Which of the following is true of the correlation coefficient $r$?

• A. A value of $r$ close to $0$ indicates a strong linear relationship.
• B. A negative value of $r$ means there is no relationship between the variables.
• C. The correlation coefficient $r$ can be greater than $1$ for some data sets.
• D. The value of $r$ is always between $-1$ and $1$, inclusive.

Answer: (D)

Verified step by step guidance

1. Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables.
2. Understand that the value of \(r\) ranges from \(-1\) to \$1\(, where \)r = 1\( indicates a perfect positive linear relationship, \)r = -1\( indicates a perfect negative linear relationship, and \)r = 0$ indicates no linear relationship.
3. Recognize that a value of \(r\) close to \$0$ does not indicate a strong linear relationship; rather, it suggests a weak or no linear relationship.
4. Note that a negative value of \(r\) indicates a negative linear relationship, meaning as one variable increases, the other tends to decrease, not that there is no relationship.
5. Remember that \(r\) cannot be greater than \$1\( or less than \)-1$ for any data set, as these are the theoretical bounds of the correlation coefficient.