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CA Foundation · Quantitative Aptitude · Correlation and Regression

For data on 8 pairs of observations, the standard deviations are σx = 6 and σy = 4.5, and the correlation coefficient is r = 0.8. What is the regression coefficient of X on Y (bxy)?

The regression coefficient of X on Y is about 1.067. It equals r times σx divided by σy, that is 0.8 multiplied by 6 over 4.5. The value 0.6 is the coefficient of Y on X, obtained by inverting the ratio.

  1. A1.067Correct
  2. B0.6
  3. C0.75
  4. D1.333

Explanation

bxy = r × σx/σy = 0.8 × 6/4.5 = 0.8 × 1.3333 = 1.0667. Check: byx = 0.8 × 4.5/6 = 0.6, and 1.0667 × 0.6 = 0.64 = r squared. The value 0.6 is wrong because it is byx, which uses the inverted ratio of standard deviations.

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