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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 4 Apr 2011 09:21:32 +0100 |

Here is a simple example with real data: . sysuse auto, clear (1978 Automobile Data) . regress price weight Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 1, 72) = 29.42 Model | 184233937 1 184233937 Prob > F = 0.0000 Residual | 450831459 72 6261548.04 R-squared = 0.2901 -------------+------------------------------ Adj R-squared = 0.2802 Total | 635065396 73 8699525.97 Root MSE = 2502.3 ------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- weight | 2.044063 .3768341 5.42 0.000 1.292857 2.795268 _cons | -6.707353 1174.43 -0.01 0.995 -2347.89 2334.475 ------------------------------------------------------------------------------ . gen weightsq = weight^2 . regress price weight* Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 2, 71) = 23.09 Model | 250285462 2 125142731 Prob > F = 0.0000 Residual | 384779934 71 5419435.69 R-squared = 0.3941 -------------+------------------------------ Adj R-squared = 0.3770 Total | 635065396 73 8699525.97 Root MSE = 2328 ------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- weight | -7.273097 2.691747 -2.70 0.009 -12.64029 -1.905906 weightsq | .0015142 .0004337 3.49 0.001 .0006494 .002379 _cons | 13418.8 3997.822 3.36 0.001 5447.372 21390.23 ------------------------------------------------------------------------------ You need to plot the data to see what is going on. . twoway lfit price weight || qfit price weight || scatter price weight, legend(order(1 "linear" 2 "quadratic") pos(11) ring(0) col(1)) ytitle("Price (USD)") Thise who live by r-squareds, P-values and t-statistics would probably be quite happy with the quadratic model, but it is still a mediocre model for these data and suggests structure -- a turning point within the range of the data -- that is implausible. Not the fault of the quadratic, as that is its nature, but a poor choice nevertheless. Nick On Fri, Apr 1, 2011 at 7:21 PM, Joerg Luedicke <joerg.luedicke@gmail.com> wrote: > On Fri, Apr 1, 2011 at 1:59 PM, Fabio Zona <fabio.zona@unibocconi.it> 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? >> > > Hi, > > 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. > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: radical change in t-stat, sign and significance***From:*Fabio Zona <fabio.zona@unibocconi.it>

**Re: st: radical change in t-stat, sign and significance***From:*Joerg Luedicke <joerg.luedicke@gmail.com>

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