A regression was run to determine if there is a relationship between hours of study per week (x) and the final exam scores (y). The results of the regression were: y=ax+b 50
A regression was run to determine if there is a relationship between hours of study per week (x) and the final exam scores (y). The results of the regression were: y=ax+b 50
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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![### Regression Analysis: Hours of Study and Final Exam Scores
A regression analysis was performed to investigate the relationship between the hours of study per week (\(x\)) and the final exam scores (\(y\)).
#### Regression Equation:
\[ y = ax + b \]
#### Results of the Regression:
- **Slope (\(a\))**: 6.59
- **Intercept (\(b\))**: 21.22
- **Coefficient of Determination (\(r^2\))**: 0.599076
- **Correlation Coefficient (\(r\))**: 0.774
### Interpretation:
- **Slope (\(a = 6.59\))**: For each additional hour of study per week, the final exam score is expected to increase by 6.59 points.
- **Intercept (\(b = 21.22\))**: If a student does not study at all, they are expected to score 21.22 points on the final exam.
- **Coefficient of Determination (\(r^2 = 0.599076\))**: Approximately 59.91% of the variability in the final exam scores can be explained by the number of hours studied per week.
- **Correlation Coefficient (\(r = 0.774\))**: There is a strong positive correlation between the number of hours studied and the final exam scores.
### Prediction:
Using the regression equation \( y = 6.59x + 21.22 \), predict the final exam score of a student who studies 7 hours per week.
#### Calculation:
\[ y = 6.59(7) + 21.22 \]
\[ y = 46.13 + 21.22 \]
\[ y = 67.35 \]
### Rounded Prediction:
Predicted final exam score: **67**
---
Use this information to better understand how your study habits may influence your final exam performance!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39923f06-0b75-41bb-9ab0-f1cf94aab574%2Fca1d7bd5-a8d7-4537-8147-45046245073a%2F0oml0xg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Regression Analysis: Hours of Study and Final Exam Scores
A regression analysis was performed to investigate the relationship between the hours of study per week (\(x\)) and the final exam scores (\(y\)).
#### Regression Equation:
\[ y = ax + b \]
#### Results of the Regression:
- **Slope (\(a\))**: 6.59
- **Intercept (\(b\))**: 21.22
- **Coefficient of Determination (\(r^2\))**: 0.599076
- **Correlation Coefficient (\(r\))**: 0.774
### Interpretation:
- **Slope (\(a = 6.59\))**: For each additional hour of study per week, the final exam score is expected to increase by 6.59 points.
- **Intercept (\(b = 21.22\))**: If a student does not study at all, they are expected to score 21.22 points on the final exam.
- **Coefficient of Determination (\(r^2 = 0.599076\))**: Approximately 59.91% of the variability in the final exam scores can be explained by the number of hours studied per week.
- **Correlation Coefficient (\(r = 0.774\))**: There is a strong positive correlation between the number of hours studied and the final exam scores.
### Prediction:
Using the regression equation \( y = 6.59x + 21.22 \), predict the final exam score of a student who studies 7 hours per week.
#### Calculation:
\[ y = 6.59(7) + 21.22 \]
\[ y = 46.13 + 21.22 \]
\[ y = 67.35 \]
### Rounded Prediction:
Predicted final exam score: **67**
---
Use this information to better understand how your study habits may influence your final exam performance!
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