IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
A regression of y on x gives a fitted slope of 0.6. The sample standard deviations are sx = 5 and sy = 10. What is the sample correlation coefficient between x and y?
The correlation is 0.30. The regression slope equals the correlation times sy over sx, so r equals 0.6 times 5 divided by 10, which is 0.30. The slope is not itself the correlation unless the two standard deviations are equal.
- A0.30Correct
- B1.20
- C0.60
- D0.75
- 0.12
Explanation
Slope b = r·sy/sx, so r = b·sx/sy = 0.6×5/10 = 0.30. Option 1.20 inverts the ratio and is impossible. Option 0.60 wrongly equates slope with correlation.
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