Which of the following is a property of the linear correlation coefficient $r$?

• A. The value of $r$ is always less than $-1$.
• B. The value of $r$ is always between $-1$ and $1$, inclusive.
• C. The value of $r$ can be any real number.
• D. The value of $r$ is always greater than $0$.

Answer: (B)

Verified step by step guidance

1. Recall that the linear correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables.
2. Understand that \(r\) is a standardized measure, meaning it is scaled to a fixed range to allow comparison across different datasets.
3. Know the fundamental property of \(r\): its value always lies between \(-1\) and \$1\(, inclusive. This means \)-1 \leq r \leq 1$.
4. Interpret the values of \(r\): a value of \$1\( indicates a perfect positive linear relationship, \)-1\( indicates a perfect negative linear relationship, and \)0$ indicates no linear relationship.
5. Therefore, any statement claiming \(r\) can be less than \(-1\), greater than \$1\(, or any real number is incorrect, and the correct property is that \)r\( is always between \)-1\( and \)1$, inclusive.