CA Foundation · Quantitative Aptitude · Correlation and Regression
For a set of paired data, the sum of products of deviations Σ(x - x̄)(y - ȳ) = 180, Σ(x - x̄)² = 400 and Σ(y - ȳ)² = 144. What is the coefficient of correlation?
The correlation coefficient is 0.75. The denominator is the square root of 400 × 144, which is 240, and the numerator is 180. So r = 180/240 = 0.75. Dividing by only one sum of squares would give a wrong result.
- A0.75Correct
- B0.45
- C1.25
- D0.60
Explanation
r = Σ(x - x̄)(y - ȳ) / √[Σ(x - x̄)² × Σ(y - ȳ)²] = 180/√(400×144) = 180/√57600 = 180/240 = 0.75. Dividing 180 by 400 alone gives 0.45, which ignores the y deviations.
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