Explanation

The White test procedure consists of two main steps:

Step 1: Estimate the original regression model and compute the residuals: $\hat{\epsilon}_i = Y_i - \hat{Y}_i$

Step 2: Regress the squared residuals on:

• A constant term
• All original explanatory variables
• The squares of all explanatory variables
• All cross-products of the explanatory variables

Why Option D is correct:

• It correctly specifies that we regress the squared residuals (not the residuals themselves)
• It includes all the necessary components: constant, original variables, their squares, and cross-products
• This complete specification allows the test to detect various forms of heteroskedasticity

Why other options are incorrect:

• Option A: Regresses residuals (not squared residuals) and misses squares and cross-products
• Option B: Regresses residuals (not squared residuals) though it includes the correct regressors
• Option C: Correctly uses squared residuals but misses the squares and cross-products of explanatory variables

After performing this auxiliary regression, the test statistic is computed as $nR^2$ from this regression, which follows a chi-square distribution under the null hypothesis of homoskedasticity.