CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
The correlation coefficient between X and Y is 0.8, with standard deviations of 5 for X and 10 for Y. What is the regression coefficient of Y on X?
The regression coefficient of Y on X is 1.6. It equals r multiplied by the ratio of the standard deviation of Y to that of X, which is 0.8 times 10 divided by 5, giving 1.6.
- A0.4
- B1.6Correct
- C4
- D0.32
Explanation
byx = r × σy/σx = 0.8 × 10/5 = 0.8 × 2 = 1.6. The option 0.4 uses σx/σy, which is the formula for bxy, the regression of X on Y. Check: bxy = 0.4 and product 1.6 × 0.4 = 0.64 = r².
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