Lecture 2_ Regression model

Lecture 2: The Linear Regression Model Đinh Thi Thanh Binh, PhD Faculty of International Economics, FTU 1 1. Introduction to regression model • The term « regression » means «regression to mediocrity» • Defined by Galton (1886) when he studied the relationship between the height of sons and the height of fathers 2 Distribution of the height of sons respects to the height of the fathers 3 The study shows that: • Given the height of fathers, the height of sons will distribute around a medium value • On average, when the height of fathers increase, the height of sons also increase • If we conect all the medium points, we will have a linear line • This line is called regression line, showing the relationship between the height of sons and the height of father on average 4 2. Population Regression Function (PRF) and Sample Regression Function (SRF) 2.1. Definition of PRF PRF is a regression function that is constructed based on the survey of the population For example: For example, Galton studied the relationship between the height of fathers and the height of sons in one city. He collected the data of all fathers having adult sons. So he can build PRF. 5 So, E(Y|Xi) is a function of independent variable Xi : E(Y/Xi)= f(Xi) = β0+ β1Xi [1] • The equation [1] is called Population regression function (PRF). – PRF shows how the expected value of Y changes at different values of X – If PRF has 1 independent variable simple regression function – If PRF has 2 or more independent variables multiple regression function 6 • Suppose that PRF E(Y|Xi) is a linear function, then: E(Y|Xi)= β0+ β1Xi [2] - β0, β1: regression coefficients/ parameters • β0: constant coefficient • β1: slope coefficient • The equation [2] is a simple regression function 7 2.2. Error/ disturbance term • Because E(Y|Xi) is expected value of Y given Xi, single values of Yi is not necessary the same with E(Y|Xi), but they are around E(Y/Xi). • Note ui is the difference between Yi and E(Y/Xi), we have: ui= Yi- E(Y|Xi) [3] Or : Yi= E(Y|Xi)+ ui [4] ui is a random variable/ component or disturbance 8