Given four scatterplots labeled $A$, $B$, $C$, and $D$, each showing a different relationship between two variables, which plot most likely represents the strongest linear correlation (either positive or negative) between the variables?

• A. Plot $D$, where the points are randomly distributed with no relationship.
• B. Plot $A$, where the points closely follow a straight line with a positive slope.
• C. Plot $B$, where the points are widely scattered with no apparent pattern.
• D. Plot $C$, where the points form a perfect $U$-shaped curve.

Answer: (B)

Verified step by step guidance

1. Understand that the strength of a linear correlation between two variables is measured by how closely the data points follow a straight line, either sloping upwards (positive correlation) or downwards (negative correlation).
2. Recognize that a scatterplot with points closely clustered around a straight line indicates a strong linear relationship, while points scattered widely or forming a curve indicate a weak or non-linear relationship.
3. Evaluate each plot based on the description: Plot A has points closely following a straight line with a positive slope, suggesting a strong positive linear correlation.
4. Note that Plot D shows points randomly distributed with no relationship, indicating no correlation; Plot B has widely scattered points with no pattern, also indicating weak or no correlation; Plot C forms a perfect U-shaped curve, which is a strong non-linear relationship, not linear.
5. Conclude that the plot representing the strongest linear correlation is the one where points closely follow a straight line, which is Plot A.