Correlation measures the extent to which two variables co-vary. Which statement is true?

• A. A lack of relationship is signified by a value close to zero, but a zero could occur for a curvilinear relationship
• B. A correlation value near zero always means no relationship
• C. Correlation proves causation
• D. Correlation is only defined for nominal data

Answer: (A)

Correlation measures how two variables tend to change together in a linear way. The value, which ranges from -1 to 1, tells you both the direction and the strength of that linear relationship. The statement that’s true highlights a key nuance: when the correlation is close to zero, there’s little linear relationship, but a zero can occur even if a curvilinear (nonlinear) relationship exists. In other words, you can have a meaningful association between the variables that a linear correlation coefficient fails to capture, because it looks only at linear co-variation.

This helps explain why a near-zero value doesn’t prove there’s no relationship at all—there could be a nonlinear pattern. It also reminds you that correlation does not imply causation, and that correlation is defined for numerical data (interval/ratio) rather than nominal data, for which other measures would be more appropriate.