st: Polynomial OLS - Interpreting results

[Claude Francoeur <claude.francoeur@hec.ca>]

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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