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, Cov(X1, X2) = 0.8 and Var(X1) = 4.0. Assuming the sample relationships hold exactly, what is the expected value of the estimated coefficient on X1 in the misspecified regression?
The expected estimate is 2.6. The bias equals the omitted variable's coefficient times the slope of X2 on X1: 3.0 times 0.8 divided by 4.0, which is 0.6. Adding this to the true coefficient of 2.0 gives 2.6.
- A2.6Correct
- B1.4
- C2.0
- D3.2
Explanation
The omitted variable bias equals beta2 x Cov(X1,X2)/Var(X1) = 3.0 x 0.8/4.0 = 0.6. The estimate is 2.0 + 0.6 = 2.6. Subtracting the bias gives 1.4, which is the wrong-sign error.
Did you get it right without looking?
One question tells you little. A timed set on Regression Diagnostics shows your real accuracy, how long you take and where you lose marks.
More Regression Diagnostics questions
- A regression of a stock's return on three factors uses 64 monthly observations. The total sum of squares is 400 and the residual sum of squa…
- An analyst fits a linear regression of monthly fund returns on a market factor and plots the residuals against the fitted values. The plot s…
- A multiple regression with 5 slope coefficients and 56 observations is tested for joint significance of all slopes. The explained sum of squ…
- In a linear regression estimated by OLS, the error variance rises with the size of an explanatory variable, but the model is otherwise corre…
- 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 omit…
- In a simple regression with n = 25 observations, one observation has a standardized (studentized) residual of 3.4, but its leverage is very …