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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

A scatter plot of 50 pairs (x, y) of vehicle age and repair cost shows points lying closely along a curve that rises steeply, with the spread of y increasing as x increases. Which action is most appropriate before fitting a simple linear regression?

Apply a log transformation to y and re-plot. Curvature with variance growing as x increases is a typical sign of multiplicative effects, and taking logs of the response often straightens the relationship and stabilises the spread, making linear regression more suitable.

  1. ADelete the points with the largest y values
  2. BApply a log transformation to y and re-plotCorrect
  3. CReplace x by its rank and use a pie chart
  4. DUse a stem-and-leaf plot of x only
  5. Fit the line without change as the correlation is positive

Explanation

Curvature together with spread increasing with x suggests a multiplicative relationship; a log transformation of y often linearises it and stabilises variance. Deleting points is unjustified, and a positive correlation does not validate the linear form.

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