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

The correlation coefficient between variables X and Y is 0.6. New variables are defined as U = 2X + 3 and V = 5 - 3Y. What is the correlation coefficient between U and V?

Correlation is unaffected by shifting origin or by multiplying by the magnitude of a constant. Since U rises with X while V falls as Y rises, the scale factors have opposite signs, so the sign of r reverses. The correlation between U and V is therefore -0.6.

  1. A0.6
  2. B-0.6Correct
  3. C-0.9
  4. D-0.2

Explanation

Correlation is independent of a change of origin and scale, but the sign changes when the two scale factors have opposite signs. U has a positive scale factor (2) and V has a negative one (-3), so r(U,V) = -0.6. Choosing 0.6 ignores the sign reversal.

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