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

• A. The value of $r$ can be greater than $1$ for strong positive relationships.
• B. The value of $r$ is unaffected by outliers in the data.
• C. The value of $r$ is always between $-1$ and $1$, inclusive.
• D. The value of $r$ is always positive.

Answer: (C)

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 calculated using the formula: \(r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}\), where \(x_i\) and \(y_i\) are data points and \(\bar{x}\) and \(\bar{y}\) are their means.
3. Recognize that by definition, the value of \(r\) is always between \(-1\) and \$1\(, inclusive. This means \)-1 \leq r \leq 1$.
4. Note that \(r = 1\) indicates a perfect positive linear relationship, \(r = -1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.
5. Be aware that \(r\) can be affected by outliers, and it is not always positive; it can take negative values depending on the direction of the relationship.