Which scatterplot shows a negative correlation between $x$ and $y$?

• A. Points follow a strong U-shaped pattern (low $y$ values in the middle $x$ range and higher $y$ values at both ends).
• B. Points tend to slope upward from left to right (as $x$ increases, $y$ increases).
• C. Points form a roughly horizontal cloud with no clear upward or downward trend.
• D. Points tend to slope downward from left to right (as $x$ increases, $y$ decreases).

Answer: (D)

Verified step by step guidance

1. Understand that correlation measures the direction and strength of a linear relationship between two variables, x and y.
2. Recall that a negative correlation means that as x increases, y tends to decrease, which is visually represented by points sloping downward from left to right on a scatterplot.
3. Analyze the given patterns: a U-shaped pattern indicates a nonlinear relationship, not a simple negative correlation; an upward slope indicates a positive correlation; a horizontal cloud indicates no correlation.
4. Identify that the only pattern consistent with a negative correlation is the one where points tend to slope downward from left to right, meaning y decreases as x increases.
5. Conclude that the scatterplot showing a negative correlation is the one where points tend to slope downward from left to right.