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Lecture Introductory Econometrics for Finance: Chapter 3 - Chris Brooks

Chapter 3 - A brief overview of the classical linear regression model. 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. | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 3 A brief overview of the classical linear regression model ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 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’ © Chris Brooks 2013 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 x dependent variable independent variables regressand regressors effect variable causal variables explained variable explanatory variable Note that there can be many x variables but we will . | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 3 A brief overview of the classical linear regression model ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 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’ © Chris Brooks 2013 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 x dependent variable independent variables regressand regressors effect variable causal variables explained variable explanatory variable 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’ © Chris Brooks 2013 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, i.e. to have a probability distribution. The x variables are, however, assumed to have fixed (“non-stochastic”) values in repeated samples. ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 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 .