The following table presents the number of hours a group of school students played video games during the weekends and the test scores attained by each of them in a test, the following Monday. 

(a.) It is believed that a linear relationship exists between the time spent on playing video
games and test score attained. Find out the strength of this linear relationship.
(b.) Estimate the line of best fit in the scenario. Use this line to find the expected test
score for a student who plays video games for 9 hours. 

Part (a): Assessing the Strength of Linear Relationship

To determine the strength of the linear relationship between the time spent playing video games and the test scores, we can calculate the correlation coefficient (also known as Pearson's correlation coefficient). This coefficient ranges from -1 to 1, where:
- 1 indicates a perfect positive linear relationship,
- -1 indicates a perfect negative linear relationship,
- 0 indicates no linear relationship.

The formula for calculating the correlation coefficient is as follows:

\[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \]

Where:
- \( n \) is the number of data points,
- \( \sum xy \) is the sum of the product of each \( x \) (time) and \( y \) (test score) value,
- \( \sum x \) is the sum of the \( x \) values,
- \( \sum y \) is the sum of the \( y \) values,
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