IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
For a sample of n = 8 paired observations, Sxx = 40, Syy = 90 and Sxy = 30. What is the sample correlation coefficient?
The correlation coefficient is 0.5. It equals Sxy divided by the square root of the product of Sxx and Syy, which is 30 divided by the square root of 3600, that is 30 divided by 60.
- A0.250
- B0.500Correct
- C0.333
- D0.750
- 0.667
Explanation
r = Sxy / sqrt(Sxx * Syy) = 30 / sqrt(3600) = 30/60 = 0.5. Option 0.750 comes from dividing by sqrt(40*90)/... incorrectly, e.g. using 40 as the denominator (30/40). Option 0.333 uses 90 as the denominator.
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