Player Distance yards Accuracy% 316.9 304.6 310.8 312.8 52.1 294.9 64.3 291.8 63.8 295.5 62.2 8 310.7 53.5 Fit the model to the data using simple linear regression and give the least squares prediction equation. 1 2 3 4 5 6 7 48.4 57.9 55.9
Player Distance yards Accuracy% 316.9 304.6 310.8 312.8 52.1 294.9 64.3 291.8 63.8 295.5 62.2 8 310.7 53.5 Fit the model to the data using simple linear regression and give the least squares prediction equation. 1 2 3 4 5 6 7 48.4 57.9 55.9
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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![### Player Distance Yards and Accuracy
Below is a table displaying data on the distance and accuracy rates for eight players:
| Player | Distance (yards) | Accuracy (%) |
|--------|-------------------|--------------|
| 1 | 316.9 | 48.4 |
| 2 | 304.6 | 57.9 |
| 3 | 310.8 | 55.9 |
| 4 | 312.8 | 52.1 |
| 5 | 294.9 | 64.3 |
| 6 | 291.8 | 63.8 |
| 7 | 295.5 | 62.2 |
| 8 | 310.7 | 53.5 |
### Simple Linear Regression Analysis
To evaluate the relationship between distance and accuracy, we can fit a model to this data using simple linear regression. This analysis will help us predict accuracy based on the distance data by determining the least squares prediction equation.
### Detailed Explanation:
1. **Plot the Data**:
- Create a scatter plot with "Distance (yards)" on the x-axis and "Accuracy (%)" on the y-axis. Each player’s data point is plotted on this chart.
2. **Fit the Linear Regression Line**:
- Using statistical software or a graphing calculator, perform a simple linear regression analysis to find the best fit line. This line is calculated by minimizing the sum of the squared differences between the observed values and the values predicted by the line (least squares method).
3. **Prediction Equation**:
- The equation of the regression line will be in the form:
\[ \widehat{y} = b_0 + b_1 x \]
- Here, \(\widehat{y}\) is the predicted accuracy, \(b_0\) is the y-intercept, and \(b_1\) is the slope of the line.
- The coefficients \(b_0\) (intercept) and \(b_1\) (slope) are determined through statistical analysis.
By fitting this model to the data, we can make informed predictions about a player's accuracy based on their distance in yards.
For educational purposes, these steps illustrate how to apply linear regression to a practical example, providing insights into how statistical](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e08cb41-5b2e-4118-8784-a24243109431%2Fc0d18854-f137-4894-9072-fac773d7e391%2Fsxcvux4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Player Distance Yards and Accuracy
Below is a table displaying data on the distance and accuracy rates for eight players:
| Player | Distance (yards) | Accuracy (%) |
|--------|-------------------|--------------|
| 1 | 316.9 | 48.4 |
| 2 | 304.6 | 57.9 |
| 3 | 310.8 | 55.9 |
| 4 | 312.8 | 52.1 |
| 5 | 294.9 | 64.3 |
| 6 | 291.8 | 63.8 |
| 7 | 295.5 | 62.2 |
| 8 | 310.7 | 53.5 |
### Simple Linear Regression Analysis
To evaluate the relationship between distance and accuracy, we can fit a model to this data using simple linear regression. This analysis will help us predict accuracy based on the distance data by determining the least squares prediction equation.
### Detailed Explanation:
1. **Plot the Data**:
- Create a scatter plot with "Distance (yards)" on the x-axis and "Accuracy (%)" on the y-axis. Each player’s data point is plotted on this chart.
2. **Fit the Linear Regression Line**:
- Using statistical software or a graphing calculator, perform a simple linear regression analysis to find the best fit line. This line is calculated by minimizing the sum of the squared differences between the observed values and the values predicted by the line (least squares method).
3. **Prediction Equation**:
- The equation of the regression line will be in the form:
\[ \widehat{y} = b_0 + b_1 x \]
- Here, \(\widehat{y}\) is the predicted accuracy, \(b_0\) is the y-intercept, and \(b_1\) is the slope of the line.
- The coefficients \(b_0\) (intercept) and \(b_1\) (slope) are determined through statistical analysis.
By fitting this model to the data, we can make informed predictions about a player's accuracy based on their distance in yards.
For educational purposes, these steps illustrate how to apply linear regression to a practical example, providing insights into how statistical
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