Explanation

The White test is used to detect heteroskedasticity in regression models. The test involves two main steps:

Step 1: Estimate the original regression model and compute the squared residuals.

Step 2: Regress the squared residuals on:

• A constant term
• All original explanatory variables
• All cross-products (squares and interactions) of the explanatory variables

For a model with one explanatory variable (X₁), the correct specification for the second step is: $\hat{\epsilon}_i^2 = \gamma_0 + \gamma_1 X_{1i} + \gamma_2 X_{1i}^2 + \eta_i$

Why Option A is correct:

• Includes the constant term (γ₀)
• Includes the original explanatory variable (X₁i)
• Includes the squared term of the explanatory variable (X₁i²)

Why other options are incorrect:

• Option B: Missing the constant term
• Option C: Missing the squared term (cross-product)
• Option D: Missing the original explanatory variable, only includes the constant and squared term

The test statistic is then computed from this auxiliary regression to determine if heteroskedasticity is present.