The Application of the Least Squares Method in Excel for Analytical and Educational Modeling

Abstract

Abstract: The article examines the application of the least squares method in the Microsoft Excel environment for analytical and educational modeling. The purpose of the research is to assess the instrumental capabilities of Excel in performing regression analysis, to identify its advantages and limitations in comparison with other digital platforms, and to develop methodological recommendations for improving its effectiveness in the educational process. The methods of analysis include a review of scientific literature on mathematical modeling, an exploration of Excel’s functional tools (LINEST, TREND, FORECAST, trendline construction, and the Data Analysis Toolpak), as well as a practical evaluation of their effectiveness on an empirical dataset. For the approbation of the method, a linear regression model was constructed, with an assessment of the equation parameters, the coefficient of determination, residuals, and the standard error of estimate. The results of the research demonstrated that Excel provides a full cycle of least squares implementation: from data preparation and model construction to the evaluation of their accuracy and visualization of results. It was established that Excel can serve as an effective tool for developing applied analytical literacy among students, enhancing their critical thinking skills, and integrating knowledge of mathematics, informatics, and economics. The conclusions emphasize the feasibility of using Excel as an educational platform for mastering regression analysis through the least squares method. The accessibility of this software, the simplicity of implementation, and the visualization capabilities determine its significant potential in training students of economic, technical, and natural sciences specialties. At the same time, the identified limitations in verifying statistical assumptions highlight the prospects for further research aimed at comparing regression analysis results in Excel with those obtained in specialized environments (R, Python, SPSS), as well as at developing integrated educational cases for multifactor and nonlinear models.