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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

A risk analyst finds that the variance of regression errors is proportional to the square of a regressor X (Var(e) = σ²X²). Which remedy yields efficient estimates under this known form?

Weighted least squares, dividing each observation by X, is the efficient remedy. Dividing by X makes the transformed error variance constant at σ², restoring the homoskedasticity needed for the best linear unbiased estimator, whereas plain OLS remains inefficient with unreliable standard errors.

  1. AWeighted least squares, dividing each observation by XCorrect
  2. BDropping X from the model
  3. CAdding a lagged dependent variable
  4. DOrdinary least squares with no changes to the standard errors

Explanation

When Var(e) = σ²X², dividing the equation by X gives errors with constant variance σ², so weighted least squares (weights 1/X²) is efficient. Dropping X would risk omitted variable bias. Plain OLS stays unbiased but is not efficient, and its standard errors are wrong.

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