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##### Subject 6. Assumptions of the Multiple Linear Regression Model
The assumptions of classical normal multiple linear regression model are as follows:

1. Linear Relation: A linear relation exists between the dependent variable, Yt, and the independent variables (X1t, X2t, ..., Xkt).

2. No perfect multicollinearity: The independent variables (X1t, X2t, ..., Xkt) 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, ..., ck such that c0 + c1X1t + c2X2t + ... + ckXkt = 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 X3t = d0 + d1X1t + d2X2t, 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 (et) 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 et is a normally distributed random variable.

Learning Outcome Statements

f. explain the assumptions of a multiple regression model;

CFA® 2023 Level I Curriculum, Volume 1, Module 2

User Comment
alejandroc Same as univariable, plus multicollinearity. 