Normal Errors Linear Model
Why
We model a real-valued output as corrupted by small random errors with a normal density. In other words, we make further distributional assumptions on the probabilistic errors linear model for the purposes of hypothesis testing and interval estimation.1
Definition
Let $(x, A, e)$ be a probabilistic errors model and assume $e$ has a normal density with mean $0$ and covariance $\sigma ^2I$. In this case we call $(x, A, e)$ a classical linear model with normality assumption. In this case $y$ is normally distributed with mean $Ax$ and variance $\sigma ^2I$.
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