In a bivariate data set, if the correlation coefficient $r$ is negative, what does this indicate about the relationship between the two variables?

• A. As one variable increases, the other variable tends to decrease (a negative linear association).
• B. One variable causes the other variable to decrease.
• C. As one variable increases, the other variable tends to increase (a positive linear association).
• D. There is no linear relationship between the variables, so $r=0$.

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient \(r\) 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 positive values indicate a positive linear association and negative values indicate a negative linear association.
3. Recognize that a negative correlation coefficient means that as one variable increases, the other variable tends to decrease, showing an inverse relationship.
4. Note that correlation does not imply causation, so a negative \(r\) does not mean one variable causes the other to decrease.
5. Conclude that a negative \(r\) indicates a negative linear association between the two variables, meaning they move in opposite directions on average.