CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
If the coefficient of correlation between X and Y is +0.6, and every X value is replaced by U = 5X − 10 while every Y value is replaced by V = 3 − 2Y, what is the correlation between U and V?
The correlation between U and V is −0.6. Correlation is unaffected by shifts of origin and by the size of scale changes, but multiplying one variable by a negative number reverses the sign, so the magnitude 0.6 stays and the sign becomes negative.
- A+0.6
- B−0.6Correct
- C−0.3
- D+0.3
Explanation
Correlation is independent of change of origin and scale. The scale factors are 5 (positive) and −2 (negative), so the sign reverses while magnitude stays 0.6. Thus r(U,V) = −0.6. Option +0.6 ignores the negative multiplier.
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