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

Each value of x is transformed to u = (x − 50)/10 and each value of y to v = (y − 200)/25. If the correlation coefficient between u and v is −0.72, what is the correlation coefficient between x and y?

The correlation between x and y is −0.72. Pearson's coefficient is unaffected by shifting the origin or dividing by positive constants, and both divisors here are positive, so the value and sign stay the same as for u and v.

  1. A−0.72Correct
  2. B+0.72
  3. C−0.288
  4. D−1.80

Explanation

Correlation is independent of change of origin and of positive change of scale. Both divisors (10 and 25) are positive, so the sign does not change. Hence r(x,y) = r(u,v) = −0.72. The option −0.288 wrongly rescales by the ratio of scales.

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