\(Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \cdots + \beta_NX_N + \epsilon_i\)
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:
\(\begin{bmatrix} \sigma^2 & 0 & 0 & \cdots & 0 \\ 0 & \sigma^2 & 0 & \cdots & 0 \\ 0 & 0 & \sigma^2 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & \sigma^2 \end{bmatrix}\)