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From |
Christopher Baum <kit.baum@bc.edu> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: Not Quite Quadratic Regression |

Date |
Sun, 5 Aug 2012 13:11:34 +0000 |

<> On Aug 5, 2012, at 2:33 AM, A. wrote: > Theory predict an u-shaped relation between two variables, y and x. > When I perform a quadratic linear regression with a model like > > y = ax + bx^2 + constant + error, > > the coefficients a and b are not significant. However, if I change the > exponent to something less than 2, e.g. 1.5, I obtain significance. In > other words a model like > > y = ax + bx^1.5 + constant + error, > > yields significant estimates of a and b. The curvature is still quite > marked using the exponent of 1.5. I can even use an exponent of 1.1 > and obtain significance and a nice shape. But I don't think I can > simply choose the exponent based on whatever yields significance. Or > can I? This is my question. > > I have tried to run a non-linear regression where the exponent was a > free parameter. Although it tend to yield an exponent around 1 to 2, > everything turns out highly insignificant. If I plug the estimated > exponent into an OLS model, like the ones above, I get significance. I > have also tried to use splines as well as a piecewise constant > formulation. Again the results are less than ideal (although I get the > same overall picture). > > The non-linearity is rather apparant in a scatterplot (although > extremely noisy), and the problem shows up when controlling for other > covariates where a simple graphical/nonparametric approach is > unfeasible. Sounds like a job for Box & Cox... help boxcox Kit Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Not Quite Quadratic Regression***From:*David Hoaglin <dchoaglin@gmail.com>

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