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CA Foundation · Quantitative Aptitude · Correlation and Regression

For a bivariate distribution, the variance of X is 25, the variance of Y is 16 and the variance of (X − Y) is 21. What is the coefficient of correlation between X and Y?

The correlation coefficient is 0.5. Using Var(X − Y) = σx² + σy² − 2rσxσy gives 21 = 41 − 40r, so r = 20/40 = 0.5. A wrong sign on the covariance term would produce −0.5.

  1. A0.5Correct
  2. B−0.5
  3. C1.0
  4. D0.8

Explanation

Var(X − Y) = σx² + σy² − 2rσxσy, so 21 = 25 + 16 − 2r(5)(4) = 41 − 40r. Then 40r = 20 and r = 0.5. Using a plus sign for the covariance term gives −0.5, and dropping the factor 2 gives r = 1.0, both wrong.

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