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FRM Part I · FRM Exam Part I · Regression Diagnostics

A regression of y on x gives a slope of 2.00 with a conventional standard error of 0.50. After applying heteroskedasticity-robust (White) standard errors, the slope's standard error is 0.80. Using a two-sided 5% test with critical value 1.96, which conclusion is correct?

The conventional t-statistic is 2.00 divided by 0.50, or 4.0, and the robust t-statistic is 2.00 divided by 0.80, or 2.5. Both exceed 1.96, so the slope is significant at 5% under either standard error, though the evidence is weaker after correction.

  1. AThe slope is significant under both standard errors, because the estimate is unchanged
  2. BThe slope is significant under conventional (t = 4.0) and not significant under robust (t = 2.5)
  3. CThe slope is significant under conventional (t = 4.0) and still significant under robust (t = 2.5)Correct
  4. DThe slope is insignificant under conventional (t = 1.0) and significant under robust

Explanation

Conventional t = 2.00/0.50 = 4.0, significant. Robust t = 2.00/0.80 = 2.5, which exceeds 1.96, so still significant. The robust standard error is larger but not enough to remove significance; the coefficient itself is unchanged.

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