Which statement about correlation is false?

• A. A correlation of $0$ means there is no relationship of any kind between the two variables.
• B. The correlation coefficient $r$ is always between $-1$ and $1$, inclusive.
• C. Correlation measures the direction and strength of a linear relationship but does not imply causation.
• D. A correlation close to $1$ indicates a strong positive linear association between two quantitative variables.

Answer: (A)

Verified step by step guidance

1. Recall the definition of the correlation coefficient \(r\): it measures the strength and direction of a linear relationship between two quantitative variables, and its value always lies between \(-1\) and \$1$, inclusive.
2. Understand that a correlation of \$0$ means there is no *linear* relationship between the two variables, but it does not imply that there is no relationship of any kind; there could be a nonlinear relationship.
3. Recognize that correlation does not imply causation; even a strong correlation does not mean one variable causes changes in the other.
4. Note that a correlation close to \$1$ indicates a strong positive linear association, meaning as one variable increases, the other tends to increase as well.
5. Identify the false statement by focusing on the interpretation of a correlation of \$0$: the claim that it means no relationship of any kind is incorrect because correlation only measures linear relationships.