Given a set of points, I'm looking to find the best possible line (within reason) to fit to these points. These points won't be from real data, so they could form any sort of curve or line. So, I would like to find the regression with multiple different types of lines, and see which one matches best. For example, I would like to do regression for linear, polynomial, exponential, logarithmic, etc. If possible, I would love to have polar or radial regression (if those even exist).
I have googled for all these different types, and I have found no results for many of them. How much of this is possible? For the ones that are possible, please point me to some links online about how to do them. Thanks!
**EDIT: the purpose of this will be to provide a general tool for finding a good model for ANY shape, not just gathered data. So There are really no constraints, I would just like to find the one with the closest possible correlation.