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# lecture5 - ECON 103 Lecture 5 The simple regression model...

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ECON 103, Lecture 5: The simple regression model Maria Casanova January 26th (version 0) Maria Casanova Lecture 5

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Requirements for this lecture: Chapter 4 of Stock and Watson up to page 123 Maria Casanova Lecture 5
1. Introduction Regression analysis is the study of the relationship between one variable ( dependent variable) and one or more other variables ( independent or explanatory variables) using a (typically linear) regression model. What do we use regression analysis for? To estimate mean or average value of the dependent variable, given the values of the independent variables. What is the average income for people 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? Maria Casanova Lecture 5

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2. Linear Regression Model (Deterministic) Population Regression Function Population regression function , E ( Y | X ), is the conditional mean of the dependent variable ( Y ) given any value of the independent variable ( X ). The population regression function represents a relationship that holds on average across the population. In general, E ( Y | X ) can have any shape as a function of X . We typically choose to represent the population regression function as a linear function of the conditioning variables. That is, we specify a linear regression model. Maria Casanova Lecture 5
2. Linear Regression Model The bivariate linear population regression function takes the form: E ( Y | X ) = β 0 + β 1 X β 0 and β 1 are the unknown regression coefficients β 0 is the intercept . It measures E ( Y | X = 0). β 1 is the slope . It measures the average marginal change in Y given a small change in X . β 1 = E ( dY dX ) β 0 and β 1 are unknown and they are the primary objects of interest. Maria Casanova Lecture 5

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2. Linear Regression Model Figure: (Deterministic) population regression function 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 3000 β 0 = β 1 = 0 . 70 = slope β 1 = E ( dY dX ) Maria Casanova Lecture 5
2. Linear Regression Model Linear Regression Model This model represents a relationship that holds for each member of the population: E ( Y | X ) = β 0 + β 1 X + ε where ε is a stochastic (or random), error term (or disturbance).

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