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I'm trying to come up with an equation for the AP grading scale. My first attempt was to just use a simple quadratic equation, and get it as close as possible to the curve, then I came up with the idea to use a polynomial regression, however, it doesn't hit each of my points exactly (tis the nature of a regression) Is there some kind of curve that hits each data point rather than roughly estimating the closest curve?

This is what I have so far:

The black dots are my data points (I added a few extra to make the regression turn the way I want it to), The orange curve is my attempt at quadratic, and the green equation is the regression. https://www.desmos.com/calculator/mg75cjdr80

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    You can use a Lagrange polynomial but even though it will hit all points it's probably not the best choice. – 2017-02-15
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    I assume you are trying to interpolate. If you have got the software to do it, then cubic splines or similar is good. – 2017-02-15

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