TAILIEUCHUNG - Lecture Introductory econometrics for finance – Chapter 4: Further development and analysis of the classical linear regression model

In this chapter, you will learn how to: Construct models with more than one explanatory variable, test multiple hypotheses using an F-test, determine how well a model fits the data, form a restricted regression, derive the OLS parameter and standard error estimators using matrix algebra, estimate multiple regression models and test multiple hypotheses in EViews. | Chapter 4 Further development and analysis of the classical linear regression model ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 Generalising the Simple Model to Multiple Linear Regression • Before, we have used the model yt = α + βxt + ut t = 1,2,.,T • But what if our dependent (y) variable depends on more than one independent variable? For example the number of cars sold might plausibly depend on 1. 2. 3. 4. the the the the price of cars price of public transport price of petrol extent of the public’s concern about global warming • Similarly, stock returns might depend on several factors. • Having just one independent variable is no good in this case - we want to have more than one x variable. It is very easy to generalise the simple model to one with k − 1 regressors (independent variables). ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 Multiple Regression and the Constant Term • Now we write yt = β1 + β2 x2t + β3 x3t + . + βk xkt + ut , t=1,2,., T • Where is x1 ? It is the constant term. In fact the constant term is usually represented by a column of ones of length T: 1 1 x1 = · · · 1 β1 is the coefficient attached to the constant term (which we called α before). ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Different Ways of Expressing the Multiple Linear Regression Model • We could write out a separate equation for every value of t: y1 = β1 + β2 x21 + β3 x31 + · · · + βk xk1 + u1 y2 = β1 + β2 x22 + β3 x32 + · · · + βk xk2 + u2 . yT . = . . β1 + β2 x2T + β3 x3T + · · · + βk xkT + uT • We can write this in matrix form y = Xβ + u where: y is T × 1 X is T × k β is k × 1 ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 u is T × 1 4 Inside the Matrices of the Multiple Linear Regression Model • . if k is 2, we have 2 regressors, one of which is a column of ones: y1 y2 . . . yT 1 1 = . . . T .

• Kinh tế học
• Econometrics for Finance
• Introductory Econometrics for Finance
• Financial data
• Financial modelling
• Classical linear regression model
• Multiple linear regression
• Regression model
• Purpose of econometrics
• Econometric model
• Straight lines
• Statistical foundations
• Regression analysis
• Statistical distributions
• Univariate time series modelling
• Stochastic processes
• Multivariate models
• Simultaneous equations models
• Modelling long run relationship
• Stochastic non stationarity
• Modelling volatility
• GARCH models
• Switching models
• Switching behaviour
• Panel data
• Fixed effects models
• Limited dependent variable models
• Linear probability model
• Simulation methods
• Random number generation
• Empirical research project
• Research project