CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
For a set of paired observations, the regression coefficient of Y on X is 0.8 and the regression coefficient of X on Y is 0.45. What is the coefficient of correlation between X and Y?
The correlation coefficient is 0.60. It equals the geometric mean of the two regression coefficients, the square root of 0.8 times 0.45, which is the square root of 0.36. Both coefficients are positive, so the sign is positive. The figure 0.36 is only r squared.
- A0.60Correct
- B0.36
- C0.625
- D0.85
Explanation
r is the geometric mean of the two regression coefficients: r = sqrt(0.8 x 0.45) = sqrt(0.36) = 0.6. Both coefficients are positive, so r is positive. The value 0.36 is r squared, not r.
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