Etemadi multiple linear regression

Abstract

Regression modeling is one of the most widely used statistical processes to estimate the relationships between dependent and independent variables, which have been frequently applied in a wide range of applications successfully. This method includes many techniques for modeling and analyzing several variables to cover real-world problems. The performance basis in conventional regression modeling is based on the assumption that maximum accuracy in inaccessible data is obtained from models with the least amount of error in modeling available data. In this type of regression modeling, in order to maximize the generalization ability of simulations, which are the main factor influencing the quality of decisions made in real-world problems, the principle of maximization of the accuracy of available historical data is used. However, in this type of modeling process, the model's reliability and results have not been considered. On the other, the generalization capability of a model is simultaneously dependent on the accuracy of the model and the reliability level of the accuracy. In this paper, a new methodology is proposed for multiple linear regression (MLR) modeling in which in contrast to traditionally developed models, the models' reliability is maximized instead of its accuracy. To comprehensively evaluate the proposed model's performance, 30 benchmark data sets are considered from the UCI. Empirical results indicate that, from a general perspective, in 19 cases, i.e., 63.333% of cases, the proposed model has better generalization ability than traditional ones. It is clearly illustrated the importance of the reliability of results and their accuracy that is considered in none of the conventional MLR modeling procedures. Therefore, the proposed MLR model can be regarded as an appropriate alternative in modeling fields, especially when more generalization is desired.