Regression variable trick I am working with a set of data with a single dependent variable $Y$ and many potential explanatory variables $c_1,\cdots, c_n$.  When I define another variable as $c_1*c_2/Y$, I find that it with a few other variables $c_3, c_4, c_5$ explains $Y$ very well.  However, my concern is that because it is defined in terms of $Y$, I am just using a math trick that will make this work.  Am I allowed to do this, or does this break some rules of regression?  And, if so, is there a way to change my model so that it does not rely on a variable defined in terms of the dependent variable?
 A: Your intuition is correct, you cannot do this.
Models are there to make predictions.  That may not always be what we use them for explicitly, but anything you learn from a model that doesn't predict its response well is dubious.  What you are advocating is predicting $Y$ using some pieces of information, one of which is $Y$ itself.  That's not really a prediction, that's just unwinding your formula to get at the information inside.
The best thing to ask yourself is what if I didn't know $Y$, could I still make a prediction?  If the answer is no, then you don't really have a predictive model.
It's like me saying "I can predict how many fingers you are holding up behind your back" and then placing a mirror so that I can cheat.  Sure, I'm getting the right answer, but am I really doing anything impressive?  Would you bet money on me doing it in public?
This type of thing is generally called data leaking, but it usually comes up in less obvious circumstances.
I'm not sure what you mean

Is there a way to change my model so that it does not rely on a variable defined in terms of the dependent variable? 

Of course, just don't use any predictors that have Y explicitly or implicitly build in.
