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CA Foundation · Quantitative Aptitude · Correlation and Regression

For a set of paired data on the monthly sales and advertising expenditure of a Pune retailer, Cov(x, y) = 12, σx = 4 and σy = 5. What is Karl Pearson's coefficient of correlation between x and y?

Karl Pearson's coefficient equals covariance divided by the product of the two standard deviations. Here that is 12 divided by (4 times 5), which gives 0.60. The other options use a wrong denominator, and 2.40 is impossible because r must lie between -1 and +1.

  1. A0.60Correct
  2. B0.48
  3. C0.75
  4. D2.40

Explanation

r = Cov(x, y)/(σx·σy) = 12/(4×5) = 12/20 = 0.60. Dividing by σy² (25) gives 0.48 and dividing by σx² (16) gives 0.75, which are wrong denominators. 2.40 comes from dividing by σy alone. Values beyond 1 are impossible for r anyway.

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