I am trying to model a OLS where I know that the hetero-skedasticity is like this

$E(\epsilon^2)$ = $\sigma_i^2$ = $\delta_0$ + $\delta_1*X_{i2}$

So, I was using the concept of feasible generalized least squares and was doing the normal OLS regression

$Y$= $\beta_0$ + $\beta_1*X_{i1}$ + $\beta_2*X_{i2}$ + .......... + $\beta_k*X_{ik} + e$

Computing the $ê^2$ and then using to for another regression

$ê^2$ = $\delta_0$ + $\delta_1*X_{i2}$

and then computing the fitted values from this model as h and using them as weights as inputs in the original OLS model

to get something like:

$h^{-1/2}Y$= $h^{-1/2}\beta_0$ + $h^{-1/2}\beta_1*X_{i1}$ + $h^{-1/2}\beta_2*X_{i2}$ + .......... + $h^{-1/2}\beta_k*X_{ik} + h^{-1/2}e$

and using this model to calculate the standard errors and test statistics?

Please let me know if I am doing it right or If I am wrong somewhere.


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