### A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique

Received: Oct. 30, 2022    Accepted: Nov. 18, 2022    Published: Nov. 30, 2022

Share

Abstract

This study explores quantile regression estimation technique and its practicality in regression analysis; hence we provide a comparative study in view of quantile regression as an alternative to the traditional ordinary least squares regression. Although the ordinary least squares (OLS) model examines the relationship between the independent variable and the conditional mean of the dependent variable, whereas the quantile regression model examines the relationship between the independent variable and the conditional quantiles of the dependent variable. Quantile regression overcomes various problems associated with OLS. First, quantile regression is defined and its advantages over ordinary least squares regression are illustrated. Also, specific comparisons are made between ordinary least squares and quantile regression estimation methods. Lastly, both estimation techniques were applied on a real life data and the results obtained from the analysis of two types of datasets in this study suggests that quantile regression provides a richer characterization of the data giving rise to the impact of a covariate on the entire distribution of the response variables as the effect can be very different for different quantiles. Quantile regression therefore gives an efficient and more complete view of the relationship amongst variables, hence, suitable in examining predictors effects at various locations of the outcome distribution.

 DOI 10.11648/j.ajmcm.20220704.11 Published in American Journal of Mathematical and Computer Modelling ( Volume 7, Issue 4, December 2022 ) Page(s) 49-54 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2024. Published by Science Publishing Group
Keywords

Regression, Ordinary Least Squares Regression, Quantile Regression, Mean Square Error, Variance

References
 [1] Abdullahi I. and Abubakar Y. (2015). Analysis of quantile regression as alternative to ordinary least squares. International Journal of Advanced Statistics and Probability. 3 (2) 138-145. [2] Austin PC, Tu JV, Daly PA, Alter DA. (2005). The use of quantile regression in health care research: a case study examining gender differences in the timeliness of thrombolytic therapy. Stat Med.: 24: 791-816. [3] Chen C., (2004). An Introduction to Quantile Regression and the Quantreg Procedure. SUGI 30, 213-30. [4] Davino C, Furno M, and Vistocco D. (2014). Quantile Regression: Theory and Applications. John Wiley & Sons, Ltd. [5] Feng, X., He, X, and Hu, J. (2011). Wild Bootstrap for Quantile Regression. Biometrica; 98: 995-999. [6] John O. O and Nduka E. C. (2009) Quantile Regression Analysis as a Robust Alternative to Ordinary Least Square. Scientia Africana, Vol 8 (2) pp: 61-65. [7] Karlson, A. (2006). Estimation and inference for Quantile Regression of Longitudinal Data, with Applications in Biostatistics. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the faculty of social sciences. 18-36. [8] Kleinbaum, D. G., Kupper, L. L., Muller, K. E., & Nizam, A. (2008). Applied regression analysis and other multivariate methods (4th ed.). Belmont, CA: Thomson Brooks/Cole. [9] Keonker, R. and G. Bassett G. Jr., (1978) Regression Quantiles, Econometrica, Vol. 1, pp: 33-50. [10] Ryan, T. P. (1997). Modern Regression Methods. John Wiley & Sons, Inc., New York. [11] Ishaq O. O., Akeem A. A., Abdulmuahymin A. S., & Audu A., (2017). Reviewing of the Relationship Between Body Mass Index and High Blood Pressure of Patients. International Journal of Statistics and Actuarial Science. Vol 1 (1); 19-23. [12] Steven J. S., Daniel. S., & David Z., (2019). Quantile Regression and its Application: A Primer for Anesthesiologist. International Anesthesia Research Society. Vol 128 (4) 820-830. [13] International Business Machines Corporation (IBM) (2021). Quantile Regression. In SPSS Statistics.
• APA Style

Runyi Emmanuel Francis, Maureen Tobe Nwakuya. (2022). A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique. American Journal of Mathematical and Computer Modelling, 7(4), 49-54. https://doi.org/10.11648/j.ajmcm.20220704.11

ACS Style

Runyi Emmanuel Francis; Maureen Tobe Nwakuya. A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique. Am. J. Math. Comput. Model. 2022, 7(4), 49-54. doi: 10.11648/j.ajmcm.20220704.11

AMA Style

Runyi Emmanuel Francis, Maureen Tobe Nwakuya. A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique. Am J Math Comput Model. 2022;7(4):49-54. doi: 10.11648/j.ajmcm.20220704.11

• ```@article{10.11648/j.ajmcm.20220704.11,
author = {Runyi Emmanuel Francis and Maureen Tobe Nwakuya},
title = {A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {7},
number = {4},
pages = {49-54},
doi = {10.11648/j.ajmcm.20220704.11},
url = {https://doi.org/10.11648/j.ajmcm.20220704.11},
abstract = {This study explores quantile regression estimation technique and its practicality in regression analysis; hence we provide a comparative study in view of quantile regression as an alternative to the traditional ordinary least squares regression. Although the ordinary least squares (OLS) model examines the relationship between the independent variable and the conditional mean of the dependent variable, whereas the quantile regression model examines the relationship between the independent variable and the conditional quantiles of the dependent variable. Quantile regression overcomes various problems associated with OLS. First, quantile regression is defined and its advantages over ordinary least squares regression are illustrated. Also, specific comparisons are made between ordinary least squares and quantile regression estimation methods. Lastly, both estimation techniques were applied on a real life data and the results obtained from the analysis of two types of datasets in this study suggests that quantile regression provides a richer characterization of the data giving rise to the impact of a covariate on the entire distribution of the response variables as the effect can be very different for different quantiles. Quantile regression therefore gives an efficient and more complete view of the relationship amongst variables, hence, suitable in examining predictors effects at various locations of the outcome distribution.},
year = {2022}
}
```
• ```TY  - JOUR
T1  - A Comparative Analysis of Ordinary Least Squares and Quantile Regression Estimation Technique
AU  - Runyi Emmanuel Francis
AU  - Maureen Tobe Nwakuya
Y1  - 2022/11/30
PY  - 2022
N1  - https://doi.org/10.11648/j.ajmcm.20220704.11
DO  - 10.11648/j.ajmcm.20220704.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 49
EP  - 54
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20220704.11
AB  - This study explores quantile regression estimation technique and its practicality in regression analysis; hence we provide a comparative study in view of quantile regression as an alternative to the traditional ordinary least squares regression. Although the ordinary least squares (OLS) model examines the relationship between the independent variable and the conditional mean of the dependent variable, whereas the quantile regression model examines the relationship between the independent variable and the conditional quantiles of the dependent variable. Quantile regression overcomes various problems associated with OLS. First, quantile regression is defined and its advantages over ordinary least squares regression are illustrated. Also, specific comparisons are made between ordinary least squares and quantile regression estimation methods. Lastly, both estimation techniques were applied on a real life data and the results obtained from the analysis of two types of datasets in this study suggests that quantile regression provides a richer characterization of the data giving rise to the impact of a covariate on the entire distribution of the response variables as the effect can be very different for different quantiles. Quantile regression therefore gives an efficient and more complete view of the relationship amongst variables, hence, suitable in examining predictors effects at various locations of the outcome distribution.
VL  - 7
IS  - 4
ER  - ```
Author Information
• Department of Statistics, Federal Polytechnic Ugep, Ugep, Nigeria

• Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria

• Section