Let's say that you have some set of data and are trying to model that data with an equation. This same set of data might be linear, quadratic, or of an even higher order polynomial.
I know that if you were to do a best-fit, you could model the data as being a number of different orders based on the approach you decide to take. What I am trying to do is write a program that looks at a set of data and says, "this is most likely a linear equation." Is there a way to determine if a set of data is considered "linear"?
Here's my thought process and example taken from my situation. For a program I am writing I ultimately have to determine if data is considered "linear" which seems rather subjective. I was thinking that I could approach it something like this... Try and model the data at a few different orders of polynomials then come back and say... well, it's somewhere between but... it's closer to being a quadratic than it is to being linear. Is there a mathematical process/method I can follow to achieve something like that?
Another one of my concerns is that a set of statistical data is not perfect, so if you were to determine that an equation for a set of data has an order of 1.01... I'd be a bit confused, because that's really close to being linear. Would you just call it linear though?