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I am trying to come up with a model that can predict movie box office. One factor that is important is competition... I want to model it as a function of several variables, including some that are variables in their own right in this fuller model.

One- if a variable would be counted twice, should I even do it that way? ie # of screens a movie is released on being its own variable, and ALSO being included as a part of the "competition" variable?

Two- Assume I do a regression for the "Competition" variable. Can I use the results of this as a new independent "competition" variable in a new regression? Can you use the results of a regression as a new variable in a new regression??

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    $\begingroup$ There are many ways to approach this. For one thing, you shouldn't expect any answer here to be the answer, nor for it to cover all the possibilities. With a question like the one you've posed, you could be about to embark on quite the voyage of discovery, if you're willing to put in the time and the effort. I'd start by reading introductory pieces and whatever more advanced books/articles you connect with, on regression, path analysis, and structural equation modeling. I especially recommend James Davis' short, $18 book, The Logic of Causal Order. Good luck! $\endgroup$
    – rolando2
    Commented Apr 30, 2012 at 23:44
  • $\begingroup$ I agree with @rolando2. You also might want to look into structural equation modeling as a way to sort this out. You should also make sure you are not predicting any dependent variables that actually precede the independent variables. $\endgroup$
    – mCorey
    Commented Aug 5, 2012 at 17:32

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To answer your specific questions:

1) Whether this approach is a problem depends on your specific goals, and how strong of a multicollinearity problem it induces. In principle, there is no problem with the approach you are taking, especially if your goal is prediction. But if you are trying to use a hypothesis-testing framework to draw inferences, then including the same variable in multiple ways (both directly and via some compound variable like 'competition') muddies the waters both conceptually and through multicollinearity.

2) Yes, this can be done and there are specific cases where this is standard practice - but these are relatively uncommon because it is unusual for this to be the best approach.

To sum up, I would say that these are both acceptable approaches in specific scenarios, but there are likely to be better ways to analyse your data. As @mCorey points out, structural equation models is likely to be a good solution to the type of problem you are facing (or given the date of the question, once faced). Being clearer about your goals and data will help the community here point you in the most productive direction.

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