Assume that var(u_i|X_i)= ?₀+?₁ $x _ { i } ^ { 2 }$ One way to estimate ?₀ and ?₁ consistently is to regress A) $\hat {\mathrm { u }}$ _i on $x _ { i } ^ { 2 }$ using OLS B) $\hat { u } _ { i } ^ { 2 }$ on $x _ { i } ^ { 2 }$ using OLS C) $\hat { u } _ { i } ^ { 2 }$ on $\sqrt { x }$ _iusing OLS D) $\hat { u } _ { i } ^ { 2 }$ on $x _ { i } ^ { 2 }$ using OLS but suppressing the constant ("restricted least squares")

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To estimate the variances $\sigma^2_{0}$ and $\sigma^2_{1}$ consistently, one should regress the squared residuals ($\hat{u}_i^2$) on the squared independent variable ($x_i^2$) using Ordinary Least Squares (OLS). This approach directly relates the variance of the residuals to the squared value of the independent variable, which is the essence of heteroskedasticity modeling.

Assume That Var(ui|Xi)= ?0+?1 xi2x _ { i } ^ { 2 }xi2​

Assume That Var(u_i|X_i)= ?₀+?₁ $x _ { i } ^ { 2 }$