Can I build a program that will tell me if a real world data set looks linear, logarithmic, exponential etc?

Question

I have a bunch of real world data sets and from manually plotting some of the data in graphs, I've discovered some data sets look pretty much logarithmic and some look linear, or exponential (and some look like a mess :). I've been reading up on curve fitting / data fitting on wikipedia and if I understand it correctly (which I seriously doubt) I can calculate a curve of best fit using least squares calculations, but I have to determine if I want to have the curve fit a logarithm, linear or exponential (etc) pattern first. What I would really like to do is to pass a data set into a function (I'm a programmer with poor math skills) and have that return something like "this data set looks more linear than logarithmic" or "this looks exponential". My question is: is that even possible, without a human looking at a graph and recognizing the pattern ? My guess is: yes. But before I invest a ton of time in figuring out how to program this, I just want to make sure I'm not barking up the wrong tree and confirm this with you guys if possible. Sorry if this is a dumb question, but just to be clear, I'm not looking for a how-to answer, just a simple yes or no will do, however if you have suggestions on how to tackle the problem, that would be awesome of course.

Answer 1

You can do both a linear AND an exponential regression,

Then you can calculate the R-coefficient and/or test for goodness of fit.

Based on those values, you can officially say one is linear as opposed to

exponential, or vice versa.