How to determine a mathematical function from a graph/set of data

[Elixir]

Hi OcUK, thought I'd attempt to tap your collective minds. I'm doing a study at the moment which is attempting to predict a particular value y (velocity) with respect to x (time).

I have a bunch of data obtained using different values of various parameters which affect the velocity, and ideally I'm trying to obtain a function which incorporates all of these parameters and describes the change in velocity over time.

Does anyone know a good way to go about trying to attach a function to a certain graph/set of data and then modifying that (which I can only assume is trial and error) to take the other parameters into account.

One of the graphs is shown below, which seems to be some kind of inverse square function, but I don't have a huge background in theoretical maths so I'm struggling to get any further!

Any pointers/websites/programs I can use to help me out? Excel doesn't seem to like fitting trendlines to inverse squares although I'm probably just not aware of how to do so!

Thanks

 

[Elixir]

Thanks for the response, I hadn't though of plotting the inverse etc. It does indeed look like an exponential decay and fits with the physical nature of what's happening.

I should be able to find an equation that fits the base case (shown in original post), but I think trying to find an equation that encompasses all of the parameters might be a bit optimistic...

A long couple of weeks fiddling with Excel ahead of me I think!

 

[Elixir]

I'll have a look at Matlab/GNU Octave, thanks.

Converting it to a linear relationship and then continuing my work from there seems to be the first step!

EDIT:

This is looking a lot more doable already!

 

[Elixir]

minitab regression quadratic fitted line plot

If you want to list your data I'll run it for you

I should be fine with my current method for now, but thanks a lot for the offer!

Cant you just run it with a line of best fit in excel and ask it to show the line equation? But use a poly/power line etc.

Cheers,

Nick

Yeah I tried that but none of the options Excel gave wanted to fit my curve, I think the first couple of points are slightly anomalous which might have thrown it off, only noticed once I plotted ln(y).