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# Re: st: Not Quite Quadratic Regression

 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>

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.

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```