文档介绍：Economics 20 - Prof. Anderson 1 The Simple Regression Model y = ? 0 + ? 1x + u Economics 20 - Prof. Anderson 2 Some Terminology In the simple linear regression model, where y = ? 0 + ? 1x + u , we typically refer to y as the ? Dependent Variable, or ? Left-Hand Side Variable, or ? Explained Variable, or ? Regressand Economics 20 - Prof. Anderson 3 Some Terminology, cont. In the simple linear regression of y on x, we typically refer to x as the ? Independent Variable, or ? Right-Hand Side Variable, or ? Explanatory Variable, or ? Regressor , or ? Covariate, or ? Control Variables Economics 20 - Prof. Anderson 4 A Simple Assumption The average value of u , the error term, in the population is 0. That is, E(u ) = 0 This is not a restrictive assumption, since we can always use ? 0 to normalize E(u ) to 0 Economics 20 - Prof. Anderson 5 Zero Conditional Mean We need to make a crucial assumption about how u and x are related We want it to be the case that knowing something about x does not give us any information about u, so that they are completely unrelated. That is, that E(u|x ) = E(u ) = 0, which implies E(y|x ) = ? 0 + ? 1x Economics 20 - Prof. Anderson 6.. x 1x 2 E( y|x ) as a linear function of x , where for any x the distribution of y is centered about E( y|x ) E(y|x ) = ? 0 + ? 1x y f(y) Economics 20 - Prof. Anderson 7 Ordinary Least Squares Basic idea of regression is to estimate the population parameters from a sample Let {( x i,y i ): i =1, …,n } denote a random sample of size n from the population For each observation in this sample, it will be the case that y i = ? 0 + ? 1x i + u i Economics 20 - Prof. Anderson 8.... y 4y 1y 2y 3x 1x 2x 3x 4 }}{ {u 1u 2u 3u 4x y Population regression line, sample data points and the associated error terms E( y|x ) = ? 0 + ? 1x Economics 20 - Prof. Anderson 9 Deriving OLS Estimates To derive the OLS estimates we need to realize that our main assumption of E(u|x