Curve Fitting Simplified: Exploring the Intuitive Features of CurvPy

Abstract: CurvPy is an open-source Python library for automated curve fitting and regression analysis, aiming to make advanced statistical and machine learning techniques more accessible. This paper explores the mathematical foundations and implementation of key CurvPy components for optimization, smoothing, imputation, summarization, visualization, regression, evaluation, and tuning. The methodology leverages well-established statistical and computational algorithms adapted through both simplification and exposure of advanced options to balance usability and customizability. Mathematical techniques utilized include least squares estimation, Savitzky-Golay filtering, matrix completion, gradient descent optimization, regularization, basis function regression, and standard model evaluation metrics.