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

From   Joerg Luedicke <>
Subject   Re: st: radical change in t-stat, sign and significance
Date   Fri, 1 Apr 2011 14:21:08 -0400

On Fri, Apr 1, 2011 at 1:59 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?


You cannot interpret that as a "change in sign of the linear
coefficient". Once you include the squared term you cant interpret the
two coefficients in isolation, they only make sense together. In your
case, you found an inverse u-shape kind of relation between your
covariate and your dependent variable: Your count is going up for some
lower part range of your covariate but then going down. Usually best
is to plot the effect to get a better sense of how it exactly looks
like. But what you find is not contradictory in any way.

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