### Basics

Observed data: $N \times (1+K)$ matrix:

$\begin{matrix} y_{1} &x_{11} &\ldots & x_{1K} \\ &&\vdots \\ y_{N} &x_{N1} &\ldots & x_{NK} \\ \end{matrix}$

In frequentist regime, the components of this matrix are random variables. And each row corresponds to a single observation. The first column is denoted as the column vector $Y$ and the remaining columns form the $N\times K$ matrix $X$.

Goal of regression analysis is to calculate $E[Y|X]$ from a set of observations.

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