In a scatterplot, a negative correlation means that as $x$ increases, what tends to happen to $y$?

• A. $y$ tends to increase
• B. There is no linear relationship between $x$ and $y$
• C. $y$ tends to decrease
• D. All points lie exactly on a straight line with positive slope

Answer: (C)

Verified step by step guidance

1. Understand the concept of correlation: Correlation measures the strength and direction of a linear relationship between two variables, typically denoted as \(x\) and \(y\).
2. Recall that a negative correlation means the two variables move in opposite directions. Specifically, as one variable increases, the other tends to decrease.
3. In the context of a scatterplot, if the correlation is negative, the points tend to slope downward from left to right, indicating that as \(x\) increases, \(y\) tends to decrease.
4. Contrast this with a positive correlation, where as \(x\) increases, \(y\) also tends to increase, and the points slope upward from left to right.
5. Therefore, the correct interpretation of a negative correlation is that \(y\) tends to decrease as \(x\) increases.