> This is incorrect. Linear regression does not require the outcomes follow a normal distribution. Rather, it requires that the residual errors are normally distributed.
No, the author's formulation and yours are mathematically equivalent statements, and specifying the conditional distribution of the outcomes is the version that generalizes to GLMs.
No, the author's formulation and yours are mathematically equivalent statements, and specifying the conditional distribution of the outcomes is the version that generalizes to GLMs.