Which of the following is true about the relationship between correlation and causation?

• A. Correlation does not imply causation; two variables can be correlated without one causing the other.
• B. Causation always results in a correlation coefficient of $0$.
• C. If two variables are correlated, it always means that one variable causes the other.
• D. A correlation coefficient of $1$ means there is no relationship between the variables.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of correlation. Correlation measures the strength and direction of a linear relationship between two variables, typically quantified by the correlation coefficient \(r\), which ranges from \(-1\) to \$1$.
2. Step 2: Understand the concept of causation. Causation means that a change in one variable directly causes a change in another variable, implying a cause-and-effect relationship.
3. Step 3: Recognize that correlation does not imply causation. Two variables can be correlated (have a non-zero correlation coefficient) due to coincidence, the presence of a lurking variable, or other factors, without one causing the other.
4. Step 4: Analyze the statements given: - "Causation always results in a correlation coefficient of 0" is false because causation typically produces some correlation, not zero. - "If two variables are correlated, it always means one causes the other" is false because correlation alone does not establish causality. - "A correlation coefficient of 1 means there is no relationship" is false because \(r=1\) indicates a perfect positive linear relationship.
5. Step 5: Conclude that the true statement is: "Correlation does not imply causation; two variables can be correlated without one causing the other." This is a fundamental principle in statistics and research.