Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
1-1-1982
Abstract
The multiple regression problem is analyzed by the model type (linear and nonlinear models) and four different minimization criteria, viz., minimization of the sum of squared errors, sum of absolute errors, sum of absolute relative errors and sum of squared relative errors. The advantages and the limitations of the eight alternatives (two model types x four minimization criteria) are discussed. The appropriateness of these alternatives for a sample data is analyzed. Methods of estimating the parameters for four of the alternatives (not covered in the literature) are given. For the linear model, the properties of the least sum of squared relative errors estimators are derived ab initio and compared with those of the ordinary least squares estimators.
Keywords
Operations research, Regression analysis, Linear models (Statistics), Nonlinear theories, Error analysis (Mathematics), Least squares, Mathematical optimization, Estimation theory, Statistical hypothesis testing
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 506 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Gajjala, Radhakrishna Murty, "A Critique of Linear and Nonlinear Regression Problems with Four Different Minimization Criteria" (1982). Research Reports from the Department of Operations. 119.
https://commons.case.edu/wsom-ops-reports/119