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

• A. The value of $r$ is always between $-1$ and $1$, inclusive.
• B. $r$ can only take positive values.
• C. $r$ measures the strength of any nonlinear relationship.
• D. $r$ is unaffected by outliers in the data.

Answer: (A)

Verified step by step guidance

1. Understand that the linear correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables.
2. Recall the range of values that \(r\) can take: it is always between \(-1\) and \$1\(, inclusive. This means \)-1 \leq r \leq 1$.
3. Recognize that a value of \(r = 1\) indicates a perfect positive linear relationship, while \(r = -1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.
4. Note that \(r\) can take both positive and negative values, so it is incorrect to say \(r\) can only be positive.
5. Understand that \(r\) specifically measures linear relationships and can be affected by outliers, so it does not measure nonlinear relationships well and is not robust to outliers.