If the correlation coefficient between X and Y is 0, what does that indicate?

If the correlation coefficient between X and Y is 0, what does that indicate?

• A. No linear relationship
• B. Perfect positive relationship
• C. Perfect negative relationship
• D. Some relationship but not linear

Answer: (B)

Correlation measures how well a straight line can describe the relationship between X and Y. If the correlation coefficient is zero, there is no linear association between the two variables—the points don’t show a clear straight-line trend. But that doesn’t mean no relationship exists at all. They can still be related in a nonlinear way. For example, if Y = X^2 and X is symmetric around zero, the correlation can be near zero even though Y clearly depends on X. To detect such nonlinear patterns, you’d look at a scatter plot and, if needed, use other measures (like Spearman’s rho) or fit nonlinear models. The main takeaway is: zero correlation means no linear relationship, not necessarily no relationship at all.

Correlation measures how well a straight line can describe the relationship between X and Y. If the correlation coefficient is zero, there is no linear association between the two variables—the points don’t show a clear straight-line trend. But that doesn’t mean no relationship exists at all. They can still be related in a nonlinear way. For example, if Y = X^2 and X is symmetric around zero, the correlation can be near zero even though Y clearly depends on X. To detect such nonlinear patterns, you’d look at a scatter plot and, if needed, use other measures (like Spearman’s rho) or fit nonlinear models. The main takeaway is: zero correlation means no linear relationship, not necessarily no relationship at all.