In statistics, what does a negative correlation coefficient (e.g., $r<0$) between two variables indicate?

• A. As one variable increases, the other tends to increase (a direct linear relationship).
• B. As one variable increases, the other tends to decrease (an inverse linear relationship).
• C. There is no linear relationship between the variables (correlation is approximately zero).
• D. One variable causes the other to decrease.

Answer: (B)

Verified step by step guidance

1. Understand that the correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables.
2. Recall that the value of \(r\) ranges from \(-1\) to \$1\(, where values close to \)1\( indicate a strong positive linear relationship, values close to \)-1\( indicate a strong negative linear relationship, and values near \)0$ indicate little to no linear relationship.
3. Recognize that a negative correlation coefficient (\(r < 0\)) means that as one variable increases, the other variable tends to decrease, which is called an inverse linear relationship.
4. Note that this does not imply causation; a negative correlation only describes the direction of the linear association, not that one variable causes the other to change.
5. Therefore, when interpreting a negative correlation coefficient, focus on the inverse relationship between the variables rather than any causal effect.