FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
The true model is Y = 1.0 + 2.0·X1 + 3.0·X2 + e. A researcher omits X2 and regresses Y on X1 alone. In the sample, regressing X2 on X1 gives a slope of 0.40. Ignoring sampling error, what slope on X1 would the short regression produce?
The short regression slope is 3.2. It equals the true coefficient of 2.0 plus the omitted variable's coefficient of 3.0 multiplied by the auxiliary slope of 0.40, which adds a bias of 1.2 to the X1 coefficient.
- A0.8
- B1.2
- C2.0
- D3.2Correct
Explanation
The short-regression slope equals the true X1 coefficient plus the X2 coefficient times the auxiliary slope: 2.0 + 3.0 × 0.40 = 2.0 + 1.2 = 3.2. Choosing 1.2 reports only the bias, and 0.8 subtracts it from the wrong base.
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