Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis

Abeer Mohamed Abd El Razek Youssef

doi:doi:10.11648/j.advances.20220303.24

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Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis

Abeer Mohamed Abd El Razek Youssef

Published in Advances (Volume 3, Issue 3)

Received: 15 August 2022 Accepted: 1 September 2022 Published: 29 September 2022

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Abstract

When we rely on the general linear regression model to represent the data, we use the ordinary least squares method to estimate the parameters of this model. This method, when applied, depends on the fulfillment of certain basic assumptions and conditions so that there is an accuracy in estimating the parameters of the regression model, and in many practical applications this hypothesis cannot be achieved, which makes the method of least squares ineffective in giving correct and accurate results, and this leads to falling into econometric problems. The estimated parameters lose the property of credibility, unbiased and make them not have the lowest possible variance and not expressive of the original theory. Most econometric models suffer from the problems of autocorrelation, multicollinearity, and heteroscedasticity. This paper presents a brief on these problems, their causes, how can be detected, tested, and minimized. The OLS method is based on several assumptions, and if these assumptions are fulfilled, we obtain unbiased, consistent, and efficient estimates (less variance compared to other methods). We discuss these problems as follows: First: the problem of multicollinearity Second: The problem of autocorrelation Third: Variation Heteroscedasticity. This article presents inference for many commonly used estimators - Variance Inflation Factors, Coefficient covariance matrix, Correlogram of Residuals, Normality Test for Residuals. Serial correlation LM test, Heteroskedasticity Test: Harvey, Actual and Estimated Residuals.

Published in	Advances (Volume 3, Issue 3)
DOI	10.11648/j.advances.20220303.24
Page(s)	140-152
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

Multicollinearity, Autocorrelation, Heteroscedasticity

References

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[2]	Mansfield, E. R., & Helms, B. P. (1982). Detecting multicollinearity. The American Statistician, 36 (3a), 158-160.‏
[3]	Daoud, J. I. (2017, December). Multicollinearity and regression analysis. In Journal of Physics: Conference Series (Vol. 949, No. 1, p. 012009). IOP Publishing.‏
[4]	Farrar, D. E., & Glauber, R. R. (1967). Multicollinearity in regression analysis: the problem revisited. The Review of Economic and Statistics, 92-107.‏
[5]	Kim, J. H. (2019). Multicollinearity and misleading statistical results. Korean journal of anesthesiology, 72 (6), 558-569.‏
[6]	Gunst, R. F., & Webster, J. T. (1975). Regression analysis and problems of multicollinearity. Communications in Statistics-Theory and Methods, 4 (3), 277-292.‏
[7]	Anderson, R. L. (1954). The problem of autocorrelation in regression analysis. Journal of the American Statistical Association, 49 (265), 113-129.‏
[8]	Kadiyala, K. R. (1968). A transformation used to circumvent the problem of autocorrelation. Econometrica: Journal of the Econometric Society, 93-96.‏
[9]	Griffith, D. A., Fischer, M. M., & LeSage, J. (2017). The spatial autocorrelation problem in spatial interaction modelling: a comparison of two common solutions. Letters in Spatial and Resource Sciences, 10 (1), 75-86.‏
[10]	Stimson, R. J., Mitchell, W., Rohde, D., & Shyy, P. (2011). Using functional economic regions to model endogenous regional performance in Australia: Implications for addressing the spatial autocorrelation problem. Regional Science Policy & Practice, 3 (3), 131-144.‏
[11]	Shrestha, N. (2020). Detecting multicollinearity in regression analysis. American Journal of Applied Mathematics and Statistics, 8 (2), 39-42.‏
[12]	Obite, C. P., Olewuezi, N. P., Ugwuanyim, G. U., & Bartholomew, D. C. (2020). Multicollinearity effect in regression analysis: A feed forward artificial neural network approach. Asian journal of probability and statistics, 6 (1), 22-33.‏
[13]	Zhang, T., Zhou, X. P., & Liu, X. F. (2020). Reliability analysis of slopes using the improved stochastic response surface methods with multicollinearity. Engineering Geology, 271, 105617.‏
[14]	Vörösmarty, G., & Dobos, I. (2020, October). Green purchasing frameworks considering firm size: a multicollinearity analysis using variance inflation factor. In Supply Chain Forum: An International Journal (Vol. 21, No. 4, pp. 290-301). Taylor & Francis.‏
[15]	Aslam, M., & Ahmad, S. (2020). The modified Liu-ridge-type estimator: a new class of biased estimators to address multicollinearity. Communications in Statistics-Simulation and Computation, 1-20.‏
[16]	Negret, P. J., Marco, M. D., Sonter, L. J., Rhodes, J., Possingham, H. P., & Maron, M. (2020). Effects of spatial autocorrelation and sampling design on estimates of protected area effectiveness. Conservation Biology, 34 (6), 1452-1462.‏
[17]	Stojkoski, V., Sandev, T., Kocarev, L., & Pal, A. (2022). Autocorrelation functions and ergodicity in diffusion with stochastic resetting. Journal of Physics A: Mathematical and Theoretical, 55 (10), 104003.‏

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Abeer Mohamed Abd El Razek Youssef. (2022). Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances, 3(3), 140-152. https://doi.org/10.11648/j.advances.20220303.24

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Abeer Mohamed Abd El Razek Youssef. Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances. 2022, 3(3), 140-152. doi: 10.11648/j.advances.20220303.24

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AMA Style

Abeer Mohamed Abd El Razek Youssef. Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances. 2022;3(3):140-152. doi: 10.11648/j.advances.20220303.24

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@article{10.11648/j.advances.20220303.24,
  author = {Abeer Mohamed Abd El Razek Youssef},
  title = {Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis},
  journal = {Advances},
  volume = {3},
  number = {3},
  pages = {140-152},
  doi = {10.11648/j.advances.20220303.24},
  url = {https://doi.org/10.11648/j.advances.20220303.24},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.advances.20220303.24},
  abstract = {When we rely on the general linear regression model to represent the data, we use the ordinary least squares method to estimate the parameters of this model. This method, when applied, depends on the fulfillment of certain basic assumptions and conditions so that there is an accuracy in estimating the parameters of the regression model, and in many practical applications this hypothesis cannot be achieved, which makes the method of least squares ineffective in giving correct and accurate results, and this leads to falling into econometric problems. The estimated parameters lose the property of credibility, unbiased and make them not have the lowest possible variance and not expressive of the original theory. Most econometric models suffer from the problems of autocorrelation, multicollinearity, and heteroscedasticity. This paper presents a brief on these problems, their causes, how can be detected, tested, and minimized. The OLS method is based on several assumptions, and if these assumptions are fulfilled, we obtain unbiased, consistent, and efficient estimates (less variance compared to other methods). We discuss these problems as follows: First: the problem of multicollinearity Second: The problem of autocorrelation Third: Variation Heteroscedasticity. This article presents inference for many commonly used estimators - Variance Inflation Factors, Coefficient covariance matrix, Correlogram of Residuals, Normality Test for Residuals. Serial correlation LM test, Heteroskedasticity Test: Harvey, Actual and Estimated Residuals.},
 year = {2022}
}

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TY  - JOUR
T1  - Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis
AU  - Abeer Mohamed Abd El Razek Youssef
Y1  - 2022/09/29
PY  - 2022
N1  - https://doi.org/10.11648/j.advances.20220303.24
DO  - 10.11648/j.advances.20220303.24
T2  - Advances
JF  - Advances
JO  - Advances
SP  - 140
EP  - 152
PB  - Science Publishing Group
SN  - 2994-7200
UR  - https://doi.org/10.11648/j.advances.20220303.24
AB  - When we rely on the general linear regression model to represent the data, we use the ordinary least squares method to estimate the parameters of this model. This method, when applied, depends on the fulfillment of certain basic assumptions and conditions so that there is an accuracy in estimating the parameters of the regression model, and in many practical applications this hypothesis cannot be achieved, which makes the method of least squares ineffective in giving correct and accurate results, and this leads to falling into econometric problems. The estimated parameters lose the property of credibility, unbiased and make them not have the lowest possible variance and not expressive of the original theory. Most econometric models suffer from the problems of autocorrelation, multicollinearity, and heteroscedasticity. This paper presents a brief on these problems, their causes, how can be detected, tested, and minimized. The OLS method is based on several assumptions, and if these assumptions are fulfilled, we obtain unbiased, consistent, and efficient estimates (less variance compared to other methods). We discuss these problems as follows: First: the problem of multicollinearity Second: The problem of autocorrelation Third: Variation Heteroscedasticity. This article presents inference for many commonly used estimators - Variance Inflation Factors, Coefficient covariance matrix, Correlogram of Residuals, Normality Test for Residuals. Serial correlation LM test, Heteroskedasticity Test: Harvey, Actual and Estimated Residuals.
VL  - 3
IS  - 3
ER  -

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Author Information

Abeer Mohamed Abd El Razek Youssef

Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

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APA Style

Abeer Mohamed Abd El Razek Youssef. (2022). Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances, 3(3), 140-152. https://doi.org/10.11648/j.advances.20220303.24

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ACS Style

Abeer Mohamed Abd El Razek Youssef. Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances. 2022, 3(3), 140-152. doi: 10.11648/j.advances.20220303.24

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AMA Style

Abeer Mohamed Abd El Razek Youssef. Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis. Advances. 2022;3(3):140-152. doi: 10.11648/j.advances.20220303.24

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@article{10.11648/j.advances.20220303.24,
  author = {Abeer Mohamed Abd El Razek Youssef},
  title = {Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis},
  journal = {Advances},
  volume = {3},
  number = {3},
  pages = {140-152},
  doi = {10.11648/j.advances.20220303.24},
  url = {https://doi.org/10.11648/j.advances.20220303.24},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.advances.20220303.24},
  abstract = {When we rely on the general linear regression model to represent the data, we use the ordinary least squares method to estimate the parameters of this model. This method, when applied, depends on the fulfillment of certain basic assumptions and conditions so that there is an accuracy in estimating the parameters of the regression model, and in many practical applications this hypothesis cannot be achieved, which makes the method of least squares ineffective in giving correct and accurate results, and this leads to falling into econometric problems. The estimated parameters lose the property of credibility, unbiased and make them not have the lowest possible variance and not expressive of the original theory. Most econometric models suffer from the problems of autocorrelation, multicollinearity, and heteroscedasticity. This paper presents a brief on these problems, their causes, how can be detected, tested, and minimized. The OLS method is based on several assumptions, and if these assumptions are fulfilled, we obtain unbiased, consistent, and efficient estimates (less variance compared to other methods). We discuss these problems as follows: First: the problem of multicollinearity Second: The problem of autocorrelation Third: Variation Heteroscedasticity. This article presents inference for many commonly used estimators - Variance Inflation Factors, Coefficient covariance matrix, Correlogram of Residuals, Normality Test for Residuals. Serial correlation LM test, Heteroskedasticity Test: Harvey, Actual and Estimated Residuals.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Detecting of Multicollinearity, Autocorrelation and Heteroscedasticity in Regression Analysis
AU  - Abeer Mohamed Abd El Razek Youssef
Y1  - 2022/09/29
PY  - 2022
N1  - https://doi.org/10.11648/j.advances.20220303.24
DO  - 10.11648/j.advances.20220303.24
T2  - Advances
JF  - Advances
JO  - Advances
SP  - 140
EP  - 152
PB  - Science Publishing Group
SN  - 2994-7200
UR  - https://doi.org/10.11648/j.advances.20220303.24
AB  - When we rely on the general linear regression model to represent the data, we use the ordinary least squares method to estimate the parameters of this model. This method, when applied, depends on the fulfillment of certain basic assumptions and conditions so that there is an accuracy in estimating the parameters of the regression model, and in many practical applications this hypothesis cannot be achieved, which makes the method of least squares ineffective in giving correct and accurate results, and this leads to falling into econometric problems. The estimated parameters lose the property of credibility, unbiased and make them not have the lowest possible variance and not expressive of the original theory. Most econometric models suffer from the problems of autocorrelation, multicollinearity, and heteroscedasticity. This paper presents a brief on these problems, their causes, how can be detected, tested, and minimized. The OLS method is based on several assumptions, and if these assumptions are fulfilled, we obtain unbiased, consistent, and efficient estimates (less variance compared to other methods). We discuss these problems as follows: First: the problem of multicollinearity Second: The problem of autocorrelation Third: Variation Heteroscedasticity. This article presents inference for many commonly used estimators - Variance Inflation Factors, Coefficient covariance matrix, Correlogram of Residuals, Normality Test for Residuals. Serial correlation LM test, Heteroskedasticity Test: Harvey, Actual and Estimated Residuals.
VL  - 3
IS  - 3
ER  -

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