LIR 832 Lecture 10 3 slides

# LIR 832 Lecture 10 3 slides - 1 Regression Continued...

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Unformatted text preview: 1 Regression Continued: Functional Form LIR 832 December 5, 2006 Topics for the Evening 1. Qualitative Variables 2. Non-linear Estimation Functional Form ¡ Not all relations among variables are linear: ¡ Our basic linear model: y= β + β 1 X 1 + β 2 X 2 +…+ β k X k + e 2 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. Functional Form Functional Form 3 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 + β 1 X 1 + β 2 X 2 +…+ β k X k + e ¡ What are we doing when we remove the intercept? y= + β 1 X 1 + β 2 X 2 +…+ β k X k + e Functional Form 4 Functional Form 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% 5 Functional Form ¡ Consequences of forcing through zero: ¡ Unless the intercept is really zero, we are going to bias both the intercept and the slope coefficients. ¡ Remember that we calculate the intercept so that the line passes through the point of means: ¡ Assures that the Σε = 0 ¡ If we impose 0 as the intercept, the line may not pass through the point of means and the sum of the errors may not equal zero. ¡ Biases the coefficients and leads to incorrect estimates of the standard errors of the β s. ¡ Never suppress the intercept, even if your theory suggests that it is not necessary. Functional Form /* What About Those Residuals? */ Descriptive Statistics: RESI1, RESI2 Variable N N* Mean SE Mean StDev Minimum Q1 Median RESI1 47576 7582 -8.67 2.45 534.38 -1180.31 -359.12 -122.21 RESI2 47576 7582 0.00 2.43 530.50 -1329.77 -340.32 -107.62 Variable Q3 Maximum RESI1 218.59 2311.61 RESI2 237.69 2494.26 Functional Form ¡ Returning to the issue of non-linearity… ¡ In our basic model: ¡ β = ∆ Y/ ∆ X = change in Y for a one-unit change in X ¡ Consider the effect of Education on base salary… 6 Functional Form Descriptive Statistics: years ed, Exp Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum years ed 55158 0 15.734 0.00941 2.211 1.000 14.000 16.000 18.000 21.00021....
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LIR 832 Lecture 10 3 slides - 1 Regression Continued...

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