First thing you do is try to make sense of the data, if I can model 15 points with 2, 3, 4 parameters and further ones don't add any improvement I'm onto something. I've always done polynomials first, you can see if there's something much simpler than Lagrange interpolation, which in my experience means you have to go straight to the literature about that kind of problem.

(Of course this works as long as you aren't seeing any peaks)

oefrha, for some reason I can't reply to your comment just yet so I'll post it here: Of course. This is just my own criterion when I start with a bunch of data I know nothing about. Is there a complicated law behind them or maybe not? Am I seeing noise or there's a signal? You can fit anything smooth with a low order polynomial, so maybe there's a differentiable function right in front of you. It's just something I do and if you see no reason for it I might even agree with you on that. It never ends up in the model, though. It's just something I find useful at a preliminary stage.

OK, We're not being responsible doing this and I'm not qualified to do it. I just have been fitting the data and maybe I've been lucky and I'm just an idiot. Having said that, this is also my problem, I have right now a hotspot in the vicinity and I'm worried. I just want to have a quantitative idea of what's going on. Now it's your job as experts to explain what's going on to the politicians and make sure they hear and they can do the right thing. I wouldn't be worried if the messages had matched the numbers when this started, they didn't. At some point we need someone to tell us "we're at this point and tomorrow we'll be at that point". I shouldn't feel compelled to find out by myself what all this is about. I feel awful by posting all this, I'm perfectly aware that non-experts in a field spout nonsense, but this is a very nonsensical situation and I'm tired of hearing we've been doing fine.