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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 354237, 6 pages
http://dx.doi.org/10.1155/2014/354237
Research Article

Time Scale in Least Square Method

1Department of Statistics, Faculty of Sciences, Hacettepe University, Beytepe, 06800 Ankara, Turkey
2Department of Statistics, Faculty of Sciences, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey
3Department of Statistics, Faculty of Sciences, Ankara University, Beşevler, 06100 Ankara, Turkey

Received 8 January 2014; Accepted 6 March 2014; Published 3 April 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Özgür Yeniay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.