \hat{y} = \boxed{} x + \boxed{} \]
*Note: The values for the slope (\( b \)) and the intercept (\( a \)) would typically be calculated based on the data but are not provided in the image.*
**Predictive Analysis:**
Using the regression equation, we can predict the ERA values for specific win values given, such as:
- \( x = 5 \) wins
- \( x = 10 \) wins
- \( x = 19 \) wins
- \( x = 15 \) wins](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F343165f5-98dc-4c63-ba2c-6098e743b2cd%2F26c31df1-9365-4e5e-8eb7-f7da02edc510%2F9s3g2vy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Wins and Earned Run Average (ERA) for Baseball Pitchers
**Objective:**
The objective of this analysis is to explore the relationship between the number of wins and the earned run averages (ERA) of eight baseball pitchers during a recent season. We will construct a scatter plot of the data, draw a regression line, and utilize the regression equation to predict ERA values based on the number of wins.
**Data Table:**
The data presented below includes the number of wins (x) and the corresponding earned run averages (y) for the pitchers:
| Wins (x) | Earned Run Average (y) |
|----------|------------------------|
| 20 | 2.76 |
| 18 | 3.35 |
| 17 | 2.72 |
| 16 | 3.77 |
| 14 | 3.89 |
| 12 | 4.32 |
| 11 | 3.74 |
| 9 | 5.04 |
**Steps for Analysis:**
1. **Scatter Plot Construction:**
- Plot the given data points on a graph with the number of wins on the x-axis and the earned run average on the y-axis.
2. **Regression Line:**
- Draw the best-fit line through the scatter plot to visually represent the trend in the data.
3. **Regression Equation:**
- The regression line can be expressed with the equation \( \hat{y} = bx + a \), where \( \hat{y} \) is the predicted ERA, \( b \) is the slope of the line, and \( a \) is the y-intercept.
**Equation of the Regression Line:**
The equation of the regression line, rounding to two decimal places, is:
\[ \hat{y} = \boxed{} x + \boxed{} \]
*Note: The values for the slope (\( b \)) and the intercept (\( a \)) would typically be calculated based on the data but are not provided in the image.*
**Predictive Analysis:**
Using the regression equation, we can predict the ERA values for specific win values given, such as:
- \( x = 5 \) wins
- \( x = 10 \) wins
- \( x = 19 \) wins
- \( x = 15 \) wins
![### Baseball Pitchers' Performance Analysis
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 a recent season. Follow the steps below to analyze the data:
1. **Construct a Scatter Plot**:
- Plot the given data points representing the number of wins and the earned run averages.
2. **Draw the Regression Line**:
- Use the plotted points to draw the best-fit line for the data, which will represent our regression line.
3. **Regression Equation**:
- Find the equation of the regression line, which will be in the form:
\[\hat{y} = mx + b\]
Here, \( \hat{y} \) is the predicted value of y (earned run average), \( m \) is the slope, \( x \) is the number of wins, and \( b \) is the y-intercept.
4. **Prediction Using Regression Equation**:
- Use the regression equation to predict the value of y (earned run average) for each of the given x-values. Evaluate the meaningfulness of the predictions. If the x-value is not meaningful, explain why not.
- Given x-values for prediction:
- (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 averages for the eight pitchers.
#### Regression Line Equation
The equation of the regression line is:
\[ \hat{y} = \_\_\_x + \_\_\_ \]
Ensure to round to two decimal places as needed.
This exercise helps in understanding and applying linear regression to real-world data, particularly in sports analytics for baseball pitchers. The regression line can aid in predicting performance metrics and making informed decisions based on statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F343165f5-98dc-4c63-ba2c-6098e743b2cd%2F26c31df1-9365-4e5e-8eb7-f7da02edc510%2Ft81if7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Baseball Pitchers' Performance Analysis
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 a recent season. Follow the steps below to analyze the data:
1. **Construct a Scatter Plot**:
- Plot the given data points representing the number of wins and the earned run averages.
2. **Draw the Regression Line**:
- Use the plotted points to draw the best-fit line for the data, which will represent our regression line.
3. **Regression Equation**:
- Find the equation of the regression line, which will be in the form:
\[\hat{y} = mx + b\]
Here, \( \hat{y} \) is the predicted value of y (earned run average), \( m \) is the slope, \( x \) is the number of wins, and \( b \) is the y-intercept.
4. **Prediction Using Regression Equation**:
- Use the regression equation to predict the value of y (earned run average) for each of the given x-values. Evaluate the meaningfulness of the predictions. If the x-value is not meaningful, explain why not.
- Given x-values for prediction:
- (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 averages for the eight pitchers.
#### Regression Line Equation
The equation of the regression line is:
\[ \hat{y} = \_\_\_x + \_\_\_ \]
Ensure to round to two decimal places as needed.
This exercise helps in understanding and applying linear regression to real-world data, particularly in sports analytics for baseball pitchers. The regression line can aid in predicting performance metrics and making informed decisions based on statistical analysis.
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