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321_09_slides4 - Week 2 The Simple Regression Model Chapter...

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Week 2: The Simple Regression Model Chapter 2 Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1
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Outline Population regression equation Deriving the OLS Estimates Interpretation and Evaluating of Results Units of measurement and functional form Properties of OLS Econ 321-Stéphanie Lluis 2
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Last Time Population with parameter (characteristic) μ for a random variable Y (household income) Random sample Y 1 ,..,Y n Estimate μ with Y Make inference about population from sample information Econ 321-Stéphanie Lluis 3
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A Conditional Model We now are interested in analyzing a variable of interest Y as a function of another variable X (bivariate regression) We establish a conditional model A model of vacation expenditure conditional on household income A model of worker productivity (job performance) conditional on training information Econ 321-Stéphanie Lluis 4
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Econ 321-Stéphanie Lluis 5 Population Regression Function
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Formally The population mean for Y is now a function of another variable X E(Y|X) = β 0 + β 1 X The mathematical expression for a straight line This is our “certainty” model What is the statistical model? Econ 321-Stéphanie Lluis 6
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Randomness Econ 321-Stéphanie Lluis 7
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Population Regression Equation Dependent Variable Intercept Slope Coefficient Explanatory Variable Error y i = β 0 + β 1 x i + u i
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Error or Disturbance Term What the econometrician cannot observe or measure It represents the influence of the variables other than X i (not included in the model) Even if we observed and measured these additional factors, there would still remain some randomness Human behaviour is not totally predictable Errors of measurement in Y Econ 321-Stéphanie Lluis 9
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