Given four scatterplots, each showing a different relationship between variables $X$ and $Y$, which scatterplot would indicate the strongest negative linear association between $X$ and $Y$?

• A. The scatterplot where the points closely follow a straight line that slopes upward from left to right.
• B. The scatterplot where the points are widely scattered with no apparent pattern.
• C. The scatterplot where the points closely follow a straight line that slopes downward from left to right.
• D. The scatterplot where the points form a curved pattern opening upward.

Answer: (C)

Verified step by step guidance

1. Understand that a negative linear association between two variables means that as one variable increases, the other decreases, and the points on the scatterplot tend to follow a straight line sloping downward from left to right.
2. Recall that the strength of a linear association is indicated by how closely the points cluster around a straight line; the closer the points are to a straight line, the stronger the linear relationship.
3. Evaluate each scatterplot description: a line sloping upward indicates a positive association, widely scattered points with no pattern indicate no association, a curved pattern indicates a nonlinear association, and a straight line sloping downward indicates a negative linear association.
4. Identify that the scatterplot with points closely following a straight line sloping downward from left to right represents the strongest negative linear association between X and Y.
5. Conclude that among the given options, the scatterplot with the points closely following a straight line sloping downward is the correct choice for the strongest negative linear association.