CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate distribution, Cov(X, Y) = 12, Var(X) = 16 and Var(Y) = 25. If every value of X is multiplied by -2 and every value of Y is increased by 10, what is the new correlation coefficient?
The new coefficient is -0.60. The original r is 12 divided by 4 times 5, which is 0.6. Correlation is unaffected by shifting origin or by positive scaling, but multiplying X by a negative number reverses the sign, so the magnitude stays 0.6 and the sign becomes negative.
- A-0.60Correct
- B0.60
- C-0.30
- D-1.20
Explanation
Original r = 12/(4×5) = 0.6. Multiplying X by a negative constant reverses the sign while the magnitude is unchanged; adding 10 to Y has no effect. New r = -0.6. Option -1.20 wrongly scales r by -2 and is also impossible since |r| ≤ 1.
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