Correlation after affine maps with opposite signs

Question

Random variables $X$ and $Y$ have correlation $-0.4$ . Find the correlation between $3X+1$ and $1-Y$ , or enter $100$ if it cannot be found.

Short answer

$0.4$ . Affine maps leave the magnitude of correlation alone; only the sign of the product of the slopes matters. Here the slopes are $3$ and $-1$ , so the sign flips: $0.4$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Covariance and Correlation
Populations, Samples, and Sampling Distributions

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