Answer: II and III only

## Explanation Omitted variable bias occurs in regression analysis when a relevant variable is excluded from the model, leading to biased and inconsistent estimates of the regression coefficients. For omitted variable bias to occur, two key conditions must be met: ### **Condition II: At least one of the included regressors must be correlated with the omitted variable** - If the omitted variable is uncorrelated with all included regressors, then omitting it does not cause bias in the coefficient estimates. - The correlation creates a situation where the included variable is "picking up" some of the effect of the omitted variable. ### **Condition III: The omitted variable must be a determinant of the dependent variable** - If the omitted variable does not affect the dependent variable, then omitting it doesn't matter. - The omitted variable must be relevant to explaining variation in the dependent variable. ### **Why the other conditions are not necessary:** **Condition I (R² vs adjusted R²):** This is irrelevant to omitted variable bias. R² and adjusted R² are measures of model fit, not conditions for bias. **Condition IV (Homoskedasticity):** Homoskedasticity relates to the variance of errors, not omitted variable bias. Heteroskedasticity affects efficiency of estimates, not bias from omitted variables. **Condition V (Number of regressors ≤ 5):** This is arbitrary and irrelevant. Omitted variable bias can occur regardless of the number of included regressors. ### **Key Insight:** Omitted variable bias is essentially a problem of **endogeneity** - when an explanatory variable is correlated with the error term. When a relevant variable is omitted and correlated with included variables, that omitted variable's effect becomes part of the error term, creating correlation between the included variable and the error term. **Mathematically:** If the true model is: $$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$$ But we estimate: $$Y = \beta_0 + \beta_1 X_1 + u$$ where $u = \beta_2 X_2 + \epsilon$ Then $\hat{\beta}_1$ will be biased if $X_1$ and $X_2$ are correlated, because $\text{Cov}(X_1, u) = \beta_2 \text{Cov}(X_1, X_2) \neq 0$.

Author: Nikitesh Somanthe