RE: st: Regression question

["Mike Kim" <kalisperos@gmail.com>]

Hi David,

Thank you for your opinion. The data structure is more complicated in fact.
Say, there are 50 different media types and each company (i) has different
number of media spending (from 1 to 50). So, setting all these as
independent variables is not possible. 

Anyway, the regression form I specified below does not seem correct.
Probably the only way is to aggregate information about (j) and make all
variables specific to only (i).
 
Thank you,
Mike.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of David Hoaglin
Sent: Friday, May 25, 2012 10:38 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Regression question

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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