What is the appropriate auxiliary regression form for conducting a White test for heteroscedasticity?

• A. ԑi = b0 +b1 x1i + b2 x2i + vi
• B. ԑi = b0 +b1 x1i + b2 x2i + b3 (x1i)2 + b4 (x2i)2 + b5 x1ix2i + vi
• C. ԑi2 = b0 +b1 x1i + b2 x2i + b3 (x1i)2 + b4 (x2i)2 + b5 x1ix2i + vi
• D. ԑi2 = b0 +b1 x1i + b2 x2i + b3 (x1i)2 + b4 (x2i)2 + vi

Answer: (C)

The appropriate auxiliary regression form for conducting a White test for heteroscedasticity is derived from the fundamental concept of identifying whether the variance of the errors changes with the independent variables. In this context, we focus on the squared residuals, which allow us to assess the nature of heteroscedasticity.

The form indicated emphasizes the squared residuals, as heteroscedasticity entails that the variance of the error terms is not constant across levels of independent variables. Therefore, modeling the squared residuals as a function of the independent variables—and potentially their squares and interactions—enables us to determine the presence of heteroscedasticity effectively.

This auxiliary regression takes the squared residuals from the original regression, setting them as the dependent variable. The independent variables include the original ones, their squares, and their cross-products. This comprehensive formulation captures a variety of potential patterns in how the error variance may vary with the predictors.

Identifying the correct formulation is crucial in hypothesis testing related to heteroscedasticity, and option C correctly represents that relationship by explicitly using the squared errors in regression. The other options either incorporate the residuals directly or employ a formulation that does not focus on the necessary aspect of examining the variance of the error terms concerning