Values of the response variable $y$ vary according to a normal distribution with standard deviation $\sigma$ for any values of the explanatory variables $x_1, x_2,\ldots,x_k.$
The quantity $\sigma$ is an unknown parameter.

Repeated values of $y$ are independent of one another.

The relationship between the mean response of $y$ (denoted as $\mu_y$) and explanatory variables $x_1, x_2,\ldots,x_k$
is linear and is given by
$\mu_y=\beta_0+\beta_1 x_1+\cdots +\beta_k x_k$ where each $\beta_i$ is an unknown parameter.