If the correlation coefficient $r$ equals $0.65$, which of the following best describes the relationship between the two variables?

• A. There is a strong negative linear relationship between the variables.
• B. There is no linear relationship between the variables.
• C. There is a perfect positive linear relationship between the variables.
• D. There is a moderate positive linear relationship between the variables.

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, and it ranges from \(-1\) to \(1\).
2. Understand that the sign of \(r\) indicates the direction: a positive \(r\) means a positive linear relationship, and a negative \(r\) means a negative linear relationship.
3. Recognize that the magnitude of \(r\) indicates the strength: values close to \(0\) suggest a weak or no linear relationship, values close to \(1\) or \(-1\) suggest a strong linear relationship, and values in between indicate moderate strength.
4. Given \(r = 0.65\), note that it is positive, so the relationship is positive, and since \(0.65\) is between \(0.5\) and \(0.7\), it typically indicates a moderate strength of linear association.
5. Therefore, the best description is that there is a moderate positive linear relationship between the two variables.