Notes 1 - Review of the Regression Model Regression Models...

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Review of the Regression Model Regression Models are the base for much of the empirical work in economics (and other social sciences). Last quarter you learned the basic theory of the regression model. In this course we will focus on applications and extensions of the basic model Review Discuss ways in which it is used Extend the basic model Aviv Nevo () Review of the Regression Model 386-2 1 / 24
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The Regression Model Assumption MLR 1: The Model Y i = β 0 + β 1 X 1 i + ... + β k X ki + u i i = 1 ... N Let X i = 2 6 6 6 4 1 X 1 i . . . X ki 3 7 7 7 5 , β = 2 6 6 6 4 β 0 β 1 . . . β k 3 7 7 7 5 , Y = 2 6 6 6 4 Y 1 Y 2 . . . Y N 3 7 7 7 5 , X = 2 6 6 6 4 X 0 1 X 0 2 . . . X 0 N 3 7 7 7 5 So Y i = X 0 i β + u i i = 1 ... N or Y = X β + u Aviv Nevo () Review of the Regression Model 386-2 2 / 24
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Data: random sampling Suppose we have data (that was generated from the model). Assumption MLR 2: random sampling We have a random sample of size N , f ( Y i , X i ) i = 1 .. N g , from the population of interest Aviv Nevo () Review of the Regression Model 386-2 3 / 24
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Data: colinearity Assumption MLR 3: no perfect colinearity in the sample No linear relationships between the X , The columns of X are linearly independent , The X This just means that any X ij cannot be written as a linear combination of other X ij Aviv Nevo () Review of the Regression Model 386-2 4 / 24
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Estimation We want to estimate the model (i.e., estimate β ) There are several ways to do this One way is to try to get the model as close as possible to the data (see graphs) We will focus on minimizing the square of the vertical di/erence Y i X 0 i ˆ β ± 2 Aviv Nevo () Review of the Regression Model 386-2 5 ± 24
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Least Squares Estimates We want to choose ˆ β to min N i = 1 Y i X 0 i ˆ β ± 2 Aviv Nevo () Review of the Regression Model 386-2 6 / 24
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Notes 1 - Review of the Regression Model Regression Models...

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