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

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

Answer: (B)

Verified step by step guidance

1. Step 1: Understand what the linear correlation coefficient \(r\) represents. It measures the strength and direction of a linear relationship between two variables.
2. Step 2: Recall the range of \(r\). The value of \(r\) always lies 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. Step 3: Recognize that \(r\) is a unitless measure, meaning it is unaffected by the units of measurement of the variables. This allows comparison across different datasets.
4. Step 4: Identify that \(r\) specifically measures linear relationships. It does not accurately describe the strength of nonlinear relationships between variables.
5. Step 5: Conclude that the statement claiming \(r\) can be used to describe the strength of any nonlinear relationship is incorrect, as \(r\) is designed only for linear relationships.