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Re: st: radical change in t-stat, sign and significance

From   Nick Cox <>
Subject   Re: st: radical change in t-stat, sign and significance
Date   Fri, 1 Apr 2011 19:18:30 +0100

This need not be worrying. The signs are only part of the information.
The magnitudes are important too. Also, remember that x and x^2 are
correlated and may to some extent serve as proxies for each other,
even if there is no declared problem of multicollinearity.

What you can easily do is plot the two terms using -twoway function-.
Your intuition can easily mislead. Also, standard calculus methods can
show you the position of the turning point, which may not be within
the range of the data.

Made-up examples can be instructive too, e.g.

twoway function -x, ra(0 10) || function -0.25 * (x^2) + 0.8 * x , ra(0 10)


On Fri, Apr 1, 2011 at 6:59 PM, Fabio Zona <> wrote:
> Dear all,
> I have a regression (zero inflated negative binomial): when I include the linear predictor alone (without its square term), the coefficient of this linear predictor is negative and significant.
> However, when I introduce the square term of the same predictor: a) the linear one changes its sign, becomes positive, and it is still significant; b) the square term gets a negative sign and is signficant.
> Is this radical change in sign and significance of the linear coefficient a signal of some problems in the model?
> the collin command says I have no prob lem of multicollinearity
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