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Unformatted text preview: 2/17/12 PADP 8130: Linear Models Func%onal Form Angela Fer:g, Ph.D. • We know how to get es:mates for parameters. • We know how to test hypotheses. • Now, we will talk about how we put in regressors (func%onal form). • Next :me, we’ll talk about how we know which regressors to put in the regression (speciﬁca%on). 1 2/17/12 Plan •
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• Polynomials Log transforma:ons Inverse Dummy variables Interac:on terms Spline func:ons Marginal eﬀects Non linear rela:onships OLS assumes a linear form, but that does not mean that the variables must be linear. There are several ways we can transform non linear variables so that they are linear in the parameters β. 2 2/17/12 First, how do we know if we should transform a regressor? Graph of residuals (y axis) on a key independent variable (x axis) A random scaZer of residuals, with no apparent paZern, is what we want to see generally. 100000 0 100000 200000 • Graph the residuals to see if there is any structure to the varia:on that you can’t explain • Residuals should be randomly distributed around zero (it’s inherent varia:on that we can’t predict). 20 40 60
Age of head in 2007 Residuals 80 100 lowess r1 agehd 3 2/17/12 100000 0 100000 200000 Can also graph residuals (y axis) on a dependent variable (x axis) 0 50000 100000
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Total family income in 2008 Residuals 200000 lowess r1 faminc Polynomials • The most common way to take account of non linearity is to use polynomial regression func3ons, e.g. 2 y = a + b1 X1 + b2 X1 + b3 X 2 + e • This is useful if we thing the rela:onship looks like: Convex b2<0 Concave b2>0 Y Y Y X Cubed term X X Note: Can’t do this with dependent variable since requires mul:ple terms. 4 2/17/12 Log transforma:on • Using the logged value of X instead of X as our variable is an alternate way of dealing with non lineari:es • This is especially useful when we...
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This note was uploaded on 03/28/2012 for the course PADP 8130 taught by Professor Fertig during the Spring '12 term at LSU.
 Spring '12
 Fertig

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