In the context of scatterplots and correlation, which statement best describes how correlation and causation differ?

• A. Correlation can only be positive, whereas causation can be positive or negative.
• B. Causation refers to any relationship visible in a scatterplot, while correlation requires a controlled experiment.
• C. Correlation measures the strength and direction of an association between two variables, but causation means that changes in one variable directly produce changes in the other.
• D. Correlation proves that one variable causes the other whenever the correlation is strong (close to $1$ or $-1$).

Answer: (C)

Verified step by step guidance

1. Understand that correlation quantifies the strength and direction of a linear relationship between two variables, typically measured by the correlation coefficient \(r\), which ranges from \(-1\) to \$1$.
2. Recognize that causation implies a cause-and-effect relationship where changes in one variable directly result in changes in another variable.
3. Note that a scatterplot visually displays the relationship between two variables but does not by itself prove causation.
4. Remember that a strong correlation (values of \(r\) close to \$1\( or \)-1$) indicates a strong association but does not guarantee that one variable causes the other.
5. Conclude that correlation measures association, while causation requires additional evidence, often from controlled experiments or studies designed to establish cause and effect.