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The table provides the number of hours a group of school students played video games (Time in hours) and their corresponding test scores. The problem consists of two parts:

(a) **Find the strength of the linear relationship** between the time spent on video games and the test score.
(b) **Estimate the line of best fit** to predict the test score for a student who plays video games for 9 hours.

### Table Summary:
- Time (in hours): 0, 1, 2, 3, 4, 5, 6, 7, 10
- Test Score: 96, 85, 82, 74, 95, 68, 58, 75, 50

Let me calculate the solution for both parts: the correlation coefficient (to measure strength) and the equation of the line of best fit. I will then use the line equation to predict the score for 9 hours of gaming.

Let’s begin by calculating these values.Here are the results:

1. **Strength of the Linear Relationship**: The correlation coefficient (\( r \)) is \(-0.813\). Since the value is close to \(-1\), this indicates a strong negative linear relationship between the number of hours spent playing video games and the test score. As the number of hours increases, the test scores tend to decrease.

2. **Line of Best Fit**: The equation of the line is:
   \[
   \text{Test Score} = -4.02 \times (\text{Time in hours}) + 92.86
   \]
   
3. **Predicted Test Score for 9 Hours**: Using the line of best fit, the estimated test score for a student who plays video games for 9 hours is approximately **56.68**.

Would you like further details on how this was calculated or any specific part of the explanation?

### Related Questions:
1. How does the slope impact the interpretation of the relationship?
2. What does the negative correlation tell us about study habits and scores?
3. How would the prediction change if a student played for 8 hours instead of 9?
4. How significant is the linear relationship based on the \( p \)-value?
5. What other methods could be used to analyze this data?

**Tip**: The closer the correlation coefficient is to \(-1\) or \(1\), the stronger the linear relationship is, while \(0\) indicates no linear correlation.

It is believed that a linear relationship exists between the time spent on playing video games and test scores. Find out the strength of this linear relationship and estimate the line of best fit to predict the test score for a student who plays video games for 9 hours.

Calculate the strength of the linear relationship between time spent on video games and test scores. Use the line of best fit equation to predict the test score for a student who plays video games for 9 hours. Learn about correlation coefficient, slope, and regression.

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