Academic Journal of Applied Mathematical Sciences

Online ISSN: 2415-2188
Print ISSN: 2415-5225

Quarterly Published (4 Issues Per Year)





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Volume 5 Number 11 November 2019

On the Pell Equations   and  


Authors: Ran yinxia
Pages: 164-167
DOI: doi.org/10.32861/ajams.511.164.167
Abstract
If ，where   or  are distinct odd primes,the system of indefinite equations in title only has positive integer solution only when  or   .


Handling Critical Multicollinearity Using Parametric Approach


Authors: Obubu Maxwell ; George Amaeze Osuji ; Ibeakuzie Precious Onyedikachi ; Chinelo Ijeoma Obi-Okpala ; Ikediuwa Udoka Chinedu ; Okpala Ikenna Frank
Pages: 150-163
DOI: doi.org/10.32861/ajams.511.150.163
Abstract
In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels (n>p) considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.