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International Journal of Academic Research in Progressive Education and Development

Open Access Journal

ISSN: 2226-6348

Multiple Regression Modelling for Mathematics Performance: Best Model Selections

Sitti Sham Amir, Siti Rahayu Mohd Hashim, Dg Siti Nurisya Sahirah Ag Isha, Mohd Khairuddin @ Jerry Abdullah

http://dx.doi.org/10.6007/IJARPED/v13-i3/21712

Open access

Initiating mastery of mathematics in primary school is pivotal for successful learning at higher levels. Multiple regression analysis stands as a cornerstone in statistical methods for modelling mathematical achievement. However, despite its prevalence, earlier studies often neglect to disclose the essential assumptions requisite for effective multiple regression modelling. Moreover, the impact of variable selection methods on model generation and subsequent identification of the optimal model remains insufficiently explored. Considering these gaps, this study was undertaken to identify significant factors influencing students' mathematics achievement while ensuring adherence to multiple regression analysis assumptions. Utilizing demographic data, the number of books, home educational resources, student attitudes, and mathematics anxiety as independent variables, two models were derived: Model 1 incorporated all variables without domains, while Model 2 included domain-specific variables and adhered to multiple regression assumptions. The findings revealed that the Model 2 is the best model since it has highest , adjusted , lowest standard error of estimation, lower values in 8 selection criteria which also fulfilled assumptions of multiple regression analysis. In conclusion, key determinants of mathematics achievement were identified as the number of books (101-200), student confidence, and mathematics learning anxiety. The constructed model elucidated 27.6% of the variance in mathematics achievement. This study underscores the importance of meeting regression test assumptions for modelling accuracy and provides actionable insights for schools to design interventions aimed at enhancing mathematics achievement among fifth-year students and the broader elementary school population.

Mayers, A. (2013). Statistics and SPSS in Psychology. Pearson Education Limited.
Barroso, C., Ganley, C. M., McGraw, A. L., Geer, E. A., Hart, S. A., & Daucourt, M. C. (2021). A Meta-analysis of the Relation Between Math Anxiety and Math Achievement. 1–21. https://doi.org/10.1037/bul0000307
Brezavš?ek, A., Jerebic, J., Rus, G., & Žnidarši?, A. (2020). Factors influencing mathematics achievement of university students of social sciences. Mathematics, 8(12), 1–24. https://doi.org/10.3390/math8122134
Carey, E., Hill, F., Devine, A., & Szucs, D. (2017). The modified abbreviated math anxiety scale: A valid and reliable instrument for use with children. Frontiers in Psychology, 8(JAN), 1–13. https://doi.org/10.3389/fpsyg.2017.00011
Copeland, K. A. F. (1997). Applied Linear Statistical Models. In Journal of Quality Technology (Vol. 29, Issue 2). https://doi.org/10.1080/00224065.1997.11979760
Field. (2018). Discovering Statistics Using IBM SPSS Statistics, 4th Edition by Andy Field. Discovering Statistics Using IBM SPSS Statistics, 4th Edition by Andy Field, 5. https://play.google.com/store/books/details?id=CPFJDwAAQBAJ&gl=ca&hl=en-CA&source=productsearch&utm_source=HA_Desktop_US&utm_medium=SEM&utm_campaign=PLA&pcampaignid=MKT-FDR-na-ca-1000189-Med-pla-bk-Evergreen-Jul1520-PLA-eBooks_Social_Science&gclid=CjwKCAj
Fox, J. (2016). Applied Regression Analyis and Generated Linear Models. In SAGE Publications, Inc.
Frank, E., Harrell, Jr. (2015). Regression Modeling Strategies. In Technometrics (Vol. 45, Issue 2). https://doi.org/10.1198/tech.2003.s158
Gamazo, A., & Martínez-Abad, F. (2020). An Exploration of Factors Linked to Academic Performance in PISA 2018 Through Data Mining Techniques. Frontiers in Psychology, 11(November), 1–17. https://doi.org/10.3389/fpsyg.2020.575167
Geesa, R. L., Izci, B., Song, H., & Chen, S. (2019). Exploring Factors of Home Resources and Attitudes Towards Mathematics in Mathematics Achievement in South Korea, Turkey, and the United States. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), 1751. https://doi.org/10.29333/ejmste/108487
Haciomeroglu, G. (2017). Reciprocal Relationships Between Mathematics Anxiety and Attitude Towards Mathematics in Elementary Students. Acta Didactica Napocensia, 60–65.
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate Data Analysis. In Multivariate Data Analysis: Vol. Seventh Ed (pp. 135–144). https://doi.org/10.1016/j.foodchem.2017.03.133
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate Data Analysis. https://doi.org/10.1002/9781119409137.ch4
James A. Ejiwale. (2013). Barriers to Successful Implementation of STEM Education. Journal of Education and Learning, 7 (2), 63–74.
Jansen, B. R. J., Louwerse, J., Straatemeier, M., Van der Ven, S. H. G., Klinkenberg, S., & Van der Maas, H. L. J. (2013). The influence of experiencing success in math on math anxiety, perceived math competence, and math performance. Learning and Individual Differences, 24(August 2021), 190–197. https://doi.org/10.1016/j.lindif.2012.12.014
Meliá, J., and Jesús, M. (2016). Methodological Analysis of the PISA Project as an International Assessment. RELIEVE - Revista Electronica de Investigacion y Evaluacion Educativa, 22, 1–25.
Jubok, Z., Gopal Pillay, K. & Abdullah, N. (2018). Model-Building Approach in Multiple Regression. In Penerbit Universiti Malaysia Sabah.
Kastberg, D., Chan, J., Murray, G., & Gonzales, P. (2015). Performance of U.S. 15-Year-Old Students in Science, Reading, and Mathematics Literacy in an International Context. National Center for Education Statistics, 1–42.
Keith, T. Z. (2015). Multiple Regression and Beyond An Introduction to Multiple Regression and Structural Equation Modeling 2nd Edition. In Routledge.
Krejcie, R. V., & Morgan, D. W. (1970). Using methods of data collection. Educational and Psychological Measurement, 30, 607–610. https://doi.org/10.1891/9780826138446.0006
Kushwaha, S. S. (2014). Trend in Researches on Mathematics Achievement. IOSR Journal of Research & Method in Education (IOSRJRME), 4(6), 53–62. https://doi.org/10.9790/7388-04625362
Lap Thi Tran, T. S. N. (2021). MOTIVATION AND MATHEMATICS ACHIEVEMENT: A VIETNAMESE CASE STUDY. EURO Advanced Tutorials on Operational Research, 12(3), 1–2. https://doi.org/10.1007/978-3-030-70990-7_1
Lim, S. Y., & Chapman, E. (2013). Development of a short form of the attitudes toward mathematics inventory. Educational Studies in Mathematics, 82(1), 145–164.
Megreya, A. M., Al-Emadi, A. A., & Moustafa, A. A. (2023). The Arabic version of the modified-abbreviated math anxiety scale: Psychometric properties, gender differences, and associations with different forms of anxiety and math achievement. Frontiers in Psychology, 13(January). https://doi.org/10.3389/fpsyg.2022.919764
Mullis, I. V. S., Martins, M. O., Foy, P., & Fishbein, B. (2020). TIMMS 2019 International Results in Mathematics and Science.
National Science Foundation. (2013). Common Guidelines for Education Research and Development. August, 53. https://doi.org/10.1080/00220973.2013.813364
OECD. (2015). Pisa 2015.
Orcan, F. (2020). Parametric or Non-parametric: Skewness to Test Normality for Mean Comparison. International Journal of Assessment Tools in Education, 7(2), 236–246. https://doi.org/10.21449/ijate.656077
Organisation for Economic Co-operation and Developement. (1999). Measuring Student Knowledge and Skills. In OECD Publication Service (Vol. 47, Issue 9). https://doi.org/10.1016/0042-207X(96)00127-3
Pituch & Stevens. (2016). Applied Multivariate Statistics for Statistics for the Social Sciences (Sixth). Taylor & Francis.
Randolph, K. A., & Myers, L. L. (2013). Basic Statistics in Multivariate Analysis. Basic Statistics in Multivariate Analysis. https://doi.org/10.1093/acprof:oso/9780199764044.001.0001
Tabachnick & Fidell. (2013). Using Multivariate Statistics. In Contemporary Psychology: A Journal of Reviews (Vol. 28, Issue 8). Perasin Education, Inc. https://doi.org/10.1037/022267
Timms, M., Moyle, K., Weldon, P. R., & Mitchell, P. R. U. (2018). CHALLENGES IN STEM LEARNING IN AUSTRALIAN SCHOOLS. Australian Council for Educational Research, 7, 9–11.
Warner, R. M. (2013). Applied Statistics: From Bivariate Through Multivariate Techniques. Sage Publications, Inc.
Wheatcroft, E. (2020). Assessing the significance of model selection in ecology. European Journal of Ecology, 6(2), 87–103. https://doi.org/10.17161/eurojecol.v6i2.13747
Wijsman, L. A., Warrens, M. J., Saab, N., van Driel, J. H., & Westenberg, P. M. (2016). Declining trends in student performance in lower secondary education. European Journal of Psychology of Education, 31(4), 595–612. https://doi.org/10.1007/s10212-015-0277-2

(Amir et al., 2024)
Amir, S. S., Hashim, S. R. M., Isha, D. S. N. S. A., & @Jerry, M. K. A. (2024). Multiple Regression Modelling for Mathematics Performance: Best Model Selections. International Journal of Academic Research in Progressive Education and Development, 13(3), 1137–1150.