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FRM Part I · FRM Exam Part I · Regression Diagnostics

An analyst regresses a stock's returns on market returns using 50 observations. She runs a Breusch-Pagan style auxiliary regression of the squared residuals on the explanatory variable and obtains R² = 0.12 from that auxiliary regression. Using the LM statistic n × R², what is the statistic, and is the null of homoskedasticity rejected at the 5% level given a chi-square critical value of 3.84 with 1 degree of freedom?

The LM statistic equals 50 times 0.12, which is 6.0. Since 6.0 exceeds the 5% chi-square critical value of 3.84 with one degree of freedom, the null hypothesis of homoskedasticity is rejected, indicating heteroskedastic errors.

  1. ALM = 6.0; reject the nullCorrect
  2. BLM = 6.0; fail to reject the null
  3. CLM = 0.12; fail to reject the null
  4. DLM = 4.2; fail to reject the null

Explanation

LM = n × R² = 50 × 0.12 = 6.0. This exceeds the critical value of 3.84, so homoskedasticity is rejected. The option with 4.2 uses an incorrect product, and 0.12 ignores the sample size.

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