Centre and Range method for fitting a linear regression model to symbolic interval data

Authors:
Eufrásio de A. Lima Neto;Francisco de A. T. de Carvalho
Affiliations:
Centro de Informática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n - Cidade Universitária - CEP 50740-540-Recife (PE), Brazil;Centro de Informática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n - Cidade Universitária - CEP 50740-540-Recife (PE), Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

This paper introduces a new approach to fitting a linear regression model to symbolic interval data. Each example of the learning set is described by a feature vector, for which each feature value is an interval. The new method fits a linear regression model on the mid-points and ranges of the interval values assumed by the variables in the learning set. The prediction of the lower and upper bounds of the interval value of the dependent variable is accomplished from its mid-point and range, which are estimated from the fitted linear regression model applied to the mid-point and range of each interval value of the independent variables. The assessment of the proposed prediction method is based on the estimation of the average behaviour of both the root mean square error and the square of the correlation coefficient in the framework of a Monte Carlo experiment. Finally, the approaches presented in this paper are applied to a real data set and their performance is compared.