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: **Step 1:** Estimate the original regression model and compute the residuals: $$\hat{\epsilon}_i = Y_i - \hat{\alpha} - \hat{\beta}X_{1i}$$ **Step 2:** Regress the squared residuals on a constant, all explanatory variables, their squares, and their cross-products. For a model with one explanatory variable $X_{1i}$, this becomes: $$\hat{\epsilon}_i^2 = \gamma_0 + \gamma_1 X_{1i} + \gamma_2 X_{1i}^2 + \eta_i$$ **Why Option A is correct:** - Includes the constant term ($\gamma_0$) - Includes the original explanatory variable ($\gamma_1 X_{1i}$) - Includes the squared term of the explanatory variable ($\gamma_2 X_{1i}^2$) - This is the complete specification for the White test with one explanatory variable **Why other options are incorrect:** - **Option B:** Missing the constant term - **Option C:** Missing the squared term of the explanatory variable - **Option D:** Missing the original explanatory variable term The test statistic is then computed from this auxiliary regression to test for heteroskedasticity.

Author: LeetQuiz .