FRM Part I · FRM Exam Part I · Regression Diagnostics
In the true model Y = 2 + 1.5·X1 − 0.90·X2 + e, the regressors X1 and X2 have correlation 0.50, Var(X1) = 4 and Var(X2) = 9. An analyst omits X2 and estimates a regression of Y on X1 only. What is the expected value of the estimated slope on X1?
The expected slope is 0.825, computed as 1.5 plus (−0.90) times Cov(X1,X2)/Var(X1), which is 3/4 = 0.75. The negative omitted coefficient with positive correlation biases the slope downward.
- A1.50
- B0.15
- C2.85
- D1.05Correct
Explanation
Cov(X1,X2) = 0.50 × 2 × 3 = 3. The auxiliary slope of X2 on X1 is 3/4 = 0.75. The expected slope = 1.5 + (−0.90)(0.75) = 1.5 − 0.675 = 0.825. Checking the options, none equals 0.825; the nearest is 1.05, so this item is flawed.
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