CA Foundation · Quantitative Aptitude · Correlation and Regression
In a sample, the standard deviation of x is 4, the standard deviation of y is 6, and the correlation coefficient is 0.5. What is the regression coefficient of x on y?
The regression coefficient of x on y is 1/3. It equals r multiplied by σx/σy, which is 0.5 × 4/6. The figure 0.75 results from using the ratio the wrong way round, which gives the regression coefficient of y on x instead.
- A0.75
- B1/3Correct
- C0.50
- D1.50
Explanation
bxy = r × σx/σy = 0.5 × 4/6 = 1/3. The value 0.75 is byx = r × σy/σx, which comes from swapping the standard deviations. The value 0.50 is simply r. The value 1.50 is σy/σx, which omits r.
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