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Re: re: re: st: Simple regression and Multiple regression?


From   gjhxmu@sina.com
To   statalist<statalist@hsphsun2.harvard.edu>
Subject   Re: re: re: st: Simple regression and Multiple regression?
Date   Mon, 15 Mar 2010 14:18:19 +0800

Dear Kit and Eric,
Thank you very much for your help, which really helps a lot!
What about the constant? Is there an existing relationship between simple regression and multiple regression?

By the way, I found the standard errors of turn were not the same in "reg epsp epst" and "reg price mpg weight turn". Just a decimal difference which can be ignored? 

. reg price epst

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =    7.23
       Model |  57963155.7     1  57963155.7           Prob > F      =  0.0089
    Residual |   577102240    72   8015308.9           R-squared     =  0.0913
-------------+------------------------------           Adj R-squared =  0.0786
       Total |   635065396    73  8699525.97           Root MSE      =  2831.1

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        epst |  -395.1902    146.957    -2.69   0.009    -688.1436   -102.2368
       _cons |   6165.257   329.1124    18.73   0.000     5509.183     6821.33
------------------------------------------------------------------------------

. reg epsp epst

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =   10.68
       Model |  57963155.7     1  57963155.7           Prob > F      =  0.0017
    Residual |   390780961    72  5427513.34           R-squared     =  0.1292
-------------+------------------------------           Adj R-squared =  0.1171
       Total |   448744116    73  6147179.68           Root MSE      =  2329.7

------------------------------------------------------------------------------
        epsp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        epst |  -395.1902    120.929    -3.27   0.002    -636.2578   -154.1226
       _cons |   1.21e-12   270.8224     0.00   1.000    -539.8746    539.8746
------------------------------------------------------------------------------

. reg price mpg weight turn

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  3,    70) =   14.59
       Model |   244284435     3  81428145.1           Prob > F      =  0.0000
    Residual |   390780961    70  5582585.15           R-squared     =  0.3847
-------------+------------------------------           Adj R-squared =  0.3583
       Total |   635065396    73  8699525.97           Root MSE      =  2362.7

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -72.86501   81.29538    -0.90   0.373    -235.0035    89.27351
      weight |   3.524339   .8171395     4.31   0.000     1.894605    5.154072
        turn |  -395.1902   122.6444    -3.22   0.002    -639.7968   -150.5836
       _cons |   12744.24   4760.102     2.68   0.009     3250.519    22237.97
------------------------------------------------------------------------------

Thank you for any help.

Best regards,
Rose

----- Original Message -----
From: Kit Baum <baum@bc.edu>
To: statalist@hsphsun2.harvard.edu
Subject: re: re: st: Simple regression and Multiple regression?
Date: 2010-3-15 02:32:07

<>
Rose said

By the way,"Frisch-Waugh-Lovell theorem says that the coefficient of turn should be the same in multiple regression or in a regression
of price on turn, with the effects of other regressors partialled-off from both." In Woodbridge's book, the effect of other regressors is only partialled-off from the concerned regressor, not from the dependent variable. 
It is also OK, right?
What I tried in stata told me it was OK.


No, if you fail to partia-offl the other regressors from the dependent variable, you get the same point estimate but a different standard error, t-stat, , R^2, RMS Error, etc. Check the example I gave for

reg epsp epst 

versus the regression 

reg price epst

You will see that they are not the same. 

Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html


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