alleryPearson's r changes sign when
Ax is multiplied by 3
Bx is replaced by x + 5
Cy is increased by 10
Dx is replaced by -x
Answer & Solution
Correct answer: D. x is replaced by -x
1. r is invariant under positive scaling and translation.
2. Replacing x by -x is multiplication by -1, a negative scale change.
3. Cov(-x, y) = -Cov(x, y); sigma of -x equals sigma of x.
4. So r flips sign; the other options leave r unchanged.
_Source: ICAI BoS Foundation Paper 3, Ch 17 'Correlation', p.7_
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