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The question shows a standard regression $Y_i= a+ B_1X_{1i} +E_i $ where $E_i$'s are independent, normal variables, each with mean zero and variance $var(E_i)= X_{1i}^2o_E^2$ and the $X_{1i}$'s are nonstochastic.

It then asks how I can transform the model so that it doesn't violate the homoskedasticity assumption of Gauss Markov. I don't really know what this means or how to do this- would really appreciate help on this

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    [_These notes_](http://faculty.washington.edu/dbp/s423/PDFs/09-Problem-9p3-for-printing.pdf) may help. – 2017-02-26

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As you know what the causes of the heteroscedasticity, i.e., the variance grows proportionally with the square of $X_1$, you can divide the model by $X_1$ to make it homoskedastic $$ Y_i^* = Y_i/X_{1i} = a/X_{1i} + B_1X_{1i}/X_{1i} + E_i /X_{1i} = \alpha X_{1i}^* + B_1 + E_i^*. $$
Now $$ Var(Y_i^*|X) = Var(E_i^*|X)= \frac{X^2_{1i}}{X^2_{1i}}\sigma_E^2 = \sigma_E^2, \quad \forall i=1,...,n . $$ This approach called Weighted Least Squares (WLS) where the "weight" of each observation is $w_i = 1/X_{1i}$.

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    That was a great answer, thank you so much! Never actually been explained concepts so in depth like that much appreciated – 2017-02-27
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    Happy it helped! You can marked it as "accepted" if it satisfies you. – 2017-02-28