Assume that the variance depends on a third variable, Wi, which does not appear in the regression function, and that var(u_i|X_i,W_i)= ?₀+?₁ $\frac { 1 } { W _ { i } }$ One way to estimate ?₀ and ?₁consistently is to regress A) $\hat {\mathrm { u }}$ _i on $w _ { i } ^ { 2 }$ using OLS B) $\hat {\mathrm { u }}$ _i on $\frac { 1 } { W _ { i } }$ using OLS C) $\hat { u } _ { i } ^ { 2 }$ on $\frac { X _ { i } } { W _ { i } }$ using OLS D) $\hat { u } _ { i } ^ { 2 }$ on $\frac { 1 } { W _ { i } }$ using OLS

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Given the variance depends on $Wi$ as $var(u|X,W) = \alpha_0 + \alpha_1 \frac{1}{W_i}$, to estimate $\alpha_0$ and $\alpha_1$ consistently, one should regress the squared residuals ($\hat{u}_i^2$) on the inverse of $W_i$ ($\frac{1}{W_i}$) using Ordinary Least Squares (OLS). This approach directly addresses the heteroscedasticity issue by modeling the variance as a function of $W_i$.

Assume That the Variance Depends on a Third Variable, Wi 1Wi\frac { 1 } { W _ { i } }Wi​1​

Assume That the Variance Depends on a Third Variable, Wi $\frac { 1 } { W _ { i } }$