The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

CHAPTER 3

Multiple Linear Regression

After reading this chapter you will understand:

• What a multiple linear regression model is.
• The assumptions about the error terms in a multiple linear regression model.
• How the regression coefficients of the model are estimated.
• The three steps necessary in designing a regression model: specification, fitting/estimating, and diagnosis.
• The tests used for determining the significance of the model and each independent variable.

It is often the case in finance that it is necessary to analyze more than one variable simultaneously. In Chapter 2, we explained how to estimate a linear dependence between two variables using the linear regression method. When there is only one independent variable, the regression model is said to be a simple linear regression or a univariate regression.

Univariate modeling in many cases is not sufficient to deal with real problems in finance. The behavior of a certain variable of interest sometimes needs to be explained by two or more variables. For example, suppose that we want to determine the financial or macroeconomic variables that affect the monthly return on the Standard & Poor's 500 (S&P 500) index. Let's suppose that economic and financial theory suggest that there are 10 such explanatory variables. Thus we have a setting of 11 dimensions—the return on the S&P 500 and the 10 explanatory variables.

In this chapter and in the next, we explain the multiple linear regression model to explain the linear relationship ...