In the context of scatterplots and correlation, which statement best describes the relationship between correlation and causation?

• A. A correlation between two variables implies that changes in one variable cause changes in the other.
• B. If a scatterplot shows a strong linear trend, then causation has been established.
• C. A zero correlation means two variables must be independent and therefore cannot have a causal relationship.
• D. Correlation does not imply causation; an association can exist even if neither variable causes the other.

Answer: (D)

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 quantified by the correlation coefficient \(r\), which ranges from \(-1\) to \$1$.
2. Recognize what causation means: Causation implies that changes in one variable directly cause changes in another variable, which requires more than just observing a relationship; it often requires controlled experiments or additional evidence.
3. Analyze the difference between correlation and causation: A correlation indicates an association or relationship between variables, but it does not prove that one variable causes the other to change.
4. Consider examples where correlation does not imply causation: For instance, two variables might be correlated due to a lurking variable or coincidence, so a strong correlation or a zero correlation does not automatically establish or rule out causation.
5. Conclude that the correct interpretation is that correlation does not imply causation; an observed association can exist even if neither variable causes the other.