A polynomial fit is a specific type of multiple regression. The simple regression model (a first-order polynomial) can be trivially extended to higher orders.
The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of polynomial equations of order p with polynomial coefficients { b0 ... bp}. The model can be expressed using data matrix x, target vector y and parameter vector ?. The ith row of X and Y will contain the x and y value for the ith data sample.
The variables will be transformed in the following way: x=> x1, ..., x^p => xp Then the model can be written as a multiple linear equation model: y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e
@author Elke Achtert