Implementing polynomial regression trees in Effective Quadratures

Effective Quadratures is an open source library used to generate polynomials for parametric computational studies. Among the applications of the library is the ability to perform polynomial regression on a dataset. I propose an implementation of a polynomial regression tree class in Effective Quadratures which will offer greater accuracy when extrapolating compared to the current polynomial regression class.

By implementing a polynomial regression tree class I believe that I will help demonstrate some of the benefits of using orthogonal polynomials in the context of model trees. For example users of the library will be able to calculate sensitivity indices and moments over subdomains of functions and datasets. This has the benefit of providing more information about the dataset than was previously possible in the library.