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


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: re: z-score as a dependent variable in a linear regression
Date   Thu, 15 Nov 2007 08:56:07 -0500

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
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EMAIL: Richard.A.Williams.5@ND.Edu
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