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Math. Comput. Appl. 2016, 21(1), 1; doi:10.3390/mca21010001

A New Perturbation Approach to Optimal Polynomial Regression

Applied Mathematics and Computation Center, Celal Bayar University, Muradiye, Manisa, 45140, Turkey
Academic Editor: Mehmet Ali Ilgın
Received: 12 April 2015 / Revised: 22 February 2016 / Accepted: 26 February 2016 / Published: 4 March 2016
View Full-Text   |   Download PDF [194 KB, uploaded 4 March 2016]

Abstract

A new approach to polynomial regression is presented using the concepts of orders of magnitudes of perturbations. The data set is normalized with the maximum values of the data first. The polynomial regression of arbitrary order is then applied to the normalized data. Theorems for special properties of the regression coefficients as well as some criteria for determining the optimum degrees of the regression polynomials are posed and proven. The new approach is numerically tested, and the criteria for determining the best degree of the polynomial for regression are discussed. View Full-Text
Keywords: polynomial regression; perturbation analysis; degree of a polynomial polynomial regression; perturbation analysis; degree of a polynomial

This paper was processed and accepted under the editorial system of the ASR before its transfer to MDPI.

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Pakdemirli, M. A New Perturbation Approach to Optimal Polynomial Regression. Math. Comput. Appl. 2016, 21, 1.

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