Correlation of X with aX+b

EasyStatistics~3m

What is the correlation between XX and aX+baX + b (for constants a0a \ne 0, bb)?

Show hints (2)+
  1. Correlation ignores positive scaling and shifts.
  2. A negative slope flips the sign.

Answer

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sign(a): +1 if a>0, −1 if a<0

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Asked at: Optiver, IMC

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