Re: st: re: z-score as a dependent variable in a linear regression

[Richard Williams <Richard.A.Williams.5@ND.edu>]

At 09:46 PM 11/14/2007, Kit Baum wrote:
> Dan said
>
> In general, is it kosher to use a z-score as a dependent variable in a
> linear regression?  Is it "better" to use some sort of ratio
> measurement?
>
> Keep in mind that if you say
>
> regress y x1 x2, beta
>
> you are in effect running an OLS of z-scored y on z-scored x1 and z- 
> scored x2.
>
> Kit
As Austin noted, it is not clear to me that this is the kind of 
z-score the original poster had in mind.  It sounded like z scores 
were being computed on an individual by individual basis.

Incidentally, if you install -spost9- from J. Scott Long's personal 
site, the command -listcoef- lets you do y-standardization, 
x-standardization, and xy-standardization.  So if, say, you just 
wanted the y's standardized but not the x's, you could run -listcoef- 
after the regress command.  Example:

. sysuse auto
(1978 Automobile Data)

. gen xprice = price/1000

. reg xprice mpg weight foreign, beta

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  3,    70) =   23.29
       Model |  317.252874     3  105.750958           Prob > F      =  0.0000
    Residual |  317.812508    70  4.54017868           R-squared     =  0.4996
-------------+------------------------------           Adj R-squared =  0.4781
       Total |  635.065382    73  8.69952578           Root MSE      =  2.1308

------------------------------------------------------------------------------
      xprice |      Coef.   Std. Err.      t    P>|t|                     Beta
-------------+----------------------------------------------------------------
         mpg |   .0218536   .0742211     0.29   0.769                 .0428664
      weight |   .0034647   .0006307     5.49   0.000                 .9129516
     foreign |    3.67306   .6839783     5.37   0.000                  .573081
       _cons |  -5.853696   3.376987    -1.73   0.087                        .
------------------------------------------------------------------------------

. listcoef

regress (N=74): Unstandardized and Standardized Estimates

 Observed SD: 2.9494959
 SD of Error: 2.1307695

-------------------------------------------------------------------------------
      xprice 
|      b         t     P>|t|    bStdX    bStdY   bStdXY      SDofX
-------------+-----------------------------------------------------------------
         mpg 
|   0.02185    0.294   0.769   0.1264   0.0074   0.0429     5.7855
      weight 
|   0.00346    5.493   0.000   2.6927   0.0012   0.9130   777.1936
     foreign 
|   3.67306    5.370   0.000   1.6903   1.2453   0.5731     0.4602
-------------------------------------------------------------------------------



-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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