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IAI Actuarial Core Principles · Actuarial Statistics · Purpose and function of data analysis

A health insurer fits a regression of claim cost (₹ thousand) on age: cost = 4.0 + 0.5 × age, using policyholders aged 25 to 60. It uses the model to forecast cost for a 40-year-old new applicant, and also for a 85-year-old. Which statement is most appropriate?

The age-40 forecast is ₹24 thousand, obtained by interpolation within the observed age range of 25 to 60. The age-85 forecast is an extrapolation beyond the data, so the linear relationship may not hold and it is less reliable.

  1. AThe forecast for age 40 is ₹24 thousand and is an interpolation; the forecast for age 85 is an extrapolation and less reliableCorrect
  2. BThe forecast for age 40 is ₹24 thousand; age 85 gives ₹46.5 thousand which is equally reliable
  3. CThe forecast for age 40 is ₹20.5 thousand; age 85 is an interpolation
  4. DThe forecast for age 40 is ₹44 thousand; age 85 cannot be computed
  5. Both forecasts are descriptive statistics, not predictions

Explanation

At age 40: 4.0 + 0.5×40 = 24. Age 40 lies within 25 to 60, so it is interpolation. Age 85 lies outside the observed range, so it is extrapolation (value 46.5) and the linear relationship may not hold.

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