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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

A scatterplot of claim size (y) against sum insured (x) shows a clear increasing relationship, but the vertical spread of points grows as x increases. Which action is most appropriate before fitting a simple linear regression?

Apply a variance-stabilising transformation such as a logarithm to the claim size and re-plot. The widening spread shows non-constant variance, which breaks a standard linear regression assumption, and transformation commonly corrects it.

  1. ADelete the points with the largest x values
  2. BUse a histogram of x only and proceed unchanged
  3. CApply a variance-stabilising transformation such as a logarithm to y and re-plotCorrect
  4. DReplace y by its mean
  5. Fit a line through the origin without checking residuals

Explanation

Increasing spread indicates non-constant variance (heteroscedasticity), violating a linear model assumption. A log transformation of y often stabilises variance, and the re-plot checks whether it worked. Deleting points discards genuine data.

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