Which of the following descriptions best represents a strong negative correlation in a scatterplot?

• A. There is no clear linear pattern between $x$ and $y$, with points scattered randomly (e.g., $r\approx 0$).
• B. As $x$ increases, $y$ tends to increase, and the points lie close to a straight upward-sloping line (e.g., $r\approx 0.9$).
• C. As $x$ increases, $y$ tends to decrease, and the points lie close to a straight downward-sloping line (e.g., $r\approx -0.9$).
• D. As $x$ increases, $y$ tends to decrease, but the points are widely scattered with only a weak linear trend (e.g., $r\approx -0.2$).

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 \(r\), which ranges from \(-1\) to \$1$.
2. Recognize that a strong negative correlation means that as one variable \(x\) increases, the other variable \(y\) tends to decrease in a predictable, linear way.
3. Visualize this relationship on a scatterplot: the points should lie close to a straight line that slopes downward from left to right.
4. Recall that the correlation coefficient \(r\) for a strong negative correlation is close to \(-1\), for example, \(r \approx -0.9\).
5. Compare the given descriptions and identify the one that matches a strong negative correlation: points close to a downward-sloping line with \(r\) near \(-0.9\).