Which of the following is not a property of the linear correlation coefficient $r$?

• A. $r$ is unaffected by changes in the scale of either variable
• B. $r$ can be used to describe the strength of any nonlinear relationship
• C. $r$ measures the strength and direction of a linear relationship between two variables
• D. $r$ is always between $-1$ and $1$ inclusive

Answer: (B)

Verified step by step guidance

1. Recall the definition of the linear correlation coefficient \(r\): it measures the strength and direction of a linear relationship between two variables.
2. Understand that \(r\) is always between \(-1\) and \$1\( inclusive, where \)-1\( indicates a perfect negative linear relationship, \)1\( indicates a perfect positive linear relationship, and \)0$ indicates no linear relationship.
3. Recognize that \(r\) is unaffected by changes in the scale of either variable, meaning if you multiply or add a constant to one variable, \(r\) remains the same.
4. Note that \(r\) specifically measures linear relationships, so it does not accurately describe the strength of nonlinear relationships.
5. Therefore, the statement that '\(r\) can be used to describe the strength of any nonlinear relationship' is not a property of the linear correlation coefficient.