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Re: st: radical change in t-stat, sign and significance
From
Nick Cox <[email protected]>
To
[email protected]
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 <[email protected]> wrote:
> On Fri, Apr 1, 2011 at 1:59 PM, Fabio Zona <[email protected]> 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.
>
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