CA Foundation · Quantitative Aptitude · Correlation and Regression
The share price (₹) of a company X and the sales index Y over seven consecutive months are: X: 40, 42, 45, 43, 46, 48, 47 and Y: 60, 63, 65, 66, 64, 68, 66. Using the concurrent deviation method, what is the coefficient of correlation?
The coefficient is +0.577. Comparing the direction of month-to-month changes, 4 of the 6 pairs agree, so C = 4 and N = 6. The value (2C − N)/N is 1/3, which is positive, so rc = +√(1/3) ≈ 0.577.
- A+0.577Correct
- B+0.333
- C-0.577
- D+0.667
Explanation
The signs for X are +, +, −, +, +, − and for Y are +, +, +, −, +, −. They agree in months 1, 2, 5 and 6, so C = 4 and N = 6. Then (2C − N)/N = (8 − 6)/6 = 1/3, which is positive, so rc = +√(1/3) = +0.577. The value +0.333 forgets to take the square root.
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