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.