Why is it important to report correlations together with scatter diagrams when analyzing the relationship between two quantitative variables?

• A. Scatter diagrams always prove causation between variables when paired with correlation.
• B. Scatter diagrams visually reveal patterns, outliers, and non-linear relationships that a correlation coefficient alone cannot show.
• C. Scatter diagrams are required to calculate the correlation coefficient.
• D. Scatter diagrams are only useful if the correlation coefficient is exactly $0$.

Answer: (B)

Verified step by step guidance

1. Understand that the correlation coefficient is a numerical measure that quantifies the strength and direction of a linear relationship between two quantitative variables. It ranges from -1 to 1.
2. Recognize that while the correlation coefficient provides a summary measure, it does not reveal the detailed structure of the data, such as the presence of outliers, clusters, or non-linear patterns.
3. Use a scatter diagram (scatter plot) to visually display the data points for the two variables, which helps to identify patterns, trends, and any unusual observations that might affect the correlation.
4. Note that scatter diagrams can show whether the relationship is linear or non-linear, something the correlation coefficient alone cannot determine, since it only measures linear association.
5. Conclude that reporting both the correlation coefficient and the scatter diagram together provides a more complete and accurate understanding of the relationship between the variables, avoiding misleading interpretations.