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CA Foundation · Quantitative Aptitude · Correlation and Regression

For two variables X and Y, the variance of X is 9, the variance of Y is 16 and the variance of (X + Y) is 37. What is the coefficient of correlation between X and Y?

The correlation coefficient is 0.50. From Var(X+Y) = Var(X) + Var(Y) + 2Cov, 37 = 25 + 2Cov gives Cov = 6. With standard deviations 3 and 4, r = 6/12 = 0.5. Omitting the factor 2 would wrongly give 1.00.

  1. A0.24
  2. B-0.50
  3. C0.50Correct
  4. D1.00

Explanation

Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y), so 37 = 25 + 2Cov and Cov = 6. σxσy = 3×4 = 12, so r = 6/12 = 0.50. Forgetting the factor 2 gives Cov = 12 and r = 1.00, which is wrong. Dividing 6 by 25 gives 0.24, which is also wrong.

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