I take Ronan's point, but there is a difference here. -regress- and
-ttest- are working with the standard Gaussian or normal machinery that
statistically minded people expect to be used for means. -qreg- as a
test for medians does not correspond to any of the customary
non-parametric tests that might be expected to be used for medians. I am
not saying that's a problem; it is more by way of a signal.
Nick
[email protected]
Ronan Conroy
On 24 Nov 2008, at 11:55, Bastian Steingros wrote:
> After creating the descriptive statistics of my sample I want to
> show that the mean of a certain variable is statistically significant.
> For example the mean of var1 is 0,45. Now I want to show that the
> positive sign is significant.
A regression without any predictor variable is a constant-only model,
and the test for significance of the constant is a test that the
constant is zero.
. sysuse auto
(1978 Automobile Data)
. regress mpg
Source | SS df MS Number of obs
= 74
-------------+------------------------------ F( 0, 73)
= 0.00
Model | 0 0 . Prob > F
= .
Residual | 2443.45946 73 33.4720474 R-squared
= 0.0000
-------------+------------------------------ Adj R-squared
= 0.0000
Total | 2443.45946 73 33.4720474 Root MSE
= 5.7855
------------------------------------------------------------------------
------
mpg | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------
+----------------------------------------------------------------
_cons | 21.2973 .6725511 31.67 0.000 19.9569
22.63769
------------------------------------------------------------------------
------
The coefficient for the constant is the mean of the data (since the
mean is the statistic that minimises prediction error, when we define
prediction error as the squared difference between observed and
expected).
Similarly, quantile regression will test that the median is zero
. qreg mpg
Iteration 1: WLS sum of weighted deviations = 330.13202
Iteration 1: sum of abs. weighted deviations = 330
Iteration 2: sum of abs. weighted deviations = 328
Median regression Number of obs
= 74
Raw sum of deviations 328 (about 20)
Min sum of deviations 328 Pseudo R2
= 0.0000
------------------------------------------------------------------------
------
mpg | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------
+----------------------------------------------------------------
_cons | 20 .7799751 25.64 0.000 18.44551
21.55449
------------------------------------------------------------------------
------
the median being the statistic which minimises error, when we define
error as the absolute difference between the observed and expected.
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