An Efficient Solution to a Multiple Non-Linear Regression Model with Interaction Effect using TORA and LINDO

  • Umesh Gupta
  • Devender Singh  Hada
  • Ankita  Mathur
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

Goal programming (GP) has been proven a valuable mathematical programming form in a number of venues. GP model serves a valuable purpose of cross-checking answers from other methodologies. Different software packages are used to solve these GP models. Likewise, multiple regression models can also be used to more accurately combine multiple criteria measures that can be used in GP model parameters. Those parameters can include the relative weighting and the goal constraint parameters. A comparative study on the solutions using TORA, LINDO, and least square method has been made in this paper. The objective of this paper is to find out a method that gives most accurate result to a nonlinear multiple regression model.

Keywords

Goal programming Multiple regression Least square method TORA LINDO 

References

  1. 1.
    Legendre, A.M.: Nouvelles méthodes pour la détermination des orbites des comètes. “Sur la Méthode des moindres quarrés” appears as an appendix (1805)Google Scholar
  2. 2.
    Gauss, C.F.: Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientum (1809)Google Scholar
  3. 3.
    Weisberg, s: Applied Linear Regression, 2nd edn. Wiley, Inc, New York (1985)MATHGoogle Scholar
  4. 4.
    Alp, S., Yavuz, E., Ersoy, N.: Using linear goal programming in surveying engineering for vertical network adjustment. Int. J. Phys. Sci. 6(8), 1982–1987 (2011)Google Scholar
  5. 5.
    Hassanpour H., Maleki R.H., Yaghoobi A.M.: Fuzzy linear regression model with crisp coefficients: a goal programming approach. Int. J. Fuzzy Syst. 7(2), 19–39 (2010)Google Scholar
  6. 6.
    Alken, L.S., West, S.G.: Multiple Regression: Testing and Interpreting Interactions. Sage Publications, Thousand Oaks (1991)Google Scholar
  7. 7.
    Curran, P.J., Bauer, D.J., Willoughby, M.T.: Testing main effects and interactions in hierarchical linear growth models. Psychol. Methods 9(2), 220–237 (2004)CrossRefGoogle Scholar
  8. 8.
    Charnes, A., Cooper, W.W., Ferguson, R.: Optimal estimation of executive compensation by linear programming. Manage. Sci. 1(2), 138–151 (1955)CrossRefMATHGoogle Scholar
  9. 9.
    Ijiri, Y.: Management Goals and Accounting for Control. North-Holland Publishing Company, Amsterdam (1965)Google Scholar
  10. 10.
    Lee, S.M.: Goal Programming for Decision Analysis. Auerbach Publishers Inc., Philadelphia (1972)Google Scholar
  11. 11.
    Spronk, J.: Interactive Multiple Goal Programming: Application to Financial Planning. Martinus Nijhoff, Amsterdam (1981)CrossRefGoogle Scholar
  12. 12.
    Ignizio, J.P.: Introduction to Linear Goal Programming. Sage Publications, Thousand Oaks, CA (1986)Google Scholar
  13. 13.
    Charnes, A., Cooper, W.W.: Goal programming and multiple objective optimizations. Eur. J. Operat. Res. 1, 39–54 (1977)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Eiselt, H.A., Pederzoli, G., Sandblom, C.L.: Continuous Optimization Models. W De G, New York (1987)MATHGoogle Scholar
  15. 15.
    Ignizio, J.P.: A review of goal programming—a tool for multiobjective analysis. J. Opl. Res. Soc. 29(11), 1109–1119 (1978)MATHGoogle Scholar
  16. 16.
    Tamiz, M., Jones, D., Darzi, E.: A review of goal programming and its applications. Ann. Oper. Res. 58(1), 39–53 (1995)Google Scholar
  17. 17.
    Machiel, K.: A goal programming approach to strategic bank balance sheet management. SAS Global Forum 2011, Centre for BMI, North-West University, South Africa, Paper 024–2011 (2011)Google Scholar
  18. 18.
    Gupta, M., Bhattacharjee, D.: Min sum weighted fuzzy goal programming model in investment management planning: a case study. Int. Res. J. Fin. Econ. Issue 56 (2010)Google Scholar
  19. 19.
    Sen, N., Nandi, M.: Goal programming, its application in management sectors–special attention into plantation management: a review. Int. J. Sci. Res. Pub. 2(9) (2012)Google Scholar
  20. 20.
    Sharma, S.C., Hada, D.S., Gupta, U.: A goal programming model for the interaction effects in multiple nonlinear regression. J. Comp. Math. Sci. 1(4), 477–481 (2010)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  • Umesh Gupta
    • 1
  • Devender Singh  Hada
    • 2
  • Ankita  Mathur
    • 3
  1. 1.Institute of Engineering and TechnologyJK Lakshmipat UniversityJaipurIndia
  2. 2.Kautilya Institute of Technology and EngineeringJaipurIndia
  3. 3.Jaipur Institute of Technology and Group of InstitutionsJaipurIndia

Personalised recommendations