nth order polynomial regression

Here is the solution to an nth order polynomial regression equation.

nth order polynomial regression

Suppose you have a set of data points, or ordered pairs (yi, xi). You want to fit a curve to that set of data points. Using this equation, you can find the function y(x) that best fits that set of points to whatever order you wish. For example, if you wanted to do a quadratic regression, you would get:

y(x) = a*x^2 + b*x + c

And my equation would give you the values for a, b, and c. So, from this you could plot the data points along with the quadratic and make predictions about future data, or to interpolate.

If you wanted to do a 5th order polynomial, you would get:

y(x) = a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0
And my equation would give you the values for a5, a4, a3, a2, a1 and a0.


You may now rest easy at night knowing that if you're ever in a life and death situation where you need to find the nth order polynomial regression equation, you'll know right where to look.