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Abstract
The ordinary least squares (OLS) method had been extensively applied to estimation of different classes of regression model under specific assumptions. However, this estimation procedure OLS does not perform well with outliers and small sample sizes. As a result, this work considered the application of the maximum likelihood method for polynomial regression model using sample sizes as against the large sample assumption in OLS. The efficiency of the maximum likelihood (ML) estimation technique was put to test by comparing its model fit to that of the OLS using some real world data sets. The results of analysis of these data sets using both methods showed that the ML outperformed the OLS since it gave better estimates with lower mean square error (MSE) values in all the four data sets considered and higher coefficient of determination (R2) values. Although, both methods resulted in overall good fit, but the ML is more efficient than the OLS because it resulted in lower MSE for small sample sizes.
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References
Polynomial regression model of making cost prediction in mixed cost analysis. The International Institute for Science,Technology and Education (IISTE)2 (2), 14-19.
Biorn E. (2017). Estimation of nonlinear models with measurement Error. Econometrica, Econometric Society,72 (1), 33-75.
Cheng,C.and Schneeweiss, H. (1998).Polynomial regression with errors in the variables, Journal of Royal Statistical Society. 6 (2), 189-199.
Cheng, C., and Van Ness, J.W. (1999).Statistical regression with measurement error. Kendall’s Library of Statistics 6, Arnold, London
Draper, N.R., and Smith H. (1981). Applied regression analysis, John Wiley, New York.
Eva Ostertagova (2012). Modelling using polynomial regression. Elsevier Procedia Engineering. 48(6), 500-506
Gergonne, J. D. (1974).The application of the method of least squares to the interpolation of sequences. Historia Mathematical 1 (4), 439–447.
Gujarati, D.N. (2004). Basic econometrics (4th Edition). McGraw-Hill Publishing Companies, New York.
Jeffrey, R.E. and Mark, E.P (1993). On the use of polynomial regression equations as an alternative to difference scores in organizational research. Academy of Management Journal 36 (6), 1577-1613.
Kmenta, J. (1990). Elements of econometrics. 2nd Ed. Macmillan publishing co. NewYork
Matloff, N.S.(1981).Use of regression functions for improved estimation of means. Biometrika, 68(3),685 – 689.
McClave, J.T. and Deitrich, F.H. (1991). Statistics, Macmillan Publishing co. New York
Mundrake G.A. and Brown B.J. (1989). A spreadsheet model for teaching regression analysis. Journal of Education for Business. 67(4): 233-237
Noraini A., Amran A. and Zainodin J. (2011). An improved volumetric estimation using Polynomial Regression. Journal of Science and Technology 3 (2),29-42.
Ogunwale, O.D., Halid, O.Y. and Sunday, J. (2010).On an alternative method of estimation of polynomial regression models. Australian Journal of Basic and Applied Sciences 4(8),3585-3590.
Stephen J. I, Raymond J.C. and David F. (2002). Polynomial regression and estimating functions in the presence of multiplicative measurement error. Journal of the Royal Statistical Society. 61(3), 859-866.
Stigler, S.M. (1974). On the design and analysis of polynomial regression experiments. Historia Mathematica.1 (4), 431–439.