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Basics of Multiple Regression and Underlying Assumptions

2025 Curriculum CFA® Program Level II Quantitative Methods

Introduction

Multiple linear regression uses two or more independent variables to describe the variation of the dependent variable rather than just one independent variable, as in simple linear regression. It allows the analyst to estimate using more complex models with multiple explanatory variables and, if used correctly, may lead to better predictions, better portfolio construction, or better understanding of the drivers of security returns. If used incorrectly, however, multiple linear regression may yield spurious relationships, lead to poor predictions, and offer a poor understanding of relationships.

The analyst must first specify the model and make several decisions in this process, answering the following, among other questions: What is the dependent variable of interest? What independent variables are important? What form should the model take? What is the goal of the model—prediction or understanding of the relationship?

The analyst specifies the dependent and independent variables and then employs software to estimate the model and produce related statistics. The good news is that the software, such as shown in Exhibit 1, does the estimation, and our primary tasks are to focus on specifying the model and interpreting the output from this software, which are the main subjects of this content.

Learning Outcomes

The candidate should be able to:

  • describe the types of investment problems addressed by multiple linear regression and the regression process;
  • formulate a multiple linear regression model, describe the relation between the dependent variable and several independent variables, and interpret estimated regression coefficients; and
  • explain the assumptions underlying a multiple linear regression model and interpret residual plots indicating potential violations of these assumptions.

0.75 PL Credit

If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.