Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA.

**x**

10

3

0

2

5

4

7

**y**

1.5

2.4

3.2

3.5

2.7

3

2.1

1. Is there a linear correlation between mean hours each week a student plays video games and GPA?
? Yes No Correct

2. If there is a linear correation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.
r=

3. If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places.
y^=

4. 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.

1. Yes, there is a linear correlation between the amount of time students play video games and their GPA, as indicated by a significant correlation coefficient.

2. The correlation coefficient is \( r = -0.8856 \).

3. The regression equation is \( \hat{y} = -0.1839x + 3.4430 \), where \( \hat{y} \) represents the predicted GPA and \( x \) represents the hours of video games played.

4. A student who plays video games for 15 hours each week is predicted to have a GPA of approximately 0.68.

Would you like more details or have any questions?

Here are 5 related questions:
1. How is the strength of correlation determined?
2. What does a negative correlation imply in this context?
3. Can correlation imply causation between video games and GPA?
4. What are potential factors that could affect GPA besides video game time?
5. How would the regression change if outliers were present?

**Tip:** Always check the p-value to confirm the statistical significance of a correlation before interpreting its strength.

Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA. Is there a linear correlation between mean hours each week a student plays video games and GPA? If so, what is the correlation coefficient and the regression equation? Additionally, predict a student's GPA when they play video games for 15 hours per week.

Discover how to calculate the correlation coefficient and regression equation to explore the relationship between time spent playing video games and GPA. Learn how to predict a student's GPA based on the number of hours spent on video games. This problem involves statistical analysis, including correlation and regression, suitable for Grades 10-12.

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