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

If the covariance between x and y is 12, the variance of x is 16 and the variance of y is 25, what is Karl Pearson's coefficient of correlation?

The coefficient is 0.60. Correlation is covariance divided by the product of the standard deviations, which are 4 and 5, giving 12 divided by 20. Using variances instead of standard deviations would give wrong values like 0.48 or 0.75.

  1. A0.60Correct
  2. B0.48
  3. C0.75
  4. D0.30

Explanation

r = Cov/(σx σy) = 12/(4×5) = 12/20 = 0.60. The value 0.48 arises from dividing by variances' product's wrong root mix (12/25), and 0.75 from 12/16, both using a variance instead of a standard deviation.

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