CA Foundation · Quantitative Aptitude · Correlation and Regression
For a data set, r = 0.8, the standard deviation of x is 5, and the regression coefficient of y on x is 1.2. What is the standard deviation of y?
The standard deviation of y is 7.5. From byx = r·σy/σx, we get σy = byx·σx/r = 1.2 × 5 ÷ 0.8 = 7.5. A check confirms that the product of the two regression coefficients is 0.64, which equals r².
- A3.33
- B6.00
- C7.50Correct
- D9.38
Explanation
byx = r × σy/σx, so σy = byx × σx / r = 1.2 × 5 / 0.8 = 7.5. Check: bxy = 0.8 × 5/7.5 = 0.533, and 1.2 × 0.533 = 0.64 = r². The value 6.00 omits division by r, and 3.33 uses r × σx / byx.
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