I have the following linear regression model:
$$Y_i = \alpha + \beta x + \varepsilon_i, i=1,...,n,$$
with $E(\varepsilon_i)=0$, and with $Var(\varepsilon_i)=a_i\sigma^2$ for all i, with $a_i$ known. I want to transform the model such that the variance is constant($Var(\varepsilon_i)=\sigma^2$), and keep $E(\varepsilon_i)=0$.
I was thinking about perhaps some type of Box-Cox transformation, but to be honest I'm quite stuck. Any ideas?
Edit: I let $\tilde{Y}_i=\frac{Y_i}{\sqrt{a_i}}$, which yields a new model with the desired constant variance.