CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate distribution, Cov(X, Y) = -18, the standard deviation of X is 6 and the variance of Y is 16. What is the coefficient of correlation between X and Y?
The coefficient of correlation is -0.75. The standard deviation of Y is the square root of 16, which is 4. Dividing the covariance -18 by the product 6×4 = 24 gives -0.75. Using the variance instead of the standard deviation is the usual error.
- A+0.75
- B-1.125
- C-0.1875
- D-0.75Correct
Explanation
σy = √16 = 4. r = Cov(X,Y)/(σx σy) = -18/(6×4) = -0.75. Using the variance 16 instead of σy gives -0.1875, which is wrong. Dividing only by 16 gives -1.125, which is impossible as it lies outside -1 to +1.
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