Which statement about correlation is false?

• A. A correlation close to $1$ indicates a strong positive linear association.
• B. The correlation coefficient $r$ must be between $-1$ and $1$.
• C. If two variables have correlation $r=0$, then there is no relationship of any kind between them.
• D. Correlation measures the strength and direction of a linear relationship between two quantitative variables.

Answer: (C)

Verified step by step guidance

1. Understand the definition of correlation: The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two quantitative variables.
2. Recall the range of the correlation coefficient: \(r\) must always lie between \(-1\) and \$1$, inclusive.
3. Interpret the meaning of correlation values close to \$1\(: A correlation close to \)1$ indicates a strong positive linear association, meaning as one variable increases, the other tends to increase as well.
4. Analyze the statement about \(r = 0\): A correlation of \(r = 0\) means there is no linear relationship between the variables, but it does not imply that there is no relationship of any kind (nonlinear relationships may still exist).
5. Identify the false statement: The false statement is the one claiming that \(r = 0\) means no relationship of any kind, because correlation only measures linear relationships.