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$$ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \cdots + \beta_NX_N + \epsilon_i $$
The coefficient matrix for the model specified above is:
$$
\begin{bmatrix}
\beta_0 \\
\beta_1 \\
\beta_2 \\
\vdots \\
\beta_N
\end{bmatrix}
$$
And the variance-covariance matrix for the errors $\epsilon_i$ in the model is typically denoted as $\sigma^2\times I$, where $\sigma^2$ is the variance of the errors and $I$ is the identity matrix. The variance-covariance matrix for the errors is:
$$
\begin{bmatrix}
\sigma^2 & 0 & 0 & \cdots & 0 \\
0 & \sigma^2 & 0 & \cdots & 0 \\
0 & 0 & \sigma^2 & \cdots & 0 \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
0 & 0 & 0 & \cdots & \sigma^2
\end{bmatrix}
$$