st: weighted regression

["Nikolaos A. Patsopoulos" <npatsop@cc.uoi.gr>]

Dear statalist members,

in a weighted regression with what do I have to divide the weighted SE 
to get the unweighted one?

Some sample data and results:
WEIGHTED
var1    var2    weight
0    3.4    1
1    4.7    2
2    9.2    2

regress  var2 var1 [aweight= weight]

(sum of wgt is   5.0000e+00)

     Source |       SS       df       MS              Number of obs 
=       3
-------------+------------------------------           F(  1,     1) 
=    9.37
      Model |  16.4437701     1  16.4437701           Prob > F      =  
0.2010
   Residual |  1.75542889     1  1.75542889           R-squared     =  
0.9035
-------------+------------------------------           Adj R-squared =  
0.8071
      Total |   18.199199     2  9.09959951           Root MSE      =  
1.3249

------------------------------------------------------------------------------
       var2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
       var1 |   3.128571   1.022203     3.06   0.201    -9.859744    
16.11689
      _cons |   2.485714   1.445613     1.72   0.335    -15.88254    
20.85397
------------------------------------------------------------------------------

UNWEIGHTED
var1    var2
0    3.4
1    4.7
2    9.2
1    4.7
2    9.2

. regress  var2 var1

     Source |       SS       df       MS              Number of obs 
=       5
-------------+------------------------------           F(  1,     3) =   
28.10
      Model |  27.4062836     1  27.4062836           Prob > F      =  
0.0131
   Residual |  2.92571481     3   .97523827           R-squared     =  
0.9035
-------------+------------------------------           Adj R-squared =  
0.8714
      Total |  30.3319984     4  7.58299959           Root MSE      =  
.98754

------------------------------------------------------------------------------
       var2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
       var1 |   3.128571   .5901689     5.30   0.013      1.25039    
5.006752
      _cons |   2.485714   .8346249     2.98   0.059    -.1704347    
5.141863
------------------------------------------------------------------------------

I believe I have to divide the weight SE (1.022203) with the ResidualMS 
(1.75542889), which gives 0.582309.


Is this correct?

Thanks in advance,

Nikos

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