- CFA Exams
- 2023 Level I
- Topic 1. Quantitative Methods
- Learning Module 2. Multiple Regression
- Subject 6. Assumptions of the Multiple Linear Regression Model

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##### Subject 6. Assumptions of the Multiple Linear Regression Model PDF Download

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 c_{0}, c_{1}, ..., c_{k}such that c_{0}+ c_{1}X_{1t}+ c_{2}X_{2t}+ ... + c_{k}X_{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 X

_{1}, X_{2}, and X_{3}, then this assumption rules out a case such as X_{3t}= d_{0}+ d_{1}X_{1t}+ d_{2}X_{2t}, for t = 1, 2, 3, ..., T. Note that if X_{3}could be perfectly explained in terms of X_{1}and X_{2}, then the variable X_{3}would provide no information that was not already included in the variables X_{1}and X_{2}. In such a case, we would not be able to determine the separate effect that X_{3}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.

**Learning Outcome Statements**

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

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**User Contributed Comments**
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Comment |
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alejandroc |
Same as univariable, plus multicollinearity. |

I used your notes and passed ... highly recommended!