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FRM Part I · FRM Exam Part I · Regression Diagnostics

An analyst runs a Breusch-Pagan test by regressing the squared residuals from an original model on the model's 3 explanatory variables. The auxiliary regression uses 200 observations and has R-squared of 0.06. Using the LM statistic n x R-squared, and a 5% chi-square critical value of 7.815 with 3 degrees of freedom, what is the conclusion?

The Breusch-Pagan LM statistic equals 200 times 0.06, which is 12.0. Because this exceeds the 5% chi-square critical value of 7.815 with 3 degrees of freedom, the analyst rejects the null hypothesis of homoskedasticity and concludes the errors show heteroskedasticity.

  1. ALM = 12.0; reject homoskedasticityCorrect
  2. BLM = 12.0; fail to reject homoskedasticity
  3. CLM = 0.06; fail to reject homoskedasticity
  4. DLM = 33.3; reject homoskedasticity

Explanation

LM = 200 x 0.06 = 12.0. This exceeds the critical value of 7.815, so the null of homoskedasticity is rejected. Option 2 has the correct statistic but the wrong decision. Option 4 divides n by R-squared (200/0.06 = 3,333, not 33.3) and is wrong.

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