# How do i estimate an equation of best fit of a sort-of exponential equation given it's points?

There is an unnessarly long table of values of an item in a game that grants experience to a player based on one's level in the chosen skill. I think it would be much more appropriate to cite the equation of the relationship between exp and level, but i don't know how. It does not appear to be exponential, but it has a similar characteristic of starting low and raising over time. The table of values can be found here. Any help would be appreciated.

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This is a difficult problem in general, because in general it is so broad. If you suspect the relationship is linear, you can use least-squares to approximate it with a linear relationship and see how well the approximation fits. If you suspect that the relationship is exponential, you can take the logarithm of all the values, and then use least-squares to find a linear relationship for the logarithms. –  MJD Mar 14 '12 at 15:09

## 1 Answer

Here's an exponential fit I did by hand using trial and error:

So it seems the data is more closely described by an exponential than you thought. There are three significant deviations. The value $3770$ at $76$ seems to be a typo; the two values around $50$ may be wrong or adjusted by hand; and it seems that the initial values up to around $15$ were adjusted by hand. So you may want to remove those values and do a standard exponential fit to the rest of the data.

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wow thanks, i guess i should have looked at more points, since there seems to be slight deviation in the data –  Alexander Momchilov Mar 15 '12 at 0:52