In the context of the correlation coefficient, what does it mean if the correlation between two variables is negative (i.e., $r<0$)?

• A. As one variable increases, the other variable tends to decrease (an inverse linear relationship).
• B. As one variable increases, the other variable also tends to increase (a direct linear relationship).
• C. One variable causes the other variable to decrease.
• D. There is no linear relationship between the variables (approximately $r=0$).

Answer: (A)

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 positive values indicate a positive linear relationship and negative values indicate a negative linear relationship.
3. Interpret a negative correlation (\(r < 0\)) as meaning that when one variable increases, the other variable tends to decrease, showing an inverse linear relationship.
4. Note that correlation does not imply causation, so a negative correlation does not mean one variable causes the other to decrease.
5. Recognize that if \(r\) is approximately zero, it suggests there is no linear relationship between the variables.