.svg){kind=logo}
LINEAR REGRESSION ANALYSIS FOR INTERVAL-VALUED DATA
Keywords:
symbolic data, interval-valued data, regression analysis, least squares, linear regressionDOI:
https://doi.org/10.17654/0972361725039Abstract
This study deals with regression analysis using data where the observations are given as interval values. Regression analysis of interval-valued data aims to estimate the upper and lower boundaries of the interval of the target variable for a given interval of the explanatory variable. Conventional methods use the centre and range of the interval of the explanatory variable and the interval of the target variable to obtain the estimated upper and lower regression lines. However, this method provides good estimates only when the slopes of the upper and lower regression lines are the same, making interpretation of the estimation results difficult. To deal with this problem, we define errors in interval-valued data and propose a method to minimize them. From simulation results, it is found that the proposed method provides good estimation with high interpretability and minimizes the problems of conventional methods.
Received: February 1, 2025
Accepted: March 6, 2025
References
L. Billard and E. Diday, Regression analysis for interval-valued data, Data Analysis, Classification and Related Methods: Proceedings of the Seventh Conference of the International Federation of Classification Societies, H. A. L. Kiers, J.-P. Rasson, P. J. F. Groenen and M. Schader, eds., IFCS-2000, Springer-Verlag, Berlin, 2000, pp. 369-374.
L. Billard and E. Diday, Symbolic Data Analysis - Conceptual Statistics and Data Mining, Wiley, England, 2006.
F. A. T. de Carvalho, E. A. Lima Neto and C. P. Tenorio, A new method to fit a linear regression model for interval-valued data, Advances in Artificial Intelligence: Proceedings of the Twenty Seventh German Conference on Artificial Intelligence, S. Biundo, T. Frühwirth and G. Palm, eds., LNAI 3238, Springer-Verlag, Berlin, 2004, pp. 295-306.
S. Dias and P. Brito, Off the beaten track: a new linear model for interval data, European J. Oper. Res. 258 (2017), 1118-1130.
E. A. Lima Neto, F. A. T. de Carvalho and E. S. Freire, Applying constrained linear regression models to predict interval-valued data, Lecture Notes in Artificial Intelligence, U. Furbach, ed., LNAI 3698, Springer-Verlag, Berlin, 2005, pp. 92-106.
E. A. Lima Neto and F. A. T. de Carvalho, Centre and range method for fitting a linear regression model to symbolic interval data, Comput. Statist. Data Anal. 52(3) (2008), 1500-1515.
E. A. Lima Neto and F. A. T. de Carvalho, Constrained linear regression models for symbolic interval-valued variables, Comput. Statist. Data Anal. 54(2) (2010), 333-347.
E. A. Lima Neto and F. A. T. de Carvalho, Nonlinear regression applied to interval-valued data, Pattern Analysis and Applications 20 (2017), 809-824.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
