Correlation under rescaling

The correlation between random variables XX and YY is ρ(X,Y)=0.56\rho(X, Y) = 0.56. What is the correlation ρ(8X, Y+7)\rho(8X,\ Y + 7)?

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  1. Write correlation as covariance divided by the two standard deviations, then push the transformations through.
  2. A positive scale multiplies both numerator and one denominator factor by the same amount; a shift changes nothing. What's left?

Answer

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0.56

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Asked at: IMC, Two Sigma

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