CA Foundation · Quantitative Aptitude · Correlation and Regression
For 5 paired observations of a stock's price index (X) and trading volume (Y), the following totals are obtained: ΣX = 15, ΣY = 20, ΣXY = 68, ΣX² = 55 and ΣY² = 90. What is Karl Pearson's coefficient of correlation?
The coefficient of correlation is 0.80. The numerator is 5×68 - 15×20 = 40, and both denominator terms equal 50, giving 40/√(50×50) = 0.8. The value 0.64 would be r squared, not r.
- A0.64
- B0.80Correct
- C0.75
- D0.56
Explanation
nΣXY - ΣXΣY = 340 - 300 = 40. nΣX² - (ΣX)² = 275 - 225 = 50 and nΣY² - (ΣY)² = 450 - 400 = 50. So r = 40/√(50×50) = 40/50 = 0.80. The value 0.64 is r², which is the wrong quantity.
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