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FRM Part I · FRM Exam Part I · Regression Diagnostics

An analyst regresses squared residuals from an OLS model on the explanatory variables as part of a Breusch-Pagan test. The auxiliary regression has an R-squared of 0.06 using 200 observations and 3 explanatory variables. The test statistic is n times R-squared, and the 5% chi-square critical value with 3 degrees of freedom is 7.81. What is the correct conclusion?

The Breusch-Pagan statistic equals 200 times 0.06, which is 12.0. This exceeds the 5% chi-square critical value of 7.81 with three degrees of freedom, so the null hypothesis of homoskedasticity is rejected, indicating evidence of heteroskedasticity.

  1. AStatistic is 12.0; reject homoskedasticityCorrect
  2. BStatistic is 12.0; fail to reject homoskedasticity
  3. CStatistic is 0.30; fail to reject homoskedasticity
  4. DStatistic is 6.0; fail to reject homoskedasticity

Explanation

The statistic is 200 x 0.06 = 12.0. Since 12.0 exceeds the critical value of 7.81, the null of constant error variance is rejected. The distractor of 6.0 comes from using 100 observations, and 0.30 from a wrong scaling.

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