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Articles
DOI: 10.32806/jkpi.v7i3.1716
Submitted: 16-04-2026
Published: 27-09-2026

STATISTICAL ASSUMPTION TESTING IN MULTIPLE LINEAR REGRESSION FOR EDUCATIONAL RESEARCH: EVIDENCE FROM A SECONDARY SCHOOL SURVEY IN INDONESIA

UIN Raden Fatah Palembang
UIN Raden Fatah Palembang
UIN Raden Fatah Palembang
UIN Raden Fatah Palembang
multiple linear regression, regression diagnostics, statistical assumptions, learning outcomes, quantitative educational research, purposive sampling, Indonesia

Abstract

Multiple linear regression is widely used in educational research to examine the statistical association of several predictors with an outcome. Its interpretation, however, depends on appropriate model specification and diagnostic evaluation. This study examined a two-predictor regression model of students’ learning outcomes and evaluated the statistical assumptions preceding model interpretation. A quantitative survey design was conducted at SMA Negeri 1 Rantau Bayur. The sample comprised 40 students selected purposively. Data were collected using Likert-scale questionnaires whose validity and reliability had been assessed and were analyzed using IBM SPSS Statistics. The analysis included descriptive statistics, distributional diagnostics, homoscedasticity, multicollinearity, heteroskedasticity diagnostics, and multiple linear regression. The reported results showed Shapiro–Wilk p values above .05 for X1, X2, and Y; a Levene statistic of 1.244 (p = .272); tolerance of .712 and VIF of 1.404 for both predictors; and no apparent heteroskedastic pattern in the residual scatterplot. The regression model yielded positive coefficients for X1 (B = 0.413, SE = 0.098, p < .001) and X2 (B = 0.287, SE = 0.081, p = .001), with R = .742, R² = .551, and adjusted R² = .526. Thus, the two predictors jointly accounted for 55.1% of the observed variance in learning outcomes in this sample. The study highlights the importance of regression diagnostics while emphasizing that purposive sampling and a single-school sample constrain generalizability and that the observed associations should not be interpreted causally.

References

  1. American Psychological Association. (2024). APA style journal article reporting standards (JARS). American Psychological Association. https://www.apa.org/pubs/journals/resources/apa-style-jars
  2. Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Sage.
  3. Appelbaum, M., Cooper, H., Kline, R. B., Mayo-Wilson, E., Nezu, A. M., & Rao, S. M. (2018). Journal article reporting standards for quantitative research in psychology: The APA Publications and Communications Board task force report. American Psychologist, 73(1), 3–25. https://doi.org/10.1037/amp0000191
  4. Arnastauskaitė, J., Ruzgas, T., & Bražėnas, M. (2021). An exhaustive power comparison of normality tests. Mathematics, 9(7), 788. https://doi.org/10.3390/math9070788
  5. Austin, P. C., & Steyerberg, E. W. (2015). The number of subjects per variable required in linear regression analyses. Journal of Clinical Epidemiology, 68(6), 627–636. https://doi.org/10.1016/j.jclinepi.2014.12.014
  6. Beckstead, J. W. (2012). Isolating and examining sources of suppression and multicollinearity in multiple linear regression. Multivariate Behavioral Research, 47(2), 224–246. https://doi.org/10.1080/00273171.2012.658331
  7. Casson, R. J., & Farmer, L. D. (2014). Understanding and checking the assumptions of linear regression: A primer for medical researchers. Clinical & Experimental Ophthalmology, 42(6), 590–596. https://doi.org/10.1111/ceo.12358
  8. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Lawrence Erlbaum Associates.
  9. Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Sage.
  10. Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Sage.
  11. Fox, J. (2016). Applied regression analysis and generalized linear models (3rd ed.). Sage.
  12. Gelman, A., Hill, J., & Vehtari, A. (2021). Regression and other stories. Cambridge University Press. https://doi.org/10.1017/9781139161879
  13. Ghozali, I. (2018). Aplikasi analisis multivariate dengan program IBM SPSS 25 (9th ed.). Badan Penerbit Universitas Diponegoro.
  14. Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499–510. https://doi.org/10.1207/s15327906mbr2603_7
  15. Grömping, U. (2007). Estimators of relative importance in linear regression based on variance decomposition. The American Statistician, 61(2), 139–147. https://doi.org/10.1198/000313007X188252
  16. Harrell, F. E., Jr. (2015). Regression modeling strategies (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-19425-7
  17. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An introduction to statistical learning (2nd ed.). Springer. https://doi.org/10.1007/978-1-0716-1418-1
  18. Kim, J. H. (2019). Multicollinearity and misleading statistical results. Korean Journal of Anesthesiology, 72(6), 558–569. https://doi.org/10.4097/kja.19087
  19. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis (6th ed.). Wiley.
  20. Nobre, J. S., & Singer, J. M. (2007). Residual analysis for linear mixed models. Biometrical Journal, 49(6), 863–875. https://doi.org/10.1002/bimj.200610341
  21. O’Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41, 673–690. https://doi.org/10.1007/s11135-006-9018-6
  22. Schmidt, A. F., & Finan, C. (2018). Linear regression and the normality assumption. Journal of Clinical Epidemiology, 98, 146–151. https://doi.org/10.1016/j.jclinepi.2017.12.006
  23. Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3–4), 591–611. https://doi.org/10.1093/biomet/52.3-4.591
  24. Midway, S., & White, J. W. (2025). Testing for normality in regression models: Mistakes abound (but may not matter). Royal Society Open Science, 12. https://doi.org/10.1098/rsos.241904
  25. Sugiyono. (2019). Metode penelitian kuantitatif, kualitatif, dan R&D. Alfabeta.
  26. Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
  27. von Elm, E., Altman, D. G., Egger, M., Pocock, S. J., Gøtzsche, P. C., & Vandenbroucke, J. P. (2007). The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: Guidelines for reporting observational studies. PLoS Medicine, 4(10), e296. https://doi.org/10.1371/journal.pmed.0040296
  28. Wilcox, R. R. (2019). Robust regression: Testing global hypotheses about the slopes when there is multicollinearity or heteroscedasticity. British Journal of Mathematical and Statistical Psychology, 72(2), 355–369. https://doi.org/10.1111/bmsp.12152
  29. Wooldridge, J. M. (2016). Introductory econometrics: A modern approach (6th ed.). Cengage Learning.
  30. Yang, K., Tu, J., & Chen, T. (2019). Homoscedasticity: An overlooked critical assumption for linear regression. General Psychiatry, 32(5), e100148. https://doi.org/10.1136/gpsych-2019-100148

How to Cite

Fitriyanti, F., Puspita, M., Ismail, F., & Afghani, M. W. (2026). STATISTICAL ASSUMPTION TESTING IN MULTIPLE LINEAR REGRESSION FOR EDUCATIONAL RESEARCH: EVIDENCE FROM A SECONDARY SCHOOL SURVEY IN INDONESIA. Jurnal Konseling Pendidikan Islam, 7(3). https://doi.org/10.32806/jkpi.v7i3.1716