CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate data set, the correlation coefficient between x and y is r = 0.8, the standard deviation of x is 5 and the standard deviation of y is 10. What is the regression coefficient of y on x?
The regression coefficient of y on x equals r multiplied by σy divided by σx, which is 0.8 × 10/5 = 1.6. Using σx/σy would wrongly give 0.4, which is the coefficient of x on y.
- A1.6Correct
- B0.4
- C0.8
- D0.25
Explanation
The regression coefficient of y on x is b_yx = r × σy/σx = 0.8 × 10/5 = 1.6. The value 0.4 comes from the inverted ratio r × σx/σy, which is b_xy (the coefficient of x on y), not b_yx.
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