In the context of scatterplots and correlation, what does the statement "correlation does not imply causation" mean?

• A. If two variables are correlated, then one variable must directly cause the other.
• B. Even if two variables have a strong correlation, it does not prove that changes in one variable cause changes in the other.
• C. A correlation of $0$ means that one variable causes the other to stay constant.
• D. Correlation can only be computed when there is a proven cause-and-effect relationship between the variables.

Answer: (B)

Verified step by step guidance

1. Understand that correlation measures the strength and direction of a linear relationship between two variables, but it does not indicate whether one variable causes the other to change.
2. Recognize that two variables can be correlated due to coincidence, the influence of a third variable (confounding factor), or other indirect relationships, rather than a direct cause-and-effect link.
3. Recall the phrase "correlation does not imply causation" means that observing a strong correlation alone is not sufficient evidence to conclude that one variable causes changes in the other.
4. Note that a correlation value of 0 means there is no linear relationship between the variables, but it does not imply causation or that one variable keeps the other constant.
5. Understand that correlation can be calculated regardless of whether a causal relationship is known or proven; it is a descriptive statistic, not a proof of causality.