CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
Given r = 0.6, standard deviation of X = 5 and standard deviation of Y = 8, what is the regression coefficient of Y on X?
The regression coefficient of Y on X is 0.96. It is found as r multiplied by the ratio of the standard deviation of Y to that of X, so 0.6 times 8/5 equals 0.96. The value 0.375 is the coefficient of X on Y.
- A0.375
- B0.96Correct
- C1.00
- D0.60
Explanation
b_yx = r x (sigma_y / sigma_x) = 0.6 x 8/5 = 0.96. Option 0.375 equals r x sigma_x / sigma_y = 0.6 x 5/8, which is b_xy, the wrong regression. Check: b_xy x b_yx = 0.375 x 0.96 = 0.36 = r squared.
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