Correlation after rescaling and shifting variables

Question

If $\operatorname{Corr}(X,Y)=0.56$ , find the correlation of $8X$ with $Y+7$ .

Short answer

$0.56$ . Adding constants does not affect covariance or standard deviations, and multiplying $X$ by the positive number $8$ scales the covariance and $\sigma_X$ by the same factor, so the correlation is unchanged.

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Lessons behind this question

Maximum Likelihood Estimation: Score and Log-Likelihood
Covariance and Correlation
Populations, Samples, and Sampling Distributions

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