Predicting Students' Academic Performance Using Multiple Linear Regression and Principal Component Analysis
With the rise of big data analytics, learning analytics has become a major trend for improving the quality of education. Learning analytics is a methodology for helping students to succeed in the classroom; the principle is to predict student's academic performance at an early stage and thus pr...
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| Published in | Journal of Information Processing Vol. 26; pp. 170 - 176 |
|---|---|
| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Tokyo
Information Processing Society of Japan
01.01.2018
Japan Science and Technology Agency |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1882-6652 1882-6652 |
| DOI | 10.2197/ipsjjip.26.170 |
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| Abstract | With the rise of big data analytics, learning analytics has become a major trend for improving the quality of education. Learning analytics is a methodology for helping students to succeed in the classroom; the principle is to predict student's academic performance at an early stage and thus provide them with timely assistance. Accordingly, this study used multiple linear regression (MLR), a popular method of predicting students' academic performance, to establish a prediction model. Moreover, we combined MLR with principal component analysis (PCA) to improve the predictive accuracy of the model. Traditional MLR has certain drawbacks; specifically, the coefficient of determination (R2) and mean square error (MSE) measures and the quantile-quantile plot (Q-Q plot) technique cannot evaluate the predictive performance and accuracy of MLR. Therefore, we propose predictive MSE (pMSE) and predictive mean absolute percentage correction (pMAPC) measures for determining the predictive performance and accuracy of the regression model, respectively. Analysis results revealed that the proposed model for predicting students' academic performance could obtain optimal pMSE and pMAPC values by using six components obtained from PCA. |
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| AbstractList | With the rise of big data analytics, learning analytics has become a major trend for improving the quality of education. Learning analytics is a methodology for helping students to succeed in the classroom; the principle is to predict student's academic performance at an early stage and thus provide them with timely assistance. Accordingly, this study used multiple linear regression (MLR), a popular method of predicting students' academic performance, to establish a prediction model. Moreover, we combined MLR with principal component analysis (PCA) to improve the predictive accuracy of the model. Traditional MLR has certain drawbacks; specifically, the coefficient of determination (R2) and mean square error (MSE) measures and the quantile-quantile plot (Q-Q plot) technique cannot evaluate the predictive performance and accuracy of MLR. Therefore, we propose predictive MSE (pMSE) and predictive mean absolute percentage correction (pMAPC) measures for determining the predictive performance and accuracy of the regression model, respectively. Analysis results revealed that the proposed model for predicting students' academic performance could obtain optimal pMSE and pMAPC values by using six components obtained from PCA. |
| Author | Huang, Jeff C.H. Huang, Anna Y.Q. Ogata, Hiroaki Lin, Albert J.Q. Yang, Stephen J.H. Lu, Owen H.T. |
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| References | [3] Baker, R.S. and Inventado, P.S.: Educational data mining and learning analytics, Learning analytics, pp.61-75, Springer (2014). [5] Peña-Ayala, A.: Learning Analytics: Fundaments, Applications, and Trends: A View of the Current State of the Art to Enhance e-Learning, Vol.94, Springer (2017). [25] Ul-Saufie, A., Yahya, A. and Ramli, N.: Improving multiple linear regression model using principal component analysis for predicting PM10 concentration in seberang prai, pulau pinang, International Journal of Environmental Sciences, Vol.2, No.2, p.403 (2011). [14] Morris, L.V., Finnegan, C. and Wu, S.-S.: Tracking student behavior, persistence, and achievement in online courses, The Internet and Higher Education, Vol.8, No.3, pp.221-231 (2005). [18] Macfadyen, L.P. and Dawson, S.: Mining lms data to develop an “early warning system” for educators: A proof of concept, Computers & education, Vol.54, No.2, pp.588-599 (2010). [4] Papamitsiou, Z. and Economides, A.A.: Learning analytics and educational data mining in practice: A systematic literature review of empirical evidence, Journal of Educational Technology & Society, Vol.17, No.4, p.49 (2014). [11] Huang, S. and Fang, N.: Predicting student academic performance in an engineering dynamics course: A comparison of four types of predictive mathematical models, Computers & Education, Vol.61, pp.133-145 (2013). [22] Hyndman, R.J. and Koehler, A.B.: Another look at measures of forecast accuracy, International Journal of Forecasting, Vol.22, No.4, pp.679-688 (2006). [23] Jolliffe, I.T.: Principal component analysis and factor analysis, Principal component analysis, pp.115-128, Springer (1986). [1] Consortium, N.M. et al.: The 2011 horizon report (2011). [29] Lamport, L.: A Document Preparation System LaTeX User's Guide & Reference Manual, Addison Wesley (1986). [13] Zacharis, N.Z.: A multivariate approach to predicting student outcomes in web-enabled blended learning courses, The Internet and Higher Education, Vol.27, pp.44-53 (2015). [16] Yoo, J. and Kim, J.: Predicting learner's project performance with dialogue features in online q&a discussions, International Conference on Intelligent Tutoring Systems, pp.570-575, Springer (2012). [10] Lu, O.H., Huang, J.C., Huang, A.Y. and Yang, S.J.: Applying learning analytics for improving students engagement and learning outcomes in an moocs enabled collaborative programming course, Interactive Learning Environments, Vol.25, No.2, pp.220-234 (2017). [28] Goossens, M., Mittelbach, F. and Samarin, A.: The LaTeX Companion, Addison Wesley (1993). [7] Meier, Y., Xu, J., Atan, O. and van der Schaar, M.: Predicting grades, IEEE Trans. Signal Processing, Vol.64, No.4, pp.959-972 (2016). [17] Marbouti, F., Diefes-Dux, H.A. and Madhavan, K.: Models for early prediction of at-risk students in a course using standards-based grading, Computers & Education, Vol.103, pp.1-15 (2016). [20] Taneja, A. and Chauhan, R.: A performance study of data mining techniques: Multiple linear regression vs. factor analysis, arXiv preprint arXiv:1108.5592 (2011). [9] Van Leeuwen, A., Janssen, J., Erkens, G. and Brekelmans, M.: Supporting teachers in guiding collaborating students: Effects of learning analytics in cscl, Computers & Education, Vol.79, pp.28-39 (2014). [12] Tempelaar, D.T., Rienties, B. and Giesbers, B.: In search for the most informative data for feedback generation: Learning analytics in a data-rich context, Computers in Human Behavior, Vol.47, pp.157-167 (2015). [6] Hu, Y.-H., Lo, C.-L. and Shih, S.-P.: Developing early warning systems to predict students' online learning performance, Computers in Human Behavior, Vol.36, pp.469-478 (2014). [21] O'Connell, R.T. and Koehler, A.B.: Forecasting, time series, and regression: An applied approach, Vol.4, South-Western Pub (2005). [24] Hira, Z.M. and Gillies, D.F.: A review of feature selection and feature extraction methods applied on microarray data, Advances in Bioinformatics, Vol.2015 (2015). [19] Agudo-Peregrina, Á.F., Iglesias-Pradas, S., Conde-González, M.Á. and Hernández-García, Á.: Can we predict success from log data in vles? classification of interactions for learning analytics and their relation with performance in vle-supported f2f and online learning, Computers in Human Behavior, Vol.31, pp.542-550 (2014). [26] Qiuhua, L., Lihai, S., Tingjing, G., Lei, Z., Teng, O., Guojia, H., Chuan, C. and Cunxiong, L.: Use of principal component scores in multiple linear regression models for simulation of chlorophyll-a and phytoplankton abundance at a karst deep reservoir, southwest of china, Acta Ecologica Sinica, Vol.34, No.1, pp.72-78 (2014). [2] Becker, S.A., Cummins, M., Davis, A., Freeman, A., Giesinger, C.H., and Ananthanarayanan, V.: NMC Horizon Report: 2017 Higher Education Edition, The New Media Consortium (2017). [27] Pires, J., Martins, F., Sousa, S., Alvim-Ferraz, M. and Pereira, M.: Selection and validation of parameters in multiple linear and principal component regressions, Environmental Modelling & Software, Vol.23, No.1, pp.50-55 (2008). [15] Sorour, S.E., Mine, T., Goda, K. and Hirokawa, S.: A predictive model to evaluate student performance, Journal of Information Processing, Vol.23, No.2, pp.192-201 (2015). [8] Arnold, K.E. and Pistilli, M.D.: Course signals at purdue: Using learning analytics to increase student success, Proc. 2nd International Conference on Learning Analytics and Knowledge, pp.267-270, ACM (2012). 22 23 24 25 26 27 28 29 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 20 21 |
| References_xml | – reference: [9] Van Leeuwen, A., Janssen, J., Erkens, G. and Brekelmans, M.: Supporting teachers in guiding collaborating students: Effects of learning analytics in cscl, Computers & Education, Vol.79, pp.28-39 (2014). – reference: [5] Peña-Ayala, A.: Learning Analytics: Fundaments, Applications, and Trends: A View of the Current State of the Art to Enhance e-Learning, Vol.94, Springer (2017). – reference: [17] Marbouti, F., Diefes-Dux, H.A. and Madhavan, K.: Models for early prediction of at-risk students in a course using standards-based grading, Computers & Education, Vol.103, pp.1-15 (2016). – reference: [18] Macfadyen, L.P. and Dawson, S.: Mining lms data to develop an “early warning system” for educators: A proof of concept, Computers & education, Vol.54, No.2, pp.588-599 (2010). – reference: [4] Papamitsiou, Z. and Economides, A.A.: Learning analytics and educational data mining in practice: A systematic literature review of empirical evidence, Journal of Educational Technology & Society, Vol.17, No.4, p.49 (2014). – reference: [8] Arnold, K.E. and Pistilli, M.D.: Course signals at purdue: Using learning analytics to increase student success, Proc. 2nd International Conference on Learning Analytics and Knowledge, pp.267-270, ACM (2012). – reference: [29] Lamport, L.: A Document Preparation System LaTeX User's Guide & Reference Manual, Addison Wesley (1986). – reference: [24] Hira, Z.M. and Gillies, D.F.: A review of feature selection and feature extraction methods applied on microarray data, Advances in Bioinformatics, Vol.2015 (2015). – reference: [7] Meier, Y., Xu, J., Atan, O. and van der Schaar, M.: Predicting grades, IEEE Trans. Signal Processing, Vol.64, No.4, pp.959-972 (2016). – reference: [28] Goossens, M., Mittelbach, F. and Samarin, A.: The LaTeX Companion, Addison Wesley (1993). – reference: [16] Yoo, J. and Kim, J.: Predicting learner's project performance with dialogue features in online q&a discussions, International Conference on Intelligent Tutoring Systems, pp.570-575, Springer (2012). – reference: [1] Consortium, N.M. et al.: The 2011 horizon report (2011). – reference: [15] Sorour, S.E., Mine, T., Goda, K. and Hirokawa, S.: A predictive model to evaluate student performance, Journal of Information Processing, Vol.23, No.2, pp.192-201 (2015). – reference: [12] Tempelaar, D.T., Rienties, B. and Giesbers, B.: In search for the most informative data for feedback generation: Learning analytics in a data-rich context, Computers in Human Behavior, Vol.47, pp.157-167 (2015). – reference: [3] Baker, R.S. and Inventado, P.S.: Educational data mining and learning analytics, Learning analytics, pp.61-75, Springer (2014). – reference: [22] Hyndman, R.J. and Koehler, A.B.: Another look at measures of forecast accuracy, International Journal of Forecasting, Vol.22, No.4, pp.679-688 (2006). – reference: [26] Qiuhua, L., Lihai, S., Tingjing, G., Lei, Z., Teng, O., Guojia, H., Chuan, C. and Cunxiong, L.: Use of principal component scores in multiple linear regression models for simulation of chlorophyll-a and phytoplankton abundance at a karst deep reservoir, southwest of china, Acta Ecologica Sinica, Vol.34, No.1, pp.72-78 (2014). – reference: [21] O'Connell, R.T. and Koehler, A.B.: Forecasting, time series, and regression: An applied approach, Vol.4, South-Western Pub (2005). – reference: [19] Agudo-Peregrina, Á.F., Iglesias-Pradas, S., Conde-González, M.Á. and Hernández-García, Á.: Can we predict success from log data in vles? classification of interactions for learning analytics and their relation with performance in vle-supported f2f and online learning, Computers in Human Behavior, Vol.31, pp.542-550 (2014). – reference: [25] Ul-Saufie, A., Yahya, A. and Ramli, N.: Improving multiple linear regression model using principal component analysis for predicting PM10 concentration in seberang prai, pulau pinang, International Journal of Environmental Sciences, Vol.2, No.2, p.403 (2011). – reference: [13] Zacharis, N.Z.: A multivariate approach to predicting student outcomes in web-enabled blended learning courses, The Internet and Higher Education, Vol.27, pp.44-53 (2015). – reference: [14] Morris, L.V., Finnegan, C. and Wu, S.-S.: Tracking student behavior, persistence, and achievement in online courses, The Internet and Higher Education, Vol.8, No.3, pp.221-231 (2005). – reference: [2] Becker, S.A., Cummins, M., Davis, A., Freeman, A., Giesinger, C.H., and Ananthanarayanan, V.: NMC Horizon Report: 2017 Higher Education Edition, The New Media Consortium (2017). – reference: [27] Pires, J., Martins, F., Sousa, S., Alvim-Ferraz, M. and Pereira, M.: Selection and validation of parameters in multiple linear and principal component regressions, Environmental Modelling & Software, Vol.23, No.1, pp.50-55 (2008). – reference: [20] Taneja, A. and Chauhan, R.: A performance study of data mining techniques: Multiple linear regression vs. factor analysis, arXiv preprint arXiv:1108.5592 (2011). – reference: [23] Jolliffe, I.T.: Principal component analysis and factor analysis, Principal component analysis, pp.115-128, Springer (1986). – reference: [6] Hu, Y.-H., Lo, C.-L. and Shih, S.-P.: Developing early warning systems to predict students' online learning performance, Computers in Human Behavior, Vol.36, pp.469-478 (2014). – reference: [10] Lu, O.H., Huang, J.C., Huang, A.Y. and Yang, S.J.: Applying learning analytics for improving students engagement and learning outcomes in an moocs enabled collaborative programming course, Interactive Learning Environments, Vol.25, No.2, pp.220-234 (2017). – reference: [11] Huang, S. and Fang, N.: Predicting student academic performance in an engineering dynamics course: A comparison of four types of predictive mathematical models, Computers & Education, Vol.61, pp.133-145 (2013). – ident: 2 – ident: 18 – ident: 4 – ident: 12 – ident: 7 doi: 10.1109/TSP.2015.2496278 – ident: 10 – ident: 16 – ident: 14 – ident: 28 – ident: 24 – ident: 9 – ident: 20 – ident: 26 – ident: 22 – ident: 17 – ident: 3 – ident: 5 – ident: 1 – ident: 11 – ident: 19 – ident: 13 – ident: 15 – ident: 29 – ident: 6 – ident: 8 – ident: 21 – ident: 27 – ident: 25 – ident: 23 |
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| SubjectTerms | Academic achievement Accuracy Analytics Data management Error analysis learning analytics Mathematical analysis Model accuracy multiple linear regression Performance prediction principal component analysis Principal components analysis Regression analysis Regression models Students |
| Title | Predicting Students' Academic Performance Using Multiple Linear Regression and Principal Component Analysis |
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