Which type of scatterplot indicates a strong association between two variables even if the correlation is nearly zero?

Which type of scatterplot indicates a strong association between two variables even if the correlation is nearly zero?

• A. Linear trend
• B. Downwards parabola
• C. Vertical line
• D. Horizontal line

Answer: (B)

A scatterplot that shows a strong association between two variables, despite the correlation being nearly zero, typically reflects a nonlinear relationship. In this case, a downward parabola indicates that as one variable increases, the other variable initially decreases rapidly, potentially stabilizing or changing direction at other points. This forms a curved shape in the scatterplot that can signify a strong relationship, even if the correlation coefficient (which primarily measures linear relationships) is close to zero. In contrast, a linear trend suggests a consistent, straightforward relationship between the two variables, which would produce a higher correlation, while a horizontal line indicates no change in the dependent variable regardless of changes in the independent variable, implying no association. A vertical line generally reflects a situation where the independent variable does not change, but this does not offer any meaningful correlation analysis between two distinct variables. Thus, the downward parabola most accurately reflects the potential for a strong, albeit nonlinear, relationship between the variables in question.

A scatterplot that shows a strong association between two variables, despite the correlation being nearly zero, typically reflects a nonlinear relationship. In this case, a downward parabola indicates that as one variable increases, the other variable initially decreases rapidly, potentially stabilizing or changing direction at other points. This forms a curved shape in the scatterplot that can signify a strong relationship, even if the correlation coefficient (which primarily measures linear relationships) is close to zero.

In contrast, a linear trend suggests a consistent, straightforward relationship between the two variables, which would produce a higher correlation, while a horizontal line indicates no change in the dependent variable regardless of changes in the independent variable, implying no association. A vertical line generally reflects a situation where the independent variable does not change, but this does not offer any meaningful correlation analysis between two distinct variables. Thus, the downward parabola most accurately reflects the potential for a strong, albeit nonlinear, relationship between the variables in question.