Modeling Monthly Internet Data Package Expenditures Using the Numerical Method of Inverse Matrices

Yohanes Gian; Natalia; Marhami

doi:10.33541/edumatsains.v11i2.7790

Authors

Yohanes Gian Universitas Kristen Indonesia
Natalia
Marhami Universitas Malikussaleh

DOI:

https://doi.org/10.33541/edumatsains.v11i2.7790

Keywords:

mathematical modeling, internet data package, inverse matrix, linear regression, numerical method

Abstract

Mobile data has become a routine monthly expense for many university students, yet few studies have modelled this expense, and fewer still show the linear algebra behind such a model. In this study we built a model of monthly internet data package expenditure using the matrix inverse method. Fourteen students from the 2023 cohort of the Mathematics Education Study Program at Universitas Kristen Indonesia completed a short questionnaire on the quota they bought each month (GB) and the amount they paid for it (thousand IDR). We arranged these responses as a design matrix, formed the normal equations, and solved them with the inverse of X^TX. After checking the arithmetic, we evaluated the model with the coefficient of determination, F- and t-tests, residual analysis, and the mean absolute percentage error (MAPE). The model obtained was Ŷ = −7.271 + 2.250X, so every extra gigabyte added roughly IDR 2,250 to a student’s monthly spending. Quota accounted for 93.6% of the variation in expenditure (F(1, 12) = 175.02, p < 0.001), and the predictions missed the actual amounts by 12.60% on average. The negative constant was not significant, which means the model should only be used between 10 and 50 GB. The 30 GB packages deviated most from the line because they cost more per gigabyte than the others. For students, the model offers a quick way to budget for data; for lecturers, it is a worked example of the matrix inverse applied to data that students produced themselves.

References

Al Mustofa, M. H., & Nurmalitasari, N. (2023). Analisis harga kuota internet menggunakan metode multiple regresi linear. Prosiding Seminar Nasional Teknologi Informasi Dan Bisnis (SENATIB) 2023, 319–325. https://ojs.udb.ac.id/Senatib/article/view/3203

Ali, C. A., & Avivor, E. K. (2026). Integration and applications of linear algebra in STEM programmes: A case study of Ghanaian universities. MATHEdunesa, 15(2), 253–273. https://doi.org/10.26740/mathedunesa.v15n2.p253-273

Amanda, N. A., Afandi, M., & Tarigan, I. M. B. (2026). Analisis akurasi dan efisiensi metode matriks invers dalam penyelesaian sistem persamaan linear menggunakan aplikasi Matlab (Studi kasus: Produksi Hannasa Cake & Dessert). Jurnal Jendela Matematika, 4(2), 167–175. https://doi.org/10.57008/jjm.v4i02.3305

Amoah, B., Kwablah, E., Angmor, E., Tobbin, P. E., Amoakohene, G., & Amoah, A. (2026). COVID-19 pandemic: Unveiling the cost burden of online learning among university students in a developing country. SN Social Sciences, 6(4), 135. https://doi.org/10.1007/s43545-026-01409-5

Bagaswara, D. I., & Astuti, Y. P. (2025). Prediksi penjualan tanaman hias menggunakan regresi linier berganda dengan perbandingan eliminasi Gauss dan Cramer. Edumatic: Jurnal Pendidikan Informatika, 9(1), 266–274. https://doi.org/10.29408/edumatic.v9i1.29627

Dorokhov, O., Malyarets, L., Yevstrat, D., & Ukrainski, K. (2022). Estimation of parameters in regression analysis based on QR decomposition of rectangular matrices by Householder reflections. Informatica, 46(4), 551–556. https://doi.org/10.31449/inf.v46i4.3984

Epperly, E. N., Meier, M., & Nakatsukasa, Y. (2026). Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers. Communications on Pure and Applied Mathematics, 79(2), 293–339. https://doi.org/10.1002/cpa.70013

Fathoni, F., Ardhani, D. A., Bahri, C. A., Widasari, Y. N., Casanova, M. P., & Ibrahim, A. (2025). Analisis pengaruh pembayaran digital aplikasi Y terhadap pengeluaran mahasiswa menggunakan metode regresi linear berganda. JATI (Jurnal Mahasiswa Teknik Informatika), 9(4), 6442–6446. https://doi.org/10.36040/jati.v9i4.14150

Hwang, S., & Han, S. (2025). Pre-service mathematics teachers’ competencies in designing mathematical modeling tasks. Journal of Mathematics Teacher Education, 28(3), 713–743. https://doi.org/10.1007/s10857-025-09678-2

Jaca, C. A. L. (2022). State university students’ learning locations and remote learning challenges during the COVID-19 pandemic. International Journal of Learning, Teaching and Educational Research, 21(2), 176–194. https://doi.org/10.26803/ijlter.21.2.11

Mahe, A. F. Y., & Kharisudin, I. (2026). Mathematical modeling in mathematics education: A bibliometric-systematic literature review highlighting current research trends and future research directions. EduMatSains: Jurnal Pendidikan, Matematika Dan Sains, 11(1), 53–67. https://ejournal.uki.ac.id/index.php/edumatsains/article/view/8249

Maimunah, M., Putri, L. N., & Sulistyaniningsih, E. (2026). Levels and dimensions of mathematics anxiety among students enrolled in the linear algebra and matrices course. EduMatSains: Jurnal Pendidikan, Matematika Dan Sains, 11(1), 344–357. https://doi.org/10.33541/edumatsains.v11i1.8511

Meier, M., Nakatsukasa, Y., Townsend, A., & Webb, M. (2024). Are sketch-and-precondition least squares solvers numerically stable? SIAM Journal on Matrix Analysis and Applications, 45(2), 905–929. https://doi.org/10.1137/23M1551973

Melani, N., Ningrum, N. A., & Tarigan, I. M. B. (2026). Analisis efektivitas algoritma Gauss-Jordan dan kofaktor-adjoint menggunakan aplikasi pembanding C++ (Studi kasus NaKeiZa Cookies). Jurnal Jendela Matematika, 4(2), 150–158. https://doi.org/10.57008/jjm.v4i02.3227

Nopriyanti, T. D., Zulkardi, Putri, R. I. I., & Aisyah, N. (2025). Designing a STEM-based learning trajectory on tangent lines to parabolas using a football context for pre-service teachers. Kreano, Jurnal Matematika Kreatif-Inovatif, 16(2), 309–328. https://doi.org/10.15294/kreano.v16i2.33871

Parandrengi, M. J., & Hiltrimartin, C. (2023). Students’ errors in solving climate change context mathematical modeling problems. Jurnal Elemen, 9(2), 388–402. https://doi.org/10.29408/jel.v9i2.11422

Putri, O. R. U., & Zukhrufurrohmah, Z. (2022). Proses translasi permasalahan realistik menjadi representasi matematis mahasiswa teknik informatika. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(2), 1343–1354. https://doi.org/10.24127/ajpm.v11i2.4856

Putriani, J. D., Rosyada, A., Hartono, Y., & Darmawijoyo. (2025). Students’ mathematical modeling ability in answering 2022 PISA-released items in scientific context. EduMatSains: Jurnal Pendidikan, Matematika Dan Sains, 10(2), 15–29. https://doi.org/10.33541/edumatsains.v10i2.6948

Rahman, M. (2023). Efficacy of subsidy quota usage to support learning in the Covid-19 pandemic. Advances in Social Science, Education and Humanities Research (Proceedings of IJCAH 2022), 724, 757–765. https://doi.org/10.2991/978-2-38476-008-4_81

Ramírez-Montes, G., Henriques, A., & Carreira, S. (2021). Undergraduate students’ learning of linear algebra through mathematical modelling routes. Canadian Journal of Science, Mathematics and Technology Education, 21(2), 357–377. https://doi.org/10.1007/s42330-021-00149-3

Simamora, R. M., & Nababan, R. (2024). Students’ experience of online learning during the COVID-19 pandemic. Jurnal Pendidikan Indonesia, 13(1), 146–158. https://doi.org/10.23887/jpiundiksha.v13i1.62723

Sugiyarto, S., Suwarto, S., & Turkamun, T. (2022). Subsidi kuota internet terhadap motivasi belajar serta dampaknya terhadap partisipasi mahasiswa pada pembelajaran daring. Derivatif: Jurnal Manajemen, 16(2), 315–322. https://doi.org/10.24127/jm.v16i2.1105

Wibawa, G. R., & Pauzy, D. M. (2022). Pengaruh pandemi Covid-19 terhadap pola konsumsi mahasiswa di Kota Tasikmalaya. Sains Manajemen, 8(1), 10–18. https://doi.org/10.30656/sm.v8i1.4934

Widiawati, T. U., Alfian, M. R., & Baskara, Z. W. (2025). Analisis faktor-faktor yang mempengaruhi besar biaya pengeluaran belanja online mahasiswa FMIPA Universitas Mataram menggunakan regresi Tobit. Indonesian Journal of Applied Statistics and Data Science, 2(2), 104–112. https://doi.org/10.29303/ijasds.v2i2.8975

Wiegand, S., & Borromeo Ferri, R. (2023). Promoting pre-service teachers’ professionalism in STEAM education and education for sustainable development through mathematical modelling activities. ZDM – Mathematics Education, 55(7), 1269–1282. https://doi.org/10.1007/s11858-023-01500-8

Winarni, S., Kamid, Marzal, J., & Asrial. (2025). Numeracy skill development in prospective mathematics teachers: Challenges and opportunities in real-world contexts. Journal on Mathematics Education, 16(1), 91–110. https://doi.org/10.22342/jme.v16i1.pp91-110

Wulandari, N. W. V, Sari, R. N., Ruliana, I., Alfiah, M. R., Ulan, D. A. S. N., Safutri, M. F., Sofiyah, N. Y., Rahmawati, R., & Utari, F. D. (2026). Pengaruh uang saku dan QRIS terhadap konsumsi mahasiswa: Analisis regresi linear berganda. RIGGS: Journal of Artificial Intelligence and Digital Business, 5(2), 15182–15190. https://doi.org/10.31004/riggs.v5i2.11351