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From |
"A. Shaul" <3c5171@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Not Quite Quadratic Regression |

Date |
Sat, 4 Aug 2012 12:56:30 +0200 |

Hello Statalisters, 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. Needless to say, I have been searching high and low for an answer before posting here. This is my first message to Statalist (although I am an avid reader of the archives). I hope my question is fine. Thank you in advance * * 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**:**st: RE: Not Quite Quadratic Regression***From:*"Jacobs, David" <jacobs.184@sociology.osu.edu>

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

**Re: st: Not Quite Quadratic Regression***From:*solafem7@yahoo.co.uk

**Re: st: Not Quite Quadratic Regression***From:*solafem7@yahoo.co.uk

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