The Simple regression model y=Bo+Bx+u Economics 20- Prof anderson
Economics 20 - Prof. Anderson 1 The Simple Regression Model y = b0 + b1 x + u
Some Terminology o In the simple linear regression model where y=Po+ Bx+ u, we typically refer to y as the Dependent variable, or a Left-Hand Side variable. or a Explained Variable, or Regressand Economics 20- Prof anderson
Economics 20 - Prof. Anderson 2 Some Terminology In the simple linear regression model, where y = b0 + b1 x + u, we typically refer to y as the ◼ Dependent Variable, or ◼ Left-Hand Side Variable, or ◼ Explained Variable, or ◼ Regressand
Some terminology, cont o In the simple linear regression of y on X we typically refer to x as the Independent variable, or Right-Hand Side variable or a Explanatory variable, or Regressor, or a Covariate or a Control variables Economics 20- Prof anderson
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
A Simple assumption o The average value of u, the error term, in the population is 0. That is ◆E(l)=0 This is not a restrictive assumption, since we can al ways use Bo to normalize E(u) to O Economics 20- Prof anderson 4
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 b0 to normalize E(u) to 0
Zero conditional mean We need to make a crucial assumption about how u and x are related o 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 DE(ux=e(u=o, which implies ◆E(vx)=B0+Bx Economics 20- Prof anderson 5
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) = b0 + b1 x