Find / "reverse engineer" a formula?

Questions
1

I have come across a formula that has been kept private for the past decade and I want to go about recreating it, however don’t know where to begin. I do know that it is deterministic and I know the inputs/outputs. I do not know the relationships of the variables. The first input is weight of the participant, the next four variables are athletic measurements. The output has no unit of measurement and is just one single number. Here are a few examples of the inputs/outputs

Inputs: 181 lbs, 4.75 s, 4.04 s, 33.6 ft, 35.5 in Output: 99.66

Inputs: 163 lbs, 4.91 s, 4.04 s, 33.6 ft, 36.5 in Output: 92.79

Inputs: 185 lbs, 4.82 s, 4 s, 33.5 ft, 31.1 in Output: 93.96

Inputs: 193 lbs, 4.7 s, 4 s, 33.5 ft, 33 in Output: 102.78

Inputs: 171 lbs, 4.69 s, 4.01 s, 33.5 ft, 32.7 in Output: 97.53

Where can I begin? What kind of formulas should I try? Any help is greatly appreciated

2

Have you tried FindFormula? Also you’ll likely need way more than four data points to get a sense for this (and anyone helping you would too).

3

I don’t think FindFormula is going to work here since the inputs are 5-dimensional and FindFormula only works on x-y type data. Realistically, I’d first throw this whole data set into Predict first and see what it comes up with. It won’t be a formula, but maybe the prediction method will tell you something. And if the predictor works well, you can use it to generate helpful plots.

Other than that, I’d recommend plotting the data in as many different ways as you can come up with. For example, try a log-log plot from the weights to the output to see if there’s some power-law that connects the two.

4

Tell us what you trying to find so we know it’s not illegal, and so we can comment on the physics,
then I’ll offer advice. :slight_smile:

5

LinearModelFit or the nonlinear alternative might be useful here. But it would really require a larger data set in order to give a plausible result.

6

If I understand correctly, DATAMODELER from Evolved Analytics should be able to do what you want (have never used it…, just saw presentations). But it is a paid “package”.