Answer: The OLS estimator is biased.

## Explanation When an important variable is omitted from a regression model, the assumption that $E(\epsilon_i | X_i) = 0$ is violated, which means: - **The OLS estimator becomes biased** (Option A is correct) - This occurs because the omitted variable might be correlated with the included variables - The error term becomes correlated with the included variables - This violates the key assumption needed for the unbiasedness of OLS estimators ### Why other options are incorrect: - **Option B**: The product of residuals and independent variables is still zero by construction in OLS - **Option C**: The sum of residuals is still zero by construction in OLS - **Option D**: The coefficient of determination (R²) is not necessarily zero - it could still be positive if other variables explain some variation The violation of $E(\epsilon_i | X_i) = 0$ specifically leads to bias in the OLS estimator, making it inconsistent and unreliable for parameter estimation.

Author: Tanishq Prabhu