If the correlation coefficient between X and Y is zero, which conclusion is most accurate?
Correct answer: C. X and Y have no linear relationship
- A. X and Y have no relationship of any kind
- B. The means of X and Y are equal
- C. X and Y have no linear relationship
- D. The variances of X and Y are zero
Explanation
A zero Pearson correlation means that no linear relationship is detected. A nonlinear relationship may still exist, so it is incorrect to conclude that the variables have no relationship at all.
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About Correlation and Regression
Correlation describes the direction and strength of association between two variables using scatter diagrams and correlation coefficients. Regression covers fitted lines, regression equations, prediction and least squares, with a clear distinction between association and causation and between estimating a response value and reversing the roles of the variables.
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