In a scatterplot, what does a negative correlation between variables $x$ and $y$ mean?

• A. As $x$ increases, $y$ tends to increase.
• B. The variables $x$ and $y$ have a perfect positive linear relationship, so $r=1$.
• C. As $x$ increases, $y$ tends to decrease.
• D. There is no linear relationship between $x$ and $y$, so the correlation is $r=0$.

Answer: (C)

Verified step by step guidance

1. Understand that correlation measures the strength and direction of a linear relationship between two variables, typically denoted as \(r\).
2. Recall that the value of the correlation coefficient \(r\) ranges from \(-1\) to \$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 negative correlation means that as one variable increases, the other variable tends to decrease.
4. Apply this to the variables \(x\) and \(y\): if the correlation between \(x\) and \(y\) is negative, then as \(x\) increases, \(y\) tends to decrease.
5. Therefore, the correct interpretation of a negative correlation in a scatterplot is: 'As \(x\) increases, \(y\) tends to decrease.'