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st: Regression Techniques


From   "Tam Phan" <tamdphan@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Regression Techniques
Date   Thu, 21 Feb 2008 22:04:14 -0400

Hello Stata Community:

I have recently encountered two methodology of linear regression
techniques.  The main objective of the two techniques is to establish
the effects of price on the demand of certain products/items.  Below
are two techniques outlined:

(1) Y=a+X'b+e  where X= explanatory variables, excluding price, Y is
the observed quantity purchased for a particular product
(2) Ynorm=e+average(Y)
(3) Ynorm= a + b(price)+Ei

After performing regression in (1), Ynorm is calculated by the sum of
the residuals and the average of the original Y.  This Ynorm is then
regress with price as the single explanatory variable.  The claim is
that the fitted values in (3) will produce the "demand" of a product
with only the effects of price and Ei.  What are your thoughts on
this?

Technique two:

(1) Y= a + X'b1 + b2(price) +e
(2) Ynorm = a +b1*(average(X)) + b(2price) +e

Technique two only has one stage of regression (1), then the demand is
"normalize" by multiplying the coefficients by the average of their
respected explanatory variables, then whats left over is the quantity
sold, in terms of price. Again, what are your thoughts?

Which technique is "better?"  Advantages/disadvantages?

TP
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