Question:
If the correlation coefficient between two variables X and Y is 0.5, then the correlation coefficient between \(Z = 3X - 2\) and \(W = 2 - 3Y\) is:
If the correlation coefficient between two variables X and Y is 0.5, then the correlation coefficient between \(Z = 3X - 2\) and \(W = 2 - 3Y\) is:
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Correlation is invariant to origin/scale changes, but a negative scaling constant on one variable flips the sign.
Updated On: Jul 4, 2026
- 0.5
- 0.15
- -0.15
- -0.5
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The Correct Option is D
Solution and Explanation
Step 1: Write \(Z=3X-2\) (coefficient of X is \(a=3\)) and \(W = 2-3Y = -3Y+2\) (coefficient of Y is \(b=-3\)).
Step 2: Correlation is unaffected by change of origin and scale up to the sign of the scaling constants: \(r(aX+c,\,bY+d) = \text{sign}(a)\,\text{sign}(b)\,r(X,Y)\).
Step 3: Here \(\text{sign}(a)=\text{sign}(3)=+1\) and \(\text{sign}(b)=\text{sign}(-3)=-1\), so the product of signs is \(-1\).
Step 4: Therefore \(r(Z,W) = -1 \times 0.5 = -0.5\).
\[\boxed{r(Z,W) = -0.5}\]Was this answer helpful?
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