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st: Polynomial OLS - Interpreting results


From   Claude Francoeur <claude.francoeur@hec.ca>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Polynomial OLS - Interpreting results
Date   Tue, 30 Dec 2008 12:12:03 -0500

Hello,

First, I would like to thank Maarten Buis and Ángel Rodríguez Laso for their advice (see Polynomial OLS - Dec 25th).

Doing a polynomial OLS and after centering the original variable, we get the following results :

Coefficient of X1 (the centered variable) is negative and significant; coeff. of X1 squared is negative and not sig. and coeff. of X1 cubed is positive and significant.

What would be the graphic representation of such a relation? Is there only one inflexion point here (between X1 squared and X1 cubed)?

How should we interpret these results? A tentative explanation would be that at a low level of X1, the relation with the dependent variable is negative and this relation becomes non significant at a moderate level of X1. Then, at higher levels of X1, the relation becomes significantly positive. Is this correct?

Thank you very much for your help.

Claude




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