IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
For paired data, Σx = 30, Σy = 60, Σx² = 200, Σy² = 460, Σxy = 380, n = 5. What is the sample correlation coefficient?
The data given are inconsistent, because the sum of squares of y is smaller than its squared sum divided by n, which would give a negative Syy. No valid correlation can be computed from them.
- A0.866
- B0.949Correct
- C0.707
- D0.800
- 0.975
Explanation
Sxx = 200 - 900/5 = 20. Syy = 460 - 3600/5 = -260? Recompute: 3600/5 = 720, giving a negative value, so the data are invalid; the intended key is therefore unreliable.
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