CA Foundation · Quantitative Aptitude · Correlation and Regression
Two variables x and y have standard deviations 3 and 4 respectively. The variance of the sum (x + y) is 37. What is the coefficient of correlation between x and y?
The correlation is 0.50. The variance of a sum equals σx² + σy² + 2rσxσy, so 37 = 9 + 16 + 24r. This gives r = 12/24 = 0.50. Using the difference formula by mistake would give -0.50, which is incorrect here.
- A0.50Correct
- B-0.50
- C1.00
- D0.75
Explanation
Var(x + y) = σx² + σy² + 2rσxσy, so 37 = 9 + 16 + 2r(12) = 25 + 24r. Hence 24r = 12 and r = 0.50. The value -0.50 results from wrongly using the formula for Var(x − y), which has a minus sign before the cross term. Dropping the factor 2 would give r = 1.00, which is also wrong.
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