In the context of scatterplots and correlation, which statement is correct?

• A. Correlation measures association, but it does not by itself establish a cause-and-effect relationship.
• B. Correlation implies causation.
• C. A strong correlation proves that changes in one variable cause changes in the other.
• D. If the correlation is negative, then one variable must be causing the other to decrease.

Answer: (A)

Verified step by step guidance

1. Understand the concept of correlation: Correlation quantifies the strength and direction of a linear relationship between two variables. It is measured by the correlation coefficient, which ranges from -1 to 1.
2. Recognize what correlation does not imply: Correlation measures association but does not establish causation. This means that even if two variables move together, it does not mean one causes the other to change.
3. Evaluate the given statements: Statements claiming that correlation implies causation or that a strong correlation proves cause-and-effect are incorrect because correlation alone cannot determine causality.
4. Consider the meaning of negative correlation: A negative correlation indicates that as one variable increases, the other tends to decrease, but it does not mean one variable causes the other to decrease.
5. Conclude that the correct statement is the one emphasizing that correlation measures association without establishing cause-and-effect relationships.