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From |
solafem7@yahoo.co.uk |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Not Quite Quadratic Regression |

Date |
Sat, 4 Aug 2012 11:41:01 +0000 |

Hi Shaul, Could it be because of the type of data you are using? Probably you have one to be in real value form and the other in growth rate. Try to Log the data for the two variables and redo it to see what happen. Sola Sent from my BlackBerry wireless device from MTN -----Original Message----- From: "A. Shaul" <3c5171@gmail.com> Sender: owner-statalist@hsphsun2.harvard.edu Date: Sat, 4 Aug 2012 12:56:30 To: <statalist@hsphsun2.harvard.edu> Reply-To: statalist@hsphsun2.harvard.eduSubject: st: Not Quite Quadratic Regression 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/ * * 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/

**References**:**st: Not Quite Quadratic Regression***From:*"A. Shaul" <3c5171@gmail.com>

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