A new perturbation approach to optimal polynomial regression

Pakdemirli M.

Mathematical and Computational Applications, cilt.21, sa.1, 2016 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3390/mca21010001
  • Dergi Adı: Mathematical and Computational Applications
  • Derginin Tarandığı İndeksler: Scopus
  • Anahtar Kelimeler: Degree of a polynomial, Perturbation analysis, Polynomial regression
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

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.