Understanding Bi-Directional Non-Linear Relationships: Why the Circle-Shaped Scatter Diagram Is a Sign of No Correlation

A researcher plots a scatter diagram of two variables. The dots on the plot are scattered roughly as a circle. This indicates that the relationship (covariation) between the two variables is:A. linear, positive.B. linear, negative.C. circular, positive.D. circular, negative.E. very close to zero.

Answer: E

The circle-shaped scatter diagram indicates that there is no linear relationship between the two variables. This means that neither a positive nor a negative correlation exists between the two variables. Therefore, options A and B can be eliminated.

Moreover, the circular shape of the scatter plot indicates that the relationship is not directional but is rather bi-directional. The relationship between the variables is not specific to one variable in the pair but rather both are equally related to each other. This rules out options C and D.

The fact that the dots are equally scattered around the circle indicates that there is no well-defined relationship between the two variables. In other words, the variables are not related to each other in any systematic way. Thus, the correct option is E, very close to zero.

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