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

CHAPTER 2

Simple Linear Regression

After reading this chapter you will understand:

• How to estimate a simple linear regression.
• What is meant by the residual or error of a regression model.
• The distributional assumptions of a regression model.
• The assumptions about mean and variance of the error term in a regression model.
• How to measure the goodness-of-fit of a regression model.
• How to estimate a linear regression for a nonlinear relationship.

In this chapter, we introduce methods to express joint behavior of two variables. It is assumed that, at least to some extent, the behavior of one variable is the result of a functional relationship between the two variables. In this chapter, we introduce the linear regression model including its ordinary least squares estimation, and the goodness-of-fit measure for a regression. Although in future chapters covering econometric tools we will not focus on estimating parameters, we will do so here in order to see how some of the basic measures are calculated. We devote Chapter 13 to explaining the various methods for estimating parameters.

Before advancing into the theory of regression, we note the basic idea behind a regression. The essential relationship between the variables is expressed by the measure of scaled linear dependence, that is, correlation.

THE ROLE OF CORRELATION

In many applications, how two entities behave together is of interest. Hence, we need to analyze their joint distribution. In particular, we are interested in the ...