Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator (OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of 0 4 β = , 1 0.4 β = , 2 1.5 β = and 3 3.6 β =. Five (5) levels of mulicollinearity are with seven (7) different sample sizes. The method's performances were compared with the aids of set confidence interval (C.I.) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.
In this paper, a new approach to estimating the model parameters in Principal Components (PCs) is developed. Principal Component Analysis (PCA) is a method of variable reduction that has found relevance in combating multicollinearity problem in Multiple Linear Regression Models. In this paper, a new approach to estimating the model parameters in Principal Components (PCs) is developed The method requires using the PCs as regressors to predict the dependent variable and further utilizing the predicted variable as a dependent variable on the original explanatory variables in an Ordinary Least Square (OLS) regression. The resulting parameter estimates are the same as the estimates from the usual Principal Components Regression Estimator. The sampling properties of the new estimator are proved to be same as the existing ones. The new approach is simpler and easier to use. Real-life data sets are used to illustrate both the conventional and the developed method.
COVID-19 has remained and continued to be a severe pandemic threatening the present and future health stability of all the countries, the West African Countries inclusive. The challenge to avert the threat by modeling the reported cases in each of these West African Countries becomes needful for future planning and a K. Ayinde (B) •
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