The assumptions of classical normal multiple linear regression model are as follows:

1. Linear Relation: A linear relation exists between the dependent variable, Y_t, and the independent variables (X_1t, X_2t, ..., X_kt).

2. No perfect multicollinearity: The independent variables (X_1t, X_2t, ..., X_kt) are not random. Also, no exact linear relation exists between two or more of the independent variables. That is, it's not possible to find a set of numbers c₀, c₁, ..., c_k such that c₀ + c₁X_1t + c₂X_2t + ... + c_kX_kt = 0 for every t = 1, 2, ... T. The purpose is to exclude independent variables that can be determined exactly as a linear function of other independent variables.

For example, if our model contains the variables X₁, X₂, and X₃, then this assumption rules out a case such as X_3t = d₀ + d₁X_1t + d₂X_2t, for t = 1, 2, 3, ..., T. Note that if X₃ could be perfectly explained in terms of X₁ and X₂, then the variable X₃ would provide no information that was not already included in the variables X₁ and X₂. In such a case, we would not be able to determine the separate effect that X₃ has on the dependent variable. As a practical matter, it is safe to assume that this assumption is not violated.

3. Zero mean: For any set of values of the independent variables, the expected value of the error term is 0.

4. Homoscedasticity: The variance of the error term is the same for all values of the independent variables.

5. No serial correlation: The error term (e_t) is uncorrelated across observations. In other words, for i ≠ j the error terms are independent of one another.

6. Normality: For any set of values of the independent variables, the error term e_t is a normally distributed random variable.