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

• A. If two variables are correlated, one must directly cause the other.
• B. Correlation does not necessarily imply causation.
• C. Correlation implies causation.
• D. A scatterplot can prove a causal relationship between two variables.

Answer: (B)

Verified step by step guidance

1. Understand the concept of correlation: Correlation measures the strength and direction of a linear relationship between two variables, typically represented by the correlation coefficient \(r\), which ranges from \(-1\) to \$1$.
2. Recognize what correlation does not imply: Even if two variables have a strong correlation, it does not mean that one variable causes the other to change. Correlation only indicates an association, not causation.
3. Consider the role of scatterplots: A scatterplot visually displays the relationship between two variables, showing patterns or trends, but it cannot prove that one variable causes changes in the other.
4. Recall the principle 'correlation does not imply causation': This is a fundamental idea in statistics that warns against assuming a causal link based solely on correlation or scatterplot patterns.
5. Evaluate the given statements: The correct statement is 'Correlation does not necessarily imply causation,' because it accurately reflects the limitations of correlation and scatterplots in establishing causal relationships.