In this chapter, we have investigated several examples of regression analysis, including linear regression, polynomial regression, multiple linear regression, and more general curve fitting. In each case, the objective is to derive from a given dataset a function that can then be used to extrapolate from the given data to predict unknown values of the function.
We've seen that these regression algorithms work by solving a system of linear equations, called the normal equations, for the problem. That part of the solution can be done by various algorithms, such as Cramer's Rule, Gaussian Elimination, or LU decomposition.
We used several approaches to implement these algorithms, including Windows Excel, direct Java implementations, and the Apache Commons Math library.