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FRM Part I · FRM Exam Part I · Regression Diagnostics

A regression of y on x gives a slope estimate of 0.80 with a conventional standard error of 0.20. After applying White's heteroskedasticity-robust standard error, the standard error becomes 0.40. Testing the null that the true slope is zero, which conclusion is correct at the 5% level using a critical value of about 1.96?

Both t-statistics exceed 1.96: 0.80/0.20 equals 4.0 under the conventional error and 0.80/0.40 equals 2.0 under the robust error. The null of a zero slope is therefore rejected under both standard errors, though with weaker evidence after the robust correction.

  1. AReject the null under both standard errors
  2. BFail to reject the null under both standard errors
  3. CReject the null using the conventional standard error but not the robust oneCorrect
  4. DReject the null using the robust standard error but not the conventional one

Explanation

Conventional t = 0.80/0.20 = 4.0, which exceeds 1.96, so reject. Robust t = 0.80/0.40 = 2.0... which is just above 1.96, so it would also reject; therefore the data must be read precisely: 2.0 > 1.96 means rejection under both.

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