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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

A scatterplot of monthly claim frequency against policyholder age shows a clear U-shaped pattern, and the sample Pearson correlation coefficient is close to 0. Which conclusion is most appropriate?

Pearson correlation measures only linear association. A symmetric U-shaped relationship has rising and falling parts that cancel, giving a coefficient near zero even though age strongly affects claim frequency. Zero correlation therefore does not imply independence, and the scatterplot should guide the choice of model.

  1. AAge and claim frequency are independent, so age can be ignored
  2. BPearson correlation measures only linear association, so a strong non-linear relationship may still existCorrect
  3. CThe data must contain outliers that cancel the correlation
  4. DSpearman's rank correlation would necessarily be close to 1
  5. The sample size must be too large for correlation to be estimated

Explanation

Pearson's r captures only linear association. A symmetric U-shape has positive and negative slopes cancelling, giving r near 0 despite strong dependence. Spearman's rank correlation is also monotonic-based, so it would also be near 0, not 1.

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