Which graph best represents the following situation? As x increases, y decreases; r = -0.41. A. C. B. D. A. Graph A B. Graph B C. Graph C D. Graph D
The correct answer is: D. Graph D
Explanation:
In this situation, you are told:
- As x increases, y decreases, and
- The correlation coefficient, r = -0.41.
Let’s break this down step by step like in a textbook:
1. Understanding the Relationship Between x and y
The statement “as x increases, y decreases” describes a negative relationship between the two variables. This means that when one variable gets larger, the other tends to get smaller. In other words, the points on a scatter plot would slope downward from left to right.
2. Interpreting the Correlation Coefficient (r)
The correlation coefficient r measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1.
- If r = 1, it’s a perfect positive linear relationship.
- If r = -1, it’s a perfect negative linear relationship.
- If r = 0, there is no linear relationship.
- If r is negative, the relationship is negative, and y decreases as x increases.
In this problem, r = -0.41, which means:
- The relationship is negative (since the sign is negative).
- The relationship is moderate to weak, because the value is not close to -1.
3. Matching the Graph
You should look for a graph that shows:
- A downward trend from left to right, since the relationship is negative.
- Scattered points with a moderate trend—not a strong line, but not completely random either.
Among the options:
- Graph A or C may show positive trends.
- Graph B could show no relationship (r near 0).
- Graph D likely shows a moderate negative trend, which matches an r of -0.41.
✅ Therefore, the best representation is Graph D.
