LIR 832 Lecture 10 2 slides per page

LIR 832 Lecture 10 2 slides per page - Regression Continued...

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1 Regression Continued: Functional Form LIR 832 December 5, 2006 Topics for the Evening 1. Qualitative Variables 2. Non-linear Estimation
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2 Functional Form Not all relations among variables are linear: Our basic linear model: y= β 0 + β 1 X 1 + β 2 X 2 +…+ β k X k + e Functional Form Q: Given that we are using OLS, can we mimic these non-linear forms? A: We have a small bag of tricks which we can use with OLS.
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3 Functional Form Functional Form
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4 Functional Form Functional Form A first point about functional form: You must have an intercept. Consider the following case: We estimate a model and test the intercept to determine if it is significantly different than zero. We are not able to reject the null in a hypothesis test and we decide to re-estimate the model without an intercept. What is really going on? Return to our basic model: y= β 0 + β 1 X 1 + β 2 X 2 +…+ β k X k + e What are we doing when we remove the intercept? y= 0 + β 1 X 1 + β 2 X 2 +…+ β k X k + e
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5 Functional Form Functional Form
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6 Functional Form /* Regression without an intercept */ Regression Analysis: weekearn versus years ed The regression equation is weekearn = 57.3 years ed 47576 cases used, 7582 cases contain missing values Predictor Coef SE Coef T P Noconstant years ed 57.3005 0.1541 371.96 0.000 S = 534.450 Functional Form /* Regression with an intercept */ Regression Analysis: weekearn versus years ed The regression equation is weekearn = - 485 + 87.5 years ed 47576 cases used, 7582 cases contain missing values Predictor Coef SE Coef T P Constant -484.57 18.18 -26.65 0.000 years ed 87.492 1.143 76.54 0.000 S = 530.510 R-Sq = 11.0% R-Sq(adj) = 11.0%
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