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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression

For five pairs of observations, Σx = 20, Σy = 30, Σxy = 140, Σx² = 90 and Σy² = 220 (n = 5). What is Karl Pearson's coefficient of correlation between x and y?

Karl Pearson's r equals 1.00, because nΣxy − ΣxΣy = 100 and the product of the square roots of nΣx² − (Σx)² and nΣy² − (Σy)² is √50 × √200 = 100, so the ratio is exactly one.

  1. A0.50
  2. B0.80
  3. C0.00Correct
  4. D1.00

Explanation

Cov numerator: nΣxy − ΣxΣy = 700 − 600 = 100. Denominator: sqrt(5·90−400)=sqrt(50) and sqrt(5·220−900)=sqrt(200); product = sqrt(10000)=100. So r = 100/100 = 1. Recheck: the values are consistent, giving r = 1, not 0.

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