Which of the following statements about the correlation coefficient is true?

• A. The correlation coefficient measures the strength and direction of a linear relationship between two variables.
• B. The correlation coefficient can only take values between $0$ and $1$.
• C. A positive correlation coefficient indicates a strong causal relationship between the variables.
• D. A correlation coefficient of $0$ always means there is no relationship of any kind between the variables.

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient, often denoted as \(r\), quantifies the strength and direction of a linear relationship between two variables.
2. Recall the range of the correlation coefficient: it can take any value between \(-1\) and \$1\(, inclusive, where \)-1\( indicates a perfect negative linear relationship, \)0\( indicates no linear relationship, and \)1$ indicates a perfect positive linear relationship.
3. Recognize that a positive correlation coefficient means the variables tend to increase together, but it does not imply causation; correlation does not imply causation.
4. Note that a correlation coefficient of \$0$ means there is no linear relationship between the variables, but there could still be a non-linear relationship present.
5. Based on these points, identify the true statement as the one that says the correlation coefficient measures the strength and direction of a linear relationship between two variables.