An Alternative Estimator for the Estimation of Polynomial Regression Model (PRM)

The maximum likelihood (ML) approach is used to fit the polynomial regression model (PRM) in the presence of small sample sizes. The ML technique is applied to the data of PPP, GDP, and output/total production cost in Nigeria between 1989 and 1999. The results of the analyses (by ML approach and that of the OLS) are presented for comparison. The analysis shows that the ML gives parameter estimates of 128.889, -5.24, -29.208, 10.523 and the OLS resulted in 128.009, 5.196, -30.376, 11.009. The analysis of the first data set (of iron content and weight loss of some specimen tested in a corrosion wheel set-up) shows that both estimators accounted for good fit because they both have high R2 values and significant t-ratios. The result of the model fit of the four data sets using ML results in reasonable parameter estimates (with lesser S.E relative to the parameter estimates), lower MSE, and very high R2-values. Although both methods were generally well adapted, ML was more effective than OLS because it led to a smaller sample size's MSE.