CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
For a data set, the standard deviation of X is 6, the standard deviation of Y is 8 and the correlation coefficient is 0.9. What is the regression coefficient of Y on X?
The regression coefficient of Y on X is 1.2. It equals the correlation coefficient times the standard deviation of Y divided by that of X, that is 0.9 × 8/6 = 1.2. Using the inverted ratio would give 0.675, which is the coefficient of X on Y.
- A0.675
- B1.2Correct
- C0.9
- D1.6
Explanation
b_yx = r × (σy / σx) = 0.9 × 8/6 = 0.9 × 4/3 = 1.2. The value 0.675 is b_xy = r × σx/σy = 0.9 × 6/8, which is the wrong ratio.
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