Skip to content

FRM Part I · FRM Exam Part I · Linear Regression

In the simple linear regression Y = a + bX + e, which set of conditions is, under the classical assumptions, sufficient for the OLS slope estimator to be unbiased?

OLS slope unbiasedness requires that the error has zero conditional mean given the regressor and that the regressor actually varies. Homoskedasticity and normality matter for efficiency and inference, not bias, and R-squared or sample size cannot cure a correlation between the regressor and the error.

  1. AThe error term has zero conditional mean given X, and X varies across observationsCorrect
  2. BThe errors are homoskedastic and normally distributed, with no restriction on their relation to X
  3. CThe sample size is large and R-squared is above 0.5
  4. DThe errors have constant variance and the regressor has a mean of zero

Explanation

Unbiasedness of the OLS slope requires E[e|X]=0 (exogeneity) and variation in X so the slope is defined. Homoskedasticity and normality affect efficiency and inference, not unbiasedness. A high R-squared or large sample does not fix a violation of exogeneity.

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.

Practise Linear RegressionFree diagnostic mock

More Linear Regression questions