st: RE: Beta coefficients are not equal to coefficients on standardized variables?

[Kieran McCaul <kieran.mccaul@uwa.edu.au>]

...


Don't standardize the dependent variable.

clear*
sysuse auto

regress weight length turn displacement, beta

egen length_std = std( length )
egen turn_std = std(turn)
egen displacement_std = std(displacement)

regress weight length_std turn_std displacement_std , beta



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Roberto Liebscher
Sent: Friday, 15 June 2012 11:23 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Beta coefficients are not equal to coefficients on standardized variables?

There is one thing that makes me puzzling about the - beta - option in 
regression commands. In a simple example using the lifeexp dataset I 
first used the built-in function - beta - :

sysuse auto

regress lexp gnppc popgrowth, beta


. regress lexp gnppc popgrowth, beta

       Source |       SS       df       MS              Number of obs = 
      63
-------------+------------------------------           F(  2,    60) = 
36.20
        Model |  777.530873     2  388.765436           Prob > F      = 
  0.0000
     Residual |  644.405635    60  10.7400939           R-squared     = 
  0.5468
-------------+------------------------------           Adj R-squared = 
0.5317
        Total |  1421.93651    62  22.9344598           Root MSE      = 
  3.2772

------------------------------------------------------------------------------
         lexp |      Coef.   Std. Err.      t    P>|t|    Beta
-------------+----------------------------------------------------------------
        gnppc |    .000293   .0000419     6.99   0.000 .6506803
    popgrowth |  -.9833919    .485387    -2.03   0.047 -.1885781
        _cons |   70.67366   .8071596    87.56   0.000       .
------------------------------------------------------------------------------



Then I standardized the variables by hand and re-ran the regression with 
the new variables:

. egen popgrowth_std = std(popgrowth)

. egen lexp_std = std(lexp)

. egen gnppc_std = std(gnppc)
(5 missing values generated)

regress lexp_std gnppc_std popgrowth_std


       Source |       SS       df       MS              Number of obs = 
      63
-------------+------------------------------           F(  2,    60) = 
  36.20
        Model |  34.9700449     2  17.4850225           Prob > F      = 
  0.0000
     Residual |  28.9826364    60  .483043939           R-squared     = 
  0.5468
-------------+------------------------------           Adj R-squared = 
0.5317
        Total |  63.9526813    62  1.03149486           Root MSE      = 
  .69501

------------------------------------------------------------------------------
     lexp_std |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
    gnppc_std |   .6608475   .0945336     6.99   0.000     .4717521 
.8499428
popgrowth_~d |  -.1942026   .0958554    -2.03   0.047    -.3859419 
-.0024633
        _cons |  -.0042032   .0875655    -0.05   0.962    -.1793602 
.1709538
------------------------------------------------------------------------------


Now the coefficients are slightly different. For example the coefficient 
on gnppc_std is 0.6608475 whereas it has been 0.6506803 in the first 
calculation.

Is this caused by rounding errors? Or is there any other explanation for 
this?

Thanks in advance.

Roberto
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