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C # Numerical polynomial regression

I'm starting one of my first C # projects - I need to find a curve match for several xy data points.

For instance:

x: 1,2,3,4,5,6 y: 0,5,5,0,5,2,5,5,0,5

As it happens, a suitable curve, suitable for me for these points, is a sixth order polynomial, according to excel.

How can I get the coefficients and indicators of this curve to write my own expression in C #? I want to stay away from libraries because it will most likely be converted to C for use on microprocessors.

I am new to C # and know little about the integration of hardware and software.

However, I am now reading about digital methodology ... the second step of this project is to take a curve and integrate numerically between successive minima ...

Any tips / pointers are welcome.

The input will be determined by the six coordinates xy ...

Problem number 1: How to write a polynomial, given the six coordinates?

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The problem of finding the coefficients of a polynomial given n points estimated for some x iis known as the problem of polynomial interpolation. You can read the details of the problem and its solution here (wikipedia.org).

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