Which of the following scatterplots best illustrates a correlation that is affected by $non-linearity$?

• A. A scatterplot where the points are widely scattered with no apparent pattern.
• B. A scatterplot where the points are tightly clustered around a straight line with a $positive$ slope.
• C. A scatterplot where the points are tightly clustered around a straight line with a $negative$ slope.
• D. A scatterplot where the points form a clear upward-curving pattern, resembling a $parabola$.

Answer: (D)

Verified step by step guidance

1. Understand that correlation measures the strength and direction of a linear relationship between two variables.
2. Recognize that a scatterplot showing points tightly clustered around a straight line (either positive or negative slope) indicates a strong linear correlation.
3. Note that a scatterplot with points widely scattered and no apparent pattern suggests little to no correlation.
4. Identify that when points form a clear curved pattern (such as an upward parabola), the relationship is non-linear, which affects the interpretation of correlation.
5. Conclude that a non-linear pattern means the correlation coefficient may not accurately describe the relationship, even if the points are closely grouped along the curve.