Least Squares Optimization with Incorporations from Haar Wavelet

This study explores the fusion of Least Squares Optimization and Haar Wavelet analysis using twenty years of climate data. Regression analysis was conducted on monthly rainfall and diurnal temperature variation data from the Climate Research Unit. Statistical methods were applied utilizing MS Excel, MINITAB 14, and MATLAB software. The research examines the background of Least Squares Optimization and its integration with Haar Wavelet analysis. It introduces a novel central tendency measure, contrasting it with traditional mean calculations and emphasizing its significance. Furthermore, the implementation of this new measure is demonstrated through a MATLAB program, detailed in the appendix. The study contributes to the understanding of optimization techniques alongside wavelet analysis, offering valuable insights into the analysis of intricate datasets such as climate data. By employing advanced statistical methodologies, this research enhances our ability to discern patterns and trends within complex environmental data, ultimately facilitating more informed decision-making in various fields reliant on climate information. This study aims to examine diverse techniques within Least Squares Optimization and explore their applications across varied domains. Additionally, it focuses on a comprehensive investigation into the Haar wavelet and its inherent properties. A central objective is to integrate the Haar wavelet methodology with Least Squares Optimization, with the goal of refining optimization processes through wavelet-based approaches. By conducting this investigation, the study endeavors to illuminate the potential advantages and consequences of incorporating the Haar wavelet within the framework of Least Squares Optimization, ultimately fostering the development of more efficient and resilient optimization strategies.