Exploring Multiple Regression Models: Key Concepts and Applications
DOI:
https://doi.org/10.61173/yjpt3s59Keywords:
linear regression model, statistical analysis, multiple independent, dependent variablesAbstract
Multiple regression analysis is a statistical method used to examine the relationship between a dependent variable and multiple independent variables. It extends the principles of simple linear regression to accommodate the complexity of real-world data, allowing researchers to study the combined effect of multiple predictors on an outcome of interest. This article provides a comprehensive overview of multiple regression analysis, including its theoretical foundations, practical applications, and key considerations. First, we discuss the basic concept of multiple regression and its historical development, tracing its evolution from simple linear regression. The article then delves into the methodology of multiple regression, covering topics such as model specification, estimation techniques, and model evaluation. Additionally, it explores advanced topics in multiple regression analysis, including multicollinearity, heteroskedasticity, and model selection. Real-world examples and case studies from a variety of fields illustrate the versatility and applicability of multiple regression analysis in empirical research. By providing a thorough understanding of multiple regression, this article aims to provide researchers with the knowledge and tools needed to effectively utilize this statistical technique in their own research.
References
[1] Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning.
[2] Fox, J. (2015). Applied Regression Analysis and Generalized Linear Models (3rd ed.). Sage Publications.
[3] Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied Linear Statistical Models (5th ed.). McGraw-Hill Education.
[4] Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). Wiley.
[5] Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd ed.). Lawrence Erlbaum Associates.
[6] McCullagh and Nelder‘s „Generalized Linear Model,“ as well as Stasinopoulos et al.‘s „Generalized Linear Model for Insurance Data.“.
[7] Hox‘s „Multi level Analysis: Techniques and Applications“ and Raudenbush and Bryk‘s „Hierarchical Linear Models: Applications and Data Analysis Methods“.
[8] Hastie and Tibshirani‘s „Generalized Additive Model“ and Wood‘s „Application Smoothing Techniques for Data Analysis“.
[9] Gelman et al.‘s „Bayesian Data Analysis“ and Rue et al.‘s „Bayesian Regression Modeling of INLA“.
[10] Maronna et al.‘s „Robust Statistics“ and Rousseeuw and Leroy‘s „Robust Regression and Outlier Detection“.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 by the authors.
This work is licensed under a Creative Commons Attribution 4.0 International License.
