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FRM Part I · FRM Exam Part I · Linear Regression

A regression gives a slope estimate of 0.54. The conventional OLS standard error is 0.20, while the heteroskedasticity-robust (White) standard error is 0.30. Using a two-sided 5% test with critical value 1.96, which conclusion is correct?

The robust t-statistic is 0.54/0.30 = 1.80, below the 1.96 critical value, so the slope is not significant at 5%. The conventional t-statistic of 2.70 overstated significance because the usual standard error was understated under heteroskedasticity.

  1. AThe robust t-statistic is 2.70, so the slope is significant
  2. BThe robust t-statistic is 1.80, so the slope is significant
  3. CThe robust t-statistic is 1.80, so the slope is not significant, and the conventional t-statistic of 2.70 overstated significanceCorrect
  4. DThe robust t-statistic is 0.60, so the slope is not significant

Explanation

Conventional t = 0.54/0.20 = 2.70, which exceeds 1.96. Robust t = 0.54/0.30 = 1.80, which is below 1.96, so the null that the slope is zero cannot be rejected. Heteroskedasticity had made the conventional standard error too small and overstated significance. The option with 1.80 and significant misapplies the critical value.

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