Normal Linear Model

Although linearity and constant variance are the most important assumptions that are needed for the inference reported by Minitab to be reliable, we also need two more:

Normal distribution
The response should have a normal distribution at each value of the explanatory variable. This is an assumption about the conditional distribution of the response at each x-value not the marginal distribution. In the context of the slug data, this assumption means that the log-weights of the 5 cm slugs should have a normal distribution. Similarly, the log-weights of the 1 cm slugs should be normally distributed, etc.
Independence
All observations must be independently obtained. Independence is a function of how the data were collected. It is most often violated when the observations are collected in sequence — outside influences may affect a series of adjacent values, making them correlated. The slug data were collected in sequence over 4 years, so there is potential for this assumption to be violated if slugs in one year (or season) are markedly different from those at other times.

When all four assumptions hold — linearity, constant variance, normality and independence — the model is called a normal linear model.

(Section 1.4 of the CAST e-book about regression contains more detail about normal linear regression models.)