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I'm working a problem, attempting to find a income tax rate that will change depending on the gross paycheck amount. Some data points:

$800 gross = 11% taxed

$1500 gross = 16% taxed

$2000 gross = 20% taxed

How would I go about finding the relationship between the gross paycheck amount and the percentage taxed? Beyond that as well, how will I then be able to apply that relationship mathematically in order to obtain other data points (\$1000 gross paycheck, $500, etc...) and get an accurate tax percentage for them as well? I have a feeling it'll be an answer lying somewhere in the statistics field, but I'm no math expert.

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    Your problem has no unique solution, there is an infinite amount of tax regulations that will generate your output.2011-11-26
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    Well I'm not looking for something that's exactly perfect in it's output, but plotting the data points it does seem to follow a trend. So hopefully from that I can ascertain a polynomial that will give me accurate answers within a given percentage.2011-11-27
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    It is possible to find a polynomial that returns exact values for finite number of points. If the relationship is truly a polynomial of degree n (or less), then every thing is fine. However, if the polynomial is of a degree > n, then any interpolation or extrapolation, may not provide an accurate value.2012-01-26

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