Main Article Content
Abstract
The linear regression model is employed when it is identified a linear relationship between the dependent and independent variables. In some cases, the relationship between the two variables does not generate a linear line, that is, there is a change point at a certain point. Therefore, the
maximum likelihood estimator for the linear regression does not produce an accurate model. The objective of this study is to presents the performance of simple linear and segmented linear regression models in which there are breakpoints in the data. The modeling is performed on
the data of depth and sea temperature. The model results display that the segmented linear regression is better in modeling data which contain changing points than the classical one.
Received September 1, 2021
Revised November 2, 2021
Accepted November 11, 2021
Keywords
Article Details
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
- D.C. Montgomery, E.A. Peck, G.G. Vining, “Introduction to linear regression analysis”, Wiley series in probability and statistics, 5th ed, 2012.
- J.D. Kelleher, and B. Tierney, “Data science”, Massachusetts Institute of Technology Press, 2018.
- J.D. Miller, “Statistics for data science; leverage the power of statistics for data analysis, classification, regression, machine learning, and neural network”, Packt Publishing, 2017.
- W. Robinson, B. Miller, B. Pflugrath, L. J. Baumgartner, A. Navarro, R. Brown, and Z. Deng, “A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fishes at river infrastructure”, Journal of Fish Biology, vol. 88(5), 2016, pp. 1677-1692. doi:https://doi.org/10.1111/jfb.12910
- E. Petrakis, E. Stamboliadis, and K. Komnitsas, “Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis”, Particulate Science and Technology, vol. 35(4), 2017, pp. 479-489. doi: https://doi.org/10.1080/02726351.2016.1168894
- M.B. Nirwana dan D. Wulandari "Estimasi titik ubah tunggal pada regresi linier dengan satu peubah bebas," Prosiding Seminar Nasional Pendidikan Sains Dan Teknologi, Universitas Muhmmadiyah Semarang, 2018.
- V.M. Muggeo, “Estimating Regression Models with Unknown Break-points”, Statistics in Medicine, vol. 22(19), 2003, pp. 3055-3071, doi:https://doi.org/10.1002/sim.1545.
- V.M. Muggeo, “Segmented: An R package to Fit Regression Models with Broken-Line Relationships”, R NEWS, vol. 8(1), 2008, pp. 20-25, https://cran.r-project.org/doc/Rnews/
- V.M. Muggeo, “Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling”, J of Statistical Computation and Simulation, vol. 86, 2016, pp. 3059-3067. doi:https://doi.org/10.1080/00949655.2016.1149855
- V.M. Muggeo, (2017). “Interval estimation for the breakpoint in segmented regression: a smoothed score-based approach”, Australian & New Zealand Journal of Statistics, vol. 59, 2017, pp. 311-322. doi: https://doi.org/10.1111/anzs.12200
References
D.C. Montgomery, E.A. Peck, G.G. Vining, “Introduction to linear regression analysis”, Wiley series in probability and statistics, 5th ed, 2012.
J.D. Kelleher, and B. Tierney, “Data science”, Massachusetts Institute of Technology Press, 2018.
J.D. Miller, “Statistics for data science; leverage the power of statistics for data analysis, classification, regression, machine learning, and neural network”, Packt Publishing, 2017.
W. Robinson, B. Miller, B. Pflugrath, L. J. Baumgartner, A. Navarro, R. Brown, and Z. Deng, “A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fishes at river infrastructure”, Journal of Fish Biology, vol. 88(5), 2016, pp. 1677-1692. doi:https://doi.org/10.1111/jfb.12910
E. Petrakis, E. Stamboliadis, and K. Komnitsas, “Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis”, Particulate Science and Technology, vol. 35(4), 2017, pp. 479-489. doi: https://doi.org/10.1080/02726351.2016.1168894
M.B. Nirwana dan D. Wulandari "Estimasi titik ubah tunggal pada regresi linier dengan satu peubah bebas," Prosiding Seminar Nasional Pendidikan Sains Dan Teknologi, Universitas Muhmmadiyah Semarang, 2018.
V.M. Muggeo, “Estimating Regression Models with Unknown Break-points”, Statistics in Medicine, vol. 22(19), 2003, pp. 3055-3071, doi:https://doi.org/10.1002/sim.1545.
V.M. Muggeo, “Segmented: An R package to Fit Regression Models with Broken-Line Relationships”, R NEWS, vol. 8(1), 2008, pp. 20-25, https://cran.r-project.org/doc/Rnews/
V.M. Muggeo, “Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling”, J of Statistical Computation and Simulation, vol. 86, 2016, pp. 3059-3067. doi:https://doi.org/10.1080/00949655.2016.1149855
V.M. Muggeo, (2017). “Interval estimation for the breakpoint in segmented regression: a smoothed score-based approach”, Australian & New Zealand Journal of Statistics, vol. 59, 2017, pp. 311-322. doi: https://doi.org/10.1111/anzs.12200