Estimating Passenger Capacity of Ships with Linear Regression Models

Year 2026, Volume: 12 Issue: 1, 65 - 88, 01.03.2026

Volkan Şahin

https://doi.org/10.52998/trjmms.1777065

https://izlik.org/JA29XB47EY

Abstract

Accurate prediction of passenger ship capacity is essential for ship design, fleet management, and planning. In this study, verified technical and operational data from about 2,000 passenger ships were analyzed. The dataset included key variables such as passenger capacity (P), gross tonnage (GT), draft (T), length (L), beam (B), deadweight tonnage (DWT), and main engine power (EP). First, the distributions and correlations of all these variables were examined. Variables that most strongly affected passenger capacity and reduced the risk of multicollinearity were carefully selected for the model. As a result, both a simplified model (GT and T) and an extended model (GT, T, L, B, EP, DWT) were developed. Ordinary Least Squares (OLS) and robust regression methods were applied to both models. In the GT–T model, passenger capacity was predicted with R² ≈ 0.73, while in the extended model, the explanatory power improved to R² ≈ 0.75. The robust regression approach limited the influence of outliers, but overall results were very similar to those of the OLS model. Diagnostic tests confirmed that the assumptions of the models were met and that the error distributions were close to normal. These findings suggest that both simplified and extended regression models can serve as effective and reliable tools for passenger capacity estimation in engineering applications.

Keywords

Passenger capacity estimation , Linear regression models , OLS regression , Robust regression , Maritime data analysis

Gemilerin Yolcu Kapasitesinin Doğrusal Regresyon Modelleri Kullanılarak Tahmini

https://izlik.org/JA29XB47EY

Abstract

Yolcu gemisi kapasitesinin doğru bir biçimde öngörülmesi, gemi tasarımı, filo yönetimi ve planlama süreçleri açısından kritik öneme sahiptir. Bu çalışmada yaklaşık 2000 yolcu gemisine ait doğrulanmış teknik ve operasyonel veriler incelenmiştir. Veri seti, yolcu kapasitesi (P), gros tonaj (GT), draft (T), boy (L), en (B), deadweight tonaj (DWT) ve ana makine gücü (EP) gibi temel değişkenleri içermektedir. İlk aşamada tüm değişkenlerin dağılımları ve aralarındaki korelasyonlar analiz edilmiştir. Yolcu kapasitesini en güçlü biçimde etkileyen ve çoklu doğrusal bağlantı riskini azaltan değişkenler model geliştirme süreci için seçilmiştir. Bu doğrultuda, bir basitleştirilmiş model (GT ve T) ile bir genişletilmiş model (GT, T, L, B, EP, DWT) oluşturulmuştur. Her iki modelde de En Küçük Kareler (OLS) ve robust regresyon yöntemleri uygulanmıştır. GT–T modelinde yolcu kapasitesi yaklaşık R² ≈ 0,73 düzeyinde tahmin edilmiştir. Genişletilmiş modelde ise açıklayıcılık gücü R² ≈ 0.75’e ulaşmıştır. Robust regresyon yaklaşımı aykırı değerlerin etkisini sınırlamış, ancak genel sonuçlar OLS modeliyle büyük ölçüde paralellik göstermiştir. Tanısal testler, modellerin varsayımlarının karşılandığını ve hata dağılımlarının normale yakın olduğunu doğrulamıştır. Elde edilen bulgular, hem basitleştirilmiş hem de genişletilmiş regresyon modellerinin mühendislik uygulamalarında yolcu kapasitesinin tahmininde etkili ve güvenilir araçlar olarak kullanılabileceğini ortaya koymaktadır.

Keywords

Yolcu kapasitesi tahmini , Doğrusal regresyon modelleri , OLS regresyonu , Robust regresyon , Denizcilik veri analizi

References

• Abramowski, T., Cepowski, T., Zvolenský, P. (2018). Determination of Regression Formulas for Key Design Characteristics of Container Ships at Preliminary Design Stage. New Trends in Production Engineering, 1(1): 247–257. doi: 10.2478/ntpe-2018-0031.
• Aguinis, H., Vassar, M., Wayant, C. (2021). On reporting and interpreting statistical significance and p values in medical research. BMJ Evidence-Based Medicine, 26(2): 39–42. doi: 10.1136/bmjebm-2019-111264.
• Alderton, P.M. (2011). Reeds Sea Transport: Operation and Economics, 6th ed., Bloomsbury Publishing.
• Bassam, A.M., Phillips, A.B., Turnock, S.R., Wilson, P.A. (2022). Ship speed prediction based on machine learning for efficient shipping operation. Ocean Engineering, 245: 110449. doi: 10.1016/j.oceaneng.2021.110449.
• Bouman, E.A., Lindstad, E., Rialland, A.I., Strømman, A.H. (2017). State-of-the-art technologies, measures, and potential for reducing GHG emissions from shipping – A review. Transportation Research Part D: Transport and Environment, 52: 408–421. doi: 10.1016/j.trd.2017.03.022.
• Cain, M.K., Zhang, Z., Yuan, K.-H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior Research Methods, 49(5): 1716–1735. doi: 10.3758/s13428-016-0814-1.
• Chatterjee, S., Hadi, A.S. (2013). Regression Analysis by Example, 5th ed., Wiley, Hoboken, NJ.
• Chen, S., Wang, Z., Lu, T., Zhu, J., Zhang, C., Zeng, X., Wang, J., et al. (2025). Research on global ship cargo capacity prediction based on multi-source heterogeneous data. Frontiers in Marine Science, 12: 1–13. doi: 10.3389/fmars.2025.1632661.
• Durbach, I.N., Stewart, T.J. (2012). Modeling uncertainty in multi-criteria decision analysis. European Journal of Operational Research, 223(1): 1–14. doi: 10.1016/j.ejor.2012.04.038.
• Durlik, I., Miller, T., Kostecka, E., Tuński, T. (2024). Artificial Intelligence in Maritime Transportation: A Comprehensive Review of Safety and Risk Management Applications. Applied Sciences, 14(18): 8420. doi: 10.3390/app14188420.
• La Ferlita, A., Qi, Y., Di Nardo, E., El Moctar, O., Schellin, T.E., Ciaramella, A. (2024). A framework of a data-driven model for ship performance. Ocean Engineering, 309: 118486. doi: 10.1016/j.oceaneng.2024.118486.
• Gelman, A., Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models, Cambridge University Press, Cambridge, UK.
• Gunes, U. (2023). Estimating bulk carriers’ main engine power and emissions. Brodogradnja, 74(1): 85–98. doi: 10.21278/brod74105.
• Heilig, L., Voß, S. (2017). Information systems in seaports: a categorization and overview. Information Technology and Management, 18(3): 179–201. doi: 10.1007/s10799-016-0269-1.
• Huber, P.J. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics, 35(1): 73–101. doi: 10.1214/aoms/1177703732.
• Huber, P.J., Ronchetti, E.M. (2009). Robust Statistics, 2nd ed., Wiley.
• International Maritime Organization, (2023). 2023 IMO Strategy on Reduction of GHG Emissions from Ships.
• James, G., Witten, D., Hastie, T., Tibshirani, R., Taylor, J. (2023). An Introduction to Statistical Learning With Applications in Python, Springer Texts in Statistics.
• Kuhn, M., Johnson, K. (2013). Applied Predictive Modeling, Springer New York, NY. doi: 10.1007/978-1-4614-6849-3.
• Kutner, M.H., Nachtsheim, C.J., Neter, J., Li, W. (2004). Applied Linear Statistical Models, 5th ed., McGraw-Hill/Irwin, Boston.
• Mauro, F., Salem, A. (2025). Development of regression models for estimating main particulars of RoPax vessels in the conceptual design stage. Ocean Engineering, 333: 121407. doi: 10.1016/j.oceaneng.2025.121407.
• Melo, R.F., Figueiredo, N.M. de, Tobias, M.S.G., Afonso, P. (2024). A Machine Learning Predictive Model for Ship Fuel Consumption. Applied Sciences, 14(17): 7534. doi: 10.3390/app14177534.
• Molland, A.F. (2011). The Maritime Engineering Reference Book: A Guide to Ship Design, Construction and Operation, Elsevier, Oxford.
• Montgomery, D.C., Runger, G.C. (2011). Applied Statistics and Probability for Engineers, 5th ed., Wiley, Hoboken, NJ.
• Munim, Z.H., Dushenko, M., Jimenez, V.J., Shakil, M.H., Imset, M. (2020). Big data and artificial intelligence in the maritime industry: a bibliometric review and future research directions. Maritime Policy & Management, 47(5): 577–597. doi: 10.1080/03088839.2020.1788731.
• Osborne, J.W., Waters, E. (2002). Four Assumptions of Multiple Regression That Researchers Should Always Test. Practical Assessment, Research and Evaluation, 8 (2): 1–5.
• Psaraftis, H.N. (2017). Green Transportation Logistics: The Quest for Win-Win Solutions, Springer, Cham.
• Psaraftis, H.N., Kontovas, C.A. (2009). CO2 emission statistics for the world commercial fleet. WMU Journal of Maritime Affairs, 8(1): 1–25. doi: 10.1007/BF03195150.
• Raza, A., Talib, M., Noor-ul-Amin, M., Gunaime, N., Boukhris, I., Nabi, M. (2024). Enhancing performance in the presence of outliers with redescending M-estimators. Scientific Reports, 14(1): 13529. doi: 10.1038/s41598-024-64239-6.
• Rinauro, B., Begovic, E., Mauro, F., Rosano, G. (2024). Regression analysis for container ships in the early design stage. Ocean Engineering, 292: 116499. doi: 10.1016/j.oceaneng.2023.116499.
• Ros Chaos, S., Pallis, A.A., Saurí Marchán, S., Pino Roca, D., Sánchez-Arcilla Conejo, A. (2021). Economies of scale in cruise shipping. Maritime Economics and Logistics, 23(4): 674–696. doi: 10.1057/s41278-020-00158-3.
• Schober, P., Boer, C., Schwarte, L.A. (2018). Correlation Coefficients: Appropriate Use and Interpretation. Anesthesia & Analgesia, 126(5): 1763–1768. doi: 10.1213/ANE.0000000000002864.
• Sii, H.S., Ruxton, T., Wang, J. (2001). A fuzzy-logic-based decision-making approach for ship safety assessment. Ocean Engineering, 28(6): 689–709. doi: 10.1016/S0029-8018(00)00046-2.
• Stopford, M. (2009). Maritime Economics, 3rd ed., Routledge.
• Tijan, E., Jović, M., Aksentijević, S., Pucihar, A. (2021). Digital transformation in the maritime transport sector. Technological Forecasting and Social Change, 170: 120879. doi: 10.1016/j.techfore.2021.120879.
• U.S. Environmental Protection Agency, (2008). Cruise Ship Discharge Assessment Report.
• Veenstra, A.W., Ludema, M.W. (2006). The relationship between design and economic performance of ships. Maritime Policy & Management, 33(2): 159–171. doi: 10.1080/03088830600612880.
• Yu, C., Yao, W. (2017). Robust linear regression: A review and comparison. Communications in Statistics - Simulation and Computation, 46(8): 6261–6282. doi: 10.1080/03610918.2016.1202271.
• Zampeta, V., Chondrokoukis, G. (2023). A Comprehensive Approach through Robust Regression and Gaussian/Mixed-Markov Graphical Models on the Example of Maritime Transportation Accidents: Evidence from a Listed-in-NYSE Shipping Company. Journal of Risk and Financial Management, 16(3): 183. doi: 10.3390/jrfm16030183.
• Zocco, F., Wang, H.-C., Van, M. (2023). Digital Twins for Marine Operations: A Brief Review on Their Implementation. doi:10.48550/arXiv.2301.09574.