FRM Part I · FRM Exam Part I · Linear Regression
In the simple linear regression Y = a + bX + e estimated by OLS, which condition is required for the OLS slope estimator to be unbiased?
The OLS slope is unbiased when the error term has zero conditional mean given the regressor, meaning the regressor is uncorrelated with the error. Normality of errors only matters for exact small-sample inference, and sample size is not required for unbiasedness.
- AThe error term has zero conditional mean given XCorrect
- BThe error term is normally distributed
- CThe dependent variable Y has a constant variance equal to one
- DThe sample size exceeds 1,000 observations
Explanation
Unbiasedness requires E[e|X] = 0 (exogeneity), so X is uncorrelated with the error. Normality is needed only for exact small-sample inference, not for unbiasedness. Variance of Y and a large sample size are not conditions for unbiasedness.
Did you get it right without looking?
One question tells you little. A timed set on Linear Regression shows your real accuracy, how long you take and where you lose marks.
More Linear Regression questions
- In a multiple regression, the estimated slopes are b1 = 0.80 and b2 = 0.30, with standard errors 0.20 and 0.15. The estimated covariance bet…
- An analyst regresses monthly fund excess returns (in %) on a dummy variable D that equals 1 in months when the market return was negative an…
- In a simple linear regression of Y on X with an intercept, the sample correlation between X and Y is 0.60, the sample standard deviation of …
- A risk analyst tests whether a regression slope is zero and obtains a p-value of 0.03. Which conclusion is correct?
- A simple regression has an estimated slope of 0.80 with standard error 0.32, estimated from 22 observations. The critical t-value for a two-…
- In a simple linear regression of Y on X with 25 observations, the total sum of squares (TSS) is 400 and the sum of squared residuals (SSR, r…