FRM Part I · FRM Exam Part I · Regression Diagnostics
The true model is Y = 1.0 + 2.0·X1 + 3.0·X2 + e. An analyst omits X2 and regresses Y on X1 only. In the sample, regressing X2 on X1 gives a slope of 0.40. What is the expected value of the estimated coefficient on X1 in the misspecified regression?
The expected coefficient is 3.2. Omitting X2 adds a bias of 3.0 times 0.40, which is 1.2, to the true coefficient of 2.0. The estimate therefore absorbs part of X2's effect through its positive correlation with X1.
- A2.0
- B1.2
- C3.2Correct
- D0.8
Explanation
The expected coefficient equals the true coefficient plus the omitted coefficient times the auxiliary slope: 2.0 + 3.0 × 0.40 = 3.2. Option B gives 3.0×0.40 alone, a missed adjustment. Option D subtracts the bias, which is the wrong sign.
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