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Re: st: Regression question


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regression question
Date   Fri, 25 May 2012 23:37:37 -0400

Hi, Mike.

I may not understand the structure of your data, but it seems that the
explanatory variable that you denote by X2(ij) is actually several
related variables.  That is, in your example, j seems to index the
various media (j = 1 for TV, j = 2 for Newspaper, etc.).  In that
situation, you should treat each of the media as a separate
explanatory variable, with its own regression coefficient.  You might
learn from the analysis that those coefficients are essentially equal,
in which case the interpretation would be that what matters is the
total amount of AD spending.  Then you could simplify the model by
using total AD spending as the explanatory variable, instead of the
amount spent on each of the types.  It seems more likely, however,
that the coefficients for the types of media will differ.

In interpreting the regression coefficients, please keep in mind that
the set of other explanatory variables in the model is part of the
definition of each coefficient, and that each estimated coefficient
reflects the contribution of its explanatory variable after adjusting
for the contributions of the other explanatory variables.

I hope you are planning to make plots of the data and use various
regression diagnostics to spot influential observations.

David Hoaglin

On Fri, May 25, 2012 at 9:52 AM, Mike Kim <kalisperos@gmail.com> wrote:
> Hi all,
>
> This question is not about Stata, but I would appreciate your opinion. I
> wonder whether the following regression (e.g., OLS) makes sense.
>
> Y(i) = b0 + b1*X1(i) + b2*X2(ij) + e(i)
> That is, Y varies by i, but some independent variables vary by i and j. Each
> Y(i) is repeated j times, so data structure is:
>
> Y     X1   X2
> 10   2    1
> 10   2    2
> 10   2    3
> 20   3    4
> 20   3    5
> ...
>
> For example:
> i: company, j: adverting spending by media (TV, Newspaper, etc.)
> REVENUE(i) = b0 + b1*R&D SPENDING(i) + b2*AD SPENDING BY MEDIA(ij) + e(i)

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