# oh4 - LECTURE 4: THE SIMPLE REGRESSION MODEL Regression...

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LECTURE 4: THE SIMPLE REGRESSION MODEL Regression Analysis : The study of the relationship be- tween one variable ( dependent variable ) and one or more other variables ( independent, or explanatory, vari- ables ) using a (typically linear) regression model. What do we use regression analysis for? To estimate the mean or average value of the dependent variable, given the values of the independent variables. What is the average income for people with a high school diploma? What is the average income for peo- ple with a college degree? To test a hypothesis implied by economic theory If we increase the price will the quantity demanded fall? To predict, or forecast, the mean value of the dependent variable given the independent variables. What will happen to GDP if we change the interest rate? 1

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THE POPULATION REGRESSION FUNCTION DETERMINISTIC POPULATION REGRESSION FUNC- TION Population Regression Function, E ( Y j X ) ; is the conditional mean of the dependent variable ( Y ) given any value of the independent variable ( X ) In general, E [ Y j X ] can have any shape as a function of X: We typically choose to think that the population regres- sion function is a linear function of the conditioning vari- able(s), that is we specify a linear regression model. The bivariate linear regression model takes the form E ( Y j X ) = 1 + 2 X 1 and 2 are the unknown population regression parameters or regression coe¢ cients 1 is the intercept. It measures E ( Y j X = 0) : 2
2 is the slope. It measures the average marginal change in Y given a small change in X: 1 = E dY dX ± 1 and 2 are unknown and they are the primary objects of interest. 3

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STOCHASTIC POPULATION REGRESSION FUNCTION Equivalently the linear regression model can be written as Y = 1 + 2 X + " where " is an unobservable stochastic, or random, error term (or disturbance). " is an random variable, i.e. it has some distribution
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## This note was uploaded on 04/02/2008 for the course ECON 103 taught by Professor Sandrablack during the Winter '07 term at UCLA.

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oh4 - LECTURE 4: THE SIMPLE REGRESSION MODEL Regression...

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