Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA. X y 10 3 1.5 2.4 0 3.2 2 3.5 5 4 7 2.7 3 2.1 1. Find the the correlation coefficient. Round your final answer to four decimal places. T= 2. Write the regression equation below. Round all numbers to four decimal places. y 3. Using the data shown above, predict a student's GPA when the student plays video games for 15 hours each week. Round your final answer to two decimal places. Submit Question 4. What percentage of variation in GPAS can be explained by the number of hours students' play video games each week? Round your final answer to two decimal places. % Question Help: Video Message instructor
Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA. X y 10 3 1.5 2.4 0 3.2 2 3.5 5 4 7 2.7 3 2.1 1. Find the the correlation coefficient. Round your final answer to four decimal places. T= 2. Write the regression equation below. Round all numbers to four decimal places. y 3. Using the data shown above, predict a student's GPA when the student plays video games for 15 hours each week. Round your final answer to two decimal places. Submit Question 4. What percentage of variation in GPAS can be explained by the number of hours students' play video games each week? Round your final answer to two decimal places. % Question Help: Video Message instructor
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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![### Exploring the Relationship Between Video Game Playtime and GPA
Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA. The following data is given with the number of hours students play video games each week (\( x \)) and their corresponding GPA (\( y \)):
```
x | 10 | 3 | 0 | 2 | 5 | 4 | 7 |
y | 1.5 | 2.4 | 3.2 | 3.5 | 2.7 | 3.3 | 2.1 |
```
**Tasks:**
1. **Find the correlation coefficient. Round your final answer to four decimal places.**
\( r = \_\_\_\_\_\_ \)
2. **Write the regression equation below. Round all numbers to four decimal places.**
\( \hat{y} = \_\_\_\_\_\_ \)
3. **Using the data shown above, predict a student's GPA when the student plays video games for 15 hours each week. Round your final answer to two decimal places.**
\( \hat{y} = \_\_\_\_\_\_ \)
4. **What percentage of variation in GPAs can be explained by the number of hours students play video games each week? Round your final answer to two decimal places.**
\( \_\_\_\_\_\_ \% \)
**Help Resources:**
- **Video**: [Watch explanatory video here]
- **Message Instructor**: [Contact your instructor for help]
**Submit Your Answers:**
[Submit Question Button]
**Explanation of Data:**
The data table contains columns and rows:
- The first row ( \( x \) ) is the number of hours students play video games in a week.
- The second row ( \( y \) ) is the corresponding GPA of those students.
This set of data is used to:
1. Identify if there is a linear relationship between video game playtime and GPA.
2. Develop a regression equation for predicting GPA based on the number of hours spent playing video games.
3. Calculate the correlation coefficient to measure the strength and direction of a linear relationship.
4. Determine the percentage of variation in GPA that can be explained by video game playtime using the coefficient of determination.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F402afc63-9cac-4d1f-a06a-b4853df74aca%2F7bc67b8e-8cf1-486f-9137-59278748bc67%2F16irusa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exploring the Relationship Between Video Game Playtime and GPA
Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA. The following data is given with the number of hours students play video games each week (\( x \)) and their corresponding GPA (\( y \)):
```
x | 10 | 3 | 0 | 2 | 5 | 4 | 7 |
y | 1.5 | 2.4 | 3.2 | 3.5 | 2.7 | 3.3 | 2.1 |
```
**Tasks:**
1. **Find the correlation coefficient. Round your final answer to four decimal places.**
\( r = \_\_\_\_\_\_ \)
2. **Write the regression equation below. Round all numbers to four decimal places.**
\( \hat{y} = \_\_\_\_\_\_ \)
3. **Using the data shown above, predict a student's GPA when the student plays video games for 15 hours each week. Round your final answer to two decimal places.**
\( \hat{y} = \_\_\_\_\_\_ \)
4. **What percentage of variation in GPAs can be explained by the number of hours students play video games each week? Round your final answer to two decimal places.**
\( \_\_\_\_\_\_ \% \)
**Help Resources:**
- **Video**: [Watch explanatory video here]
- **Message Instructor**: [Contact your instructor for help]
**Submit Your Answers:**
[Submit Question Button]
**Explanation of Data:**
The data table contains columns and rows:
- The first row ( \( x \) ) is the number of hours students play video games in a week.
- The second row ( \( y \) ) is the corresponding GPA of those students.
This set of data is used to:
1. Identify if there is a linear relationship between video game playtime and GPA.
2. Develop a regression equation for predicting GPA based on the number of hours spent playing video games.
3. Calculate the correlation coefficient to measure the strength and direction of a linear relationship.
4. Determine the percentage of variation in GPA that can be explained by video game playtime using the coefficient of determination.
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