Encyclopedia of Financial Models II

Regression Analysis: Theory and Estimation

SERGIO M. FOCARDI, PhD

Partner, The Intertek Group

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: The tools of financial econometrics play an important role in financial model building. The most basic tool is in financial econometrics is regression analysis. The purpose in regression analysis is to estimate the relationship between a random variable and one or more independent variables. To understand and apply regression analysis one must understand the theory and the methodologies for estimating the parameters of the regression model. Moreover, when the assumptions underlying the model are violated, it is necessary to know how to remedy the problem.

Our first basic tool in econometrics is regression analysis. In regression analysis, we estimate the relationship between a random variable Y and one or more variables Xi. The variables Xi can be either deterministic variables or random variables. The variable Y is said to be the dependent variable because its value is assumed to be dependent on the value of the Xi’s. The Xi’s are referred to as the independent variables, regressor variables, or explanatory variables. Our primary focus is on the linear regression model. We will be more precise about what we mean by a “linear” regression model later in this entry. Let’s begin with a discussion of the concept of dependence.

THE CONCEPT OF DEPENDENCE

Regressions are about dependence between variables. ...