
Answer-first summary for fast verification
Answer: $\hat{\epsilon}_i^2 = \gamma_0 + \gamma_1 X_{1i} + \gamma_2 X_{1i}^2 + \eta_i$
## Explanation The White test for heteroskedasticity involves two main steps: 1. **First step**: Estimate the original regression model and compute the residuals 2. **Second step**: Regress the squared residuals on the original explanatory variables, their squares, and their cross-products, including a constant term In this case, since there is only one explanatory variable (X₁), the correct specification for the second step should include: - A constant term (γ₀) - The original variable (X₁) - The squared term of the variable (X₁²) Therefore, option A correctly represents the second step of the White test: $\hat{\epsilon}_i^2 = \gamma_0 + \gamma_1 X_{1i} + \gamma_2 X_{1i}^2 + \eta_i$ This specification allows testing whether the variance of the errors is related to the level of X₁ (through γ₁) and/or the squared level of X₁ (through γ₂).
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