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I am trying to create an equation that can be used with data points I have collected. They are of the type

 [FirstParameter] [SomeEquation] = [SecondParameter]   

I know the first and second parameter, but not the equation that can generate them correctly for any first/second parameter input

As an example, my data points look like this:

[160] [some equation] = 10000

[1500079] [some equation] = 23000

What equation could fit both lines above to yield the correct result? If I added a new line of data and the first parameter was 2389 and I had the correct equation, I would like to be able to use that to figure out the second parameter.

To be clear, I am looking for a general equation that can solve for any new line instead of a specific equation that only works for the current line. If I just use multiplication I have a specific equation that works for each individual line, but does not work for every line. I am not looking for what is shown below (since 62.5 != 0.015332526)

160 * [62.5] = 10000

1500079 * [0.015332526] = 23000

Thanks!

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  • $\begingroup$ Welcome to MSE! If I understand, you're asking a question of "interpolation", i.e., you're seeking a function $f$ (given by some kind of formula) such that $f(\text{FirstParameter}) = \text{SecondParameter}$. In addition to your data, you need to settle on (i) the type of function/formula you're willing or able to entertain, and (ii) some way of quantifying "error", namely, assigning a "penalty" to the fact that your formula won't always generate exact answers. It will help if you can say something about where your data originate; otherwise this is probably too broad of a question to answer. $\endgroup$ – Andrew D. Hwang Mar 9 '15 at 16:46
  • $\begingroup$ Hi, thanks for responding! The first parameter is a distance an object is from the ground. The second parameter is how much higher than the first parameter the eye level should be to look down on that object (aka zoomed out). So, the higher an object is from the ground, the zoom will increase slighter. 100% accuracy is not necessary so I shouldn't have to account for error in this scenario. $\endgroup$ – user2992188 Mar 9 '15 at 16:54
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We can make an exact polynomial that fits every $x$ you have with their exact corresponding "$y$" needed but the more points you have, the larger the polynomial is, and that road does not really care about having any "predictive" accuracy. So we should actually use some statistical approach, we need to plot the data, $x$ vs $y$, see if there is some sensible function that we could approach and then fit some simpler curve. Can you provide a list $(x,y)$ of the points you want to fit to a function?

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  • $\begingroup$ Hi, thanks for responding. Those are the only 2 line I have at the moment where I know the second parameter. Is it possible to base it off of what is already in the original post? How many lines at a minimum have to be known to produce a decent curve? $\endgroup$ – user2992188 Mar 9 '15 at 17:50

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