Four scatterplots (A–D) are shown. Which plot shows the strongest linear correlation (i.e., has the correlation coefficient $r$ with the greatest absolute value)?

• A. Plot B: points form a clear U-shaped (curved) pattern.
• B. Plot C: points are widely scattered with no clear pattern.
• C. Plot D: points show a weak downward trend with substantial scatter.
• D. Plot A: points are tightly clustered around an upward-sloping straight line.

Answer: (D)

Verified step by step guidance

1. Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. Its value ranges from \(-1\) (perfect negative linear correlation) to \(+1\) (perfect positive linear correlation), with values close to 0 indicating little or no linear correlation.
2. Examine each scatterplot to identify the pattern of the points: a strong linear correlation means points lie close to a straight line, either sloping upward (positive \(r\)) or downward (negative \(r\)).
3. For Plot B, the points form a U-shaped curve, which is a nonlinear pattern. Even if the points are close to the curve, the linear correlation coefficient \(r\) will be close to zero because \(r\) only measures linear relationships.
4. Plot C shows points widely scattered with no clear pattern, indicating a very weak or no linear correlation, so \(r\) will be near zero.
5. Plot D shows a weak downward trend with substantial scatter, suggesting a small negative correlation, but not very strong.
6. Plot A shows points tightly clustered around an upward-sloping straight line, indicating a strong positive linear correlation. Therefore, Plot A has the correlation coefficient \(r\) with the greatest absolute value.