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Estimators of Linear Regression Model and Prediction under Some Assumptions Violation

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DOI: 10.4236/ojs.2012.25069    4,096 Downloads   7,186 Views   Citations

ABSTRACT

The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This notwithstanding, regression analysis may aim at prediction. Consequently, this paper examines the performances of the Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis in prediction of linear regression model under the joint violations of the assumption of non-stochastic regressors, independent regressors and error terms. With correlated stochastic normal variables as regressors and autocorrelated error terms, Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. From the results, it is observed that the performances of COR at each level of correlation (multicollinearity) and that of ML, especially when the sample size is large, over the levels of autocorrelation have a convex-like pattern while that of OLS and PC are concave-like. Also, as the levels of multicollinearity increase, the estimators, except the PC estimators when multicollinearity is negative, rapidly perform better over the levels autocorrelation. The COR and ML estimators are generally best for prediction in the presence of multicollinearity and autocorrelated error terms. However, at low levels of autocorrelation, the OLS estimator is either best or competes consistently with the best estimator, while the PC estimator is either best or competes with the best when multicollinearity level is high(λ>0.8 or λ<-0.49).

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

K. Ayinde, E. Apata and O. Alaba, "Estimators of Linear Regression Model and Prediction under Some Assumptions Violation," Open Journal of Statistics, Vol. 2 No. 5, 2012, pp. 534-546. doi: 10.4236/ojs.2012.25069.

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