IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
For a sample, the variances are sx² = 16 and sy² = 25, and the sample covariance is 15. Each x is then transformed to u = 3 - 2x, while y is unchanged. What is the correlation between u and y?
The correlation is -0.75. The original correlation is 15 divided by 4 times 5, which is 0.75. Correlation is unaffected by shifting or rescaling, but multiplying x by a negative number reverses its sign, so the new value is minus 0.75.
- A0.75
- B-0.75Correct
- C-1.50
- D-0.375
- 0.375
Explanation
Original r = 15/(4×5) = 0.75. Transforming by a negative multiple, u = 3 - 2x, reverses the sign but leaves magnitude unchanged, since correlation is invariant to location and scale apart from sign. So r(u,y) = -0.75. The value -1.50 comes from scaling the covariance only, which is impossible as correlation lies within [-1, 1].
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