A general model of regression using iterative series

TL;DR

This paper introduces a versatile iterative series-based weighted least squares regression method that expands the dependent variable into a series of functions, improving fit accuracy with more terms.

Contribution

It proposes a novel general framework for univariate regression using iterative series expansion and residual minimization.

Findings

The method effectively reduces residual sum of squares.

It allows flexible function choices for series expansion.

The approach improves regression accuracy with more series terms.

Abstract

We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an iterative process which reduces the sum of the square of the residuals. Thus by evaluating the regression series to a sufficiently large number of terms we can, in principle, reduce the sum of the square of residuals and improve the accuracy of the fit.