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

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 that the value of the correlation coefficient ranges between \(-1\) and \$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 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 zero means there is no linear relationship, but there could still be a non-linear relationship between the variables.
5. Conclude that the true statement is: 'The correlation coefficient measures the strength and direction of a linear relationship between two variables.'