Goals 36 58 66 71 # ? # 87 Save Percentage 9.61 9.42 9.35 9.11 8.98 C $ % 5 DE > 6
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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Question
Transcribed Image Text:### Goals and Save Percentages
The table below illustrates the relationship between the number of goals and their corresponding save percentages. This data can help in analyzing trends or evaluating performance based on these metrics.
| Goals | Save Percentage |
|-------|------------------|
| 36 | 9.61 |
| 58 | 9.42 |
| 66 | 9.35 |
| 71 | 9.11 |
| 87 | 8.98 |
#### Explanation:
- **Goals**: Represents the number of goals achieved or attempted.
- **Save Percentage**: Indicates the percentage of successful saves relative to the number of goals.
From the table, it's evident that as the number of goals increases, the save percentage tends to decrease. This inverse relationship can be useful in understanding the efficiency or effectiveness of strategies employed in achieving goals.
For further detailed analysis and graphs illustrating this relationship, students can refer to the advanced analytics section.
*Note: This table is an example and may not represent actual data used in specific sports or activities.*
![### Educational Website Content
---
**Title: Understanding Linear Regression: Solving for Slope, y-Intercept, Equation of the Trend Line, Correlation Coefficient, and Coefficient of Determination**
**Problem Statement:**
Solve for the slope, y-intercept, equation of the trend line, the correlation coefficient, and the coefficient of determination for the following dataset. Show your work and explain the steps you used to solve. Round your answer to the nearest hundredth.
**Dataset:**
| Goals | Save Percentage |
|-------|------------------|
| 36 | 9.61 |
| 58 | 9.42 |
| 66 | 9.35 |
**Explanation: Deconstructing Linear Regression Analysis**
1. **Identify Variables:**
- Independent Variable (X): Goals
- Dependent Variable (Y): Save Percentage
2. **Calculate the Slope (m):**
The slope of a line in linear regression is calculated using the formula:
\[
m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2}
\]
Where:
- \( n \) is the number of data points,
- \( x \) are the values of the independent variable (Goals),
- \( y \) are the values of the dependent variable (Save Percentage).
3. **Calculate the y-Intercept (b):**
The y-intercept is calculated using the formula:
\[
b = \frac{\sum{y} \cdot \sum{x^2} - \sum{x} \cdot \sum{xy}}{n \cdot \sum{x^2} - (\sum{x})^2}
\]
4. **Equation of the Trend Line:**
The linear equation is given by:
\[
y = mx + b
\]
5. **Correlation Coefficient (r):**
The correlation coefficient is given by:
\[
r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n(\sum{x^2}) - (\sum{x})^2][n(\sum{y^2}) - (\sum{y})^2]}}
\]
6. **Coefficient](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4056cef-3867-489f-a260-f13d42f9bf0e%2Fcfa7c096-bb8c-4970-9a72-3fc3ed180199%2F50u4xjo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Website Content
---
**Title: Understanding Linear Regression: Solving for Slope, y-Intercept, Equation of the Trend Line, Correlation Coefficient, and Coefficient of Determination**
**Problem Statement:**
Solve for the slope, y-intercept, equation of the trend line, the correlation coefficient, and the coefficient of determination for the following dataset. Show your work and explain the steps you used to solve. Round your answer to the nearest hundredth.
**Dataset:**
| Goals | Save Percentage |
|-------|------------------|
| 36 | 9.61 |
| 58 | 9.42 |
| 66 | 9.35 |
**Explanation: Deconstructing Linear Regression Analysis**
1. **Identify Variables:**
- Independent Variable (X): Goals
- Dependent Variable (Y): Save Percentage
2. **Calculate the Slope (m):**
The slope of a line in linear regression is calculated using the formula:
\[
m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2}
\]
Where:
- \( n \) is the number of data points,
- \( x \) are the values of the independent variable (Goals),
- \( y \) are the values of the dependent variable (Save Percentage).
3. **Calculate the y-Intercept (b):**
The y-intercept is calculated using the formula:
\[
b = \frac{\sum{y} \cdot \sum{x^2} - \sum{x} \cdot \sum{xy}}{n \cdot \sum{x^2} - (\sum{x})^2}
\]
4. **Equation of the Trend Line:**
The linear equation is given by:
\[
y = mx + b
\]
5. **Correlation Coefficient (r):**
The correlation coefficient is given by:
\[
r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n(\sum{x^2}) - (\sum{x})^2][n(\sum{y^2}) - (\sum{y})^2]}}
\]
6. **Coefficient
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