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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 •  •  •  •  •  •  •  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 150000 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.

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