Based on the scatter diagrams provided, the correct graph for part (a) can be determined by observing the relationship between the $x$ and $y$ values.

The given data shows a pattern with a negative correlation (as indicated by the negative value for the correlation coefficient, $r = -0.9314$). This suggests that as $x$ increases, $y$ decreases, which aligns with a negative linear relationship.

Looking at the options:

• Graph A shows a scattered set of points that doesn’t seem to show a clear negative trend.
• Graph B shows a downward trend, aligning well with the negative relationship.
• Graph C seems to show points that do not follow any consistent negative or linear pattern.
• Graph D appears to show a negative relationship, but not as pronounced as in Graph B.

Thus, Graph B is the best fit to represent the negative linear relationship between $x$ and $y$.

Let me know if you'd like me to proceed with the next part or if you need more clarification!

Here are some related questions:

1. What is the interpretation of the correlation coefficient $r$?
2. How can we calculate the least-squares regression line?
3. What do the slope and intercept of the regression line represent in the context of this problem?
4. How can we interpret the strength of the relationship between $x$ and $y$?
5. What would the regression line look like if the correlation coefficient was positive?

Tip: The closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables.