In this chapter, you will learn how to: Derive the OLS formulae for estimating parameters and their standard errors, explain the desirable properties that a good estimator should have, discuss the factors that affect the sizes of standard errors, test hypotheses using the test of significance and confidence interval approaches, interpret p-values, estimate regression models and test single hypotheses in EViews. | Chapter 3 A brief overview of the classical linear regression model ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 Regression • Regression is probably the single most important tool at the econometrician’s disposal. But what is regression analysis? • It is concerned with describing and evaluating the relationship between a given variable (usually called the dependent variable) and one or more other variables (usually known as the independent variable(s)). ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 Some Notation • Denote the dependent variable by y and the independent variable(s) by x1 , x2 , ., xk where there are k independent variables. • Some alternative names for the y and x variables: y dependent variable regressand effect variable explained variable x independent variables regressors causal variables explanatory variabl • Note that there can be many x variables but we will limit ourselves to the case where there is only one x variable to start with. In our set-up, there is only one y variable. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Regression is different from Correlation • If we say y and x are correlated, it means that we are treating y and x in a completely symmetrical way. • In regression, we treat the dependent variable (y) and the independent variable(s) (x’s) very differently. The y variable is assumed to be random or “stochastic” in some way, . to have a probability distribution. The x variables are, however, assumed to have fixed (“non-stochastic”) values in repeated samples. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 4 Simple Regression • For simplicity, say k=1. This is the situation where y depends on only one x variable. • Examples of the kind of relationship that may be of interest include: – How asset returns vary with their level of market risk – Measuring the long-term relationship between stock prices and dividends. – Constructing an
