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st: re: beta coefficients for interaction terms


From   Kit Baum <kitbaum@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: beta coefficients for interaction terms
Date   Sun, 21 Jun 2009 09:58:41 -0400

<>

Lisa said

but it is important for my paper to show the value of the intercept,
and I get different values if I use either the standardized or the not
standardized dependent variable. If I have the null hypothesis that is
is equal to zero, do I have to use the standardized or not
standardized dependent variable? And coming back to my original
question: Why do I have to standardize the dependent variable?

and in fact if you do standardize both dep and indep vars as suggested by an earlier post, the constant term is by definition zero. The regression surface passes through the multivariate point of means, and that is now (0,0,0,0,0).

When you do run the regression of *un*standardized dep var on standardized regressors as you would now like to do, the constant term is by construction the *un*conditional mean of the dep var:

. reg mpg shead slength sia2

Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 3, 70) = 41.45 Model | 1563.44248 3 521.147494 Prob > F = 0.0000 Residual | 880.016979 70 12.5716711 R-squared = 0.6398 -------------+------------------------------ Adj R-squared = 0.6244 Total | 2443.45946 73 33.4720474 Root MSE = 3.5457

------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval] ------------- +---------------------------------------------------------------- shead | -.1288064 .4934882 -0.26 0.795 -1.113038 .8554248 slength | -4.598606 .4846015 -9.49 0.000 -5.565113 -3.632098 sia2 | .4815198 .4260752 1.13 0.262 -. 3682604 1.3313 _cons | 21.2973 .4121741 51.67 0.000 20.47524 22.11935
------------------------------------------------------------------------------

.
end of do-file

. su mpg

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         mpg |        74     21.2973    5.785503         12         41


so it is not telling you anything for which you need to estimate the regression to find out.

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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