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st: Simple regression and Multiple regression?


From   gjhxmu@sina.com
To   statalist<statalist@hsphsun2.harvard.edu>
Subject   st: Simple regression and Multiple regression?
Date   Sun, 14 Mar 2010 17:41:24 +0800

Dear statalists,
Suppose there are situations as follows,
situation1:
reg y x1 x2 x3 x4

situation2:
reg y x1 x2 x3
predict re,re
reg re x4

Whether the coefficients and significance on x4 in two situations are the same in fact though a little difference in decimal part?

The results of a random sample are as follows,
situation1:coefficient=-.0039743 significance=0.675
situation2:coefficient=-.0038959 significance=0.677


 reg y x1 x2 x3 x4

      Source |       SS       df       MS              Number of obs =     278
-------------+------------------------------           F(  4,   273) =   15.88
       Model |  .309280434     4  .077320108           Prob > F      =  0.0000
    Residual |  1.32893274   273  .004867885           R-squared     =  0.1888
-------------+------------------------------           Adj R-squared =  0.1769
       Total |  1.63821317   277  .005914127           Root MSE      =  .06977

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .1284174   .0299903     4.28   0.000     .0693757    .1874591
          x2 |   .0617595   .0393121     1.57   0.117    -.0156338    .1391529
          x3 |   .0131323   .0020908     6.28   0.000     .0090162    .0172484
          x4 |  -.0039743   .0094827    -0.42   0.675    -.0226428    .0146943
       _cons |   .0603695    .011657     5.18   0.000     .0374204    .0833185
------------------------------------------------------------------------------

. reg y x1 x2 x3

      Source |       SS       df       MS              Number of obs =     278
-------------+------------------------------           F(  3,   274) =   21.18
       Model |  .308425392     3  .102808464           Prob > F      =  0.0000
    Residual |  1.32978778   274   .00485324           R-squared     =  0.1883
-------------+------------------------------           Adj R-squared =  0.1794
       Total |  1.63821317   277  .005914127           Root MSE      =  .06967

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .1280548   .0299327     4.28   0.000     .0691275    .1869822
          x2 |   .0638026   .0389499     1.64   0.103    -.0128765    .1404818
          x3 |   .0130832   .0020844     6.28   0.000     .0089799    .0171866
       _cons |   .0588763   .0110825     5.31   0.000     .0370586    .0806941
------------------------------------------------------------------------------

. predict re,re

. reg re x4

      Source |       SS       df       MS              Number of obs =     278
-------------+------------------------------           F(  1,   276) =    0.17
       Model |  .000838193     1  .000838193           Prob > F      =  0.6768
    Residual |  1.32894959   276  .004815035           R-squared     =  0.0006
-------------+------------------------------           Adj R-squared = -0.0030
       Total |  1.32978778   277  .004800678           Root MSE      =  .06939

------------------------------------------------------------------------------
          re |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x4 |  -.0038959   .0093377    -0.42   0.677    -.0222781    .0144862
       _cons |   .0010651   .0048823     0.22   0.827    -.0085462    .0106763
------------------------------------------------------------------------------

Thank you for any help!

Best regards,
Rose
 

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