Hi all. I need some advice in a project I'm into. I have some experimental (simulation) data and i need to find a function that fits to it. The experimental data behaviour change when I modify some parameters I have. My goal is, from that single function, been able to predict how the experimental data will change, acording to the parameters: I mean, been able to find an analytical expression that represents all the information I have. For the characteristics of my problem, I've decided to try with a polynomial function. To been able to see how the factors varies, i've done some fits with mathematica. However, every time i change the polynom degree, not only the factor changes of value, but its signs can also change (for example, the factor of the cuadratic part, in a 4-degree polynom fit is positive, and in a 5-degree polynom fit is negative). I'm aware that there is not a unique function that can represent some data. However, this behaviour is a big problem to my goal since this breaks down any truly generalization attempt of my solution. As far as I suspect, a possible solution for this problem is trying to make the fit in a set of orthogonal functions: particularly, in orthogonal polynomial functions. However i would like to know your opinion on this. In particular two aspects worries me of this aproach: the first one is if making my fit in orthogonal polynomials (or orthogonal functions in general), would really solve my problem of changing cofficients with the degree of the function that i use to make the fit. The second one is that some of this sets (the few I know), like the Legendre polynomials, have even in their high degree polynomials, terms that include cuadratic dependence: i wonder if this would not be a problem, since I believe that the data have a strong dependence on this term (this is more an observational hunch, nothing rigorous) I hope I make myself clear. Any suggestion or advice would be really apreciated. Also, any bibliography to develop the orthogonal fit would be nice (if it is still a good idea, of course).