Can I use dependent variable from a regression analysis as an independent variable in yet another regression analysis? 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??
 A: 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.
