On the R^2, your starting point is now a prediction of zero,
not a prediction of the mean response.
In a much simpler case, below, dropping the constant
gives a higher R-sq but a totally ludicrous model. Why then
does the R-sq look so good? Because the predictions
-- which range from 11 to 30 mpg -- are much closer to
the data than a prediction of 0 than the predictions of
the first model to the mean of -mpg-. Your model is more
complicated, and I can't see your data, but I guess that
the same applies. If there is a really good reason,
like a law of physics, to force predictions through
the origin, then do it. (One can certainly improve
on a linear regression of -mpg- on -weight-, a secondary
point.)
. sysuse auto, clear
(1978 Automobile Data)
. reg mpg weight
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 1, 72) = 134.62
Model | 1591.9902 1 1591.9902 Prob > F = 0.0000
Residual | 851.469256 72 11.8259619 R-squared = 0.6515
-------------+------------------------------ Adj R-squared = 0.6467
Total | 2443.45946 73 33.4720474 Root MSE = 3.4389
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | -.0060087 .0005179 -11.60 0.000 -.0070411 -.0049763
_cons | 39.44028 1.614003 24.44 0.000 36.22283 42.65774
------------------------------------------------------------------------------
. reg mpg weight , noconst
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 1, 73) = 259.18
Model | 28094.8545 1 28094.8545 Prob > F = 0.0000
Residual | 7913.14549 73 108.399253 R-squared = 0.7802
-------------+------------------------------ Adj R-squared = 0.7772
Total | 36008 74 486.594595 Root MSE = 10.411
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | .006252 .0003883 16.10 0.000 .0054781 .007026
------------------------------------------------------------------------------
Nick
[email protected]
chris carambas
> I estimated an xtpcse model, and I observed that any of my
> runs without
> noconstant option has very low R-squared (i.e. 0.08--and this
> is the same
> result if I run it in xtreg which has no nocons option) but
> with noconstant
> option, all R-squared become high (i.e. from 0.80).Does anyone have
> explanation for that?
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