Title: The multiple regression and hierarchical clustering analysis for research in higher mathematics

Authors: Tongzhi Lin; Tengyi Liu; Chuantao Li

Addresses: School of Mathematics and Statistics, Guilin University of Technology, Guilin, Guangxi Province, 541004, China ' Peking University, Beijing, 100000, China ' China University of Geosciences (Beijing), Beijing, 100000, China

Abstract: This study evaluates the effectiveness of various teaching methods in advanced mathematics education by integrating hierarchical clustering with multiple regression analysis, taking into account the heterogeneity of student groups. A two-stage analytical framework was adopted. First, hierarchical clustering was applied to data such as student performance and classroom participation to classify students into distinct groups. Second, separate multiple regression models were developed for each group to examine the influence of key instructional factors - including teaching methods, frequency of technology use, and timeliness of assignment feedback - on academic performance. The experimental data were drawn from three semesters of student records from a university's mathematics department, supplemented by interaction data from an online learning platform. This study offers a novel approach to advanced mathematics instruction, emphasising the value of differentiated teaching and the benefits of integrating technology with pedagogical content to enhance learning outcomes.

Keywords: advanced mathematics instruction; hierarchical clustering; multiple regression; differentiated teaching; blended learning.

DOI: 10.1504/IJDSDE.2025.150071

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.5, pp.406 - 424

Received: 09 Jun 2025
Accepted: 05 Aug 2025
Published online: 28 Nov 2025 *

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