FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
The true model is Y = 2 + 1.5·X1 + 0.8·X2 + e. An analyst omits X2 and regresses Y on X1 only. Sample data show Cov(X1,X2)=0.6 and Var(X1)=2.0. What is the expected value of the estimated slope on X1 in the misspecified regression?
The expected slope is 1.74. Omitting X2 adds bias of 0.8 × (0.6/2.0) = 0.24 to the true coefficient of 1.5, because X2 has a positive effect on Y and is positively correlated with X1.
- A1.50
- B1.74Correct
- C1.26
- D0.24
Explanation
Omitted variable bias = beta2 × Cov(X1,X2)/Var(X1) = 0.8 × 0.6/2.0 = 0.24. The expected slope = 1.5 + 0.24 = 1.74. Subtracting the bias gives 1.26 (wrong sign), and 0.24 reports only the bias.
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