I have some economic data in hand, and I would like to make forecasting out of it (e.g., consumer demand, price elasticity and so on). As far as I understand, these characteristics can be (to some extent) approximated by polynomials. I know about Lagrange interpolation. If there were some data of input variable X and output F(x) I would easily interpolate by Lagrange, and predict F(x) for the future values. But there is a lot of input variables in my data, and I am not sure where to start. How should I analyze this data? Maybe fix some input variables and try to interpolate the rest? Maybe I have not enough data to make these predictions?
So I would like to get some directions on where to start. If you could suggest some books or articles on this subject (preferrably focused on practice), that would be perfect. I know basic algebra and calculus, but haven't worked with optimization and prediction on real data.
UPD. When I asked this on mathoverflow, it was suggested to ask it here, so I apologize for multiple postings. Folks there recommended Ken Judd's Numerical Methods in Economics book, but as far as I get out of Google Books, it is too theoretical for me, because what I want is to solve a practical problem. Ideally, I would like the examples in the books to be solved with Matlab/Mathematica/Excel.
UPD2. Ok, answering a clarification, I would be more specific. I have a data of a production and trade company for some period. It is monthly-tabulated and contains money spent for advertisement in that month (in journals and Internet, let's denote A1 and A2 respectively), good price P for that month, number of good units sold for that month S (filled post-factum). In fact, S = S(A1, A2, P) is a multivariable function. In reality, number of input variables is slightly larger (seasonal changes that affect customers' demand, competitors prices that are also tabulated, let's say up to 6 input variables). What I want to do is to predict S(A1, A2, P) for the coming month given A1, A2, P, i.e. to predict sales.