To solve this problem, let’s carefully analyze each graph and match it to its correlation coefficient based on the strength and direction of the linear relationship between the variables.

1. Graph A: The points in this graph form a clear upward linear pattern with very little scatter. A positive, strong correlation is evident. Thus, the correlation coefficient is closest to r = 0.98.

2. Graph B: This graph shows a downward trend, meaning the correlation is negative. The points are tightly clustered along the line, which suggests a strong negative correlation. Therefore, the correlation coefficient is r = -0.97.

3. Graph C: The points in this graph are scattered with no clear upward or downward trend, indicating no correlation between the variables. This means the correlation coefficient is approximately r = 0.

4. Graph D: Here, the points show a weak positive trend. While the points are somewhat spread out, there is still a general upward direction, indicating a moderate positive correlation. Thus, the correlation coefficient is r = 0.69.

Final Matching:

• A: r = 0.98
• B: r = -0.97
• C: r = 0
• D: r = 0.69

Explanation:

The correlation coefficient $r$ measures the strength and direction of a linear relationship. A value close to $1$ or $-1$ indicates a strong correlation, while a value near $0$ suggests no correlation. Graph A has a strong positive correlation, Graph B a strong negative correlation, Graph C no correlation, and Graph D a moderate positive correlation.

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Related Questions:

1. What does a positive or negative correlation coefficient signify?
2. How do you calculate a correlation coefficient $r$ for a set of data points?
3. What are examples of strong and weak correlations in real-life data?
4. How does the scatterplot pattern reflect the value of $r$?
5. What would the graph look like if $r = -1$ or $r = 1$?

Tip:

A strong correlation (positive or negative) means the points are closely clustered around a straight line, while weak or no correlation shows scattered points.