When Multicollinearity exists in a data set, the data is considered deficient. Multicollinearity is frequently encountered in observational studies. It creates difficulties when building regression models. It is a phenomenon whereby two or more explanatory variable in a multiple regression model are highly correlated. Variable selection is an important aspect of model building as such the choice of the best subset among many variables to be included in a model is the most difficult part of model building in regression analysis. Data was obtained from Nigerian Stock Exchange Fact Book, Nigerian Stock Exchange Annual Report and Account, CBN Statistical Bulletin and FOS Statistical bulletin from 1987 to 2018. Variance Inflation Factor (VIF) and correlation matrices were used to detect the presence of multicollinearity. Ridge regression and Least Square Regression were applied using R-package, Minitab and SPSS Packages. Ridge Models with constant range of 0.01 ≤ K ≤ 1.5 and Least Square Regression models were considered for each value of P = 2, 3, …,7. The optimal Ridge and Least Square model from the Ridge and Least Square Regression models were obtained by taking the average rank of the Coefficient of Determination and Mean Square Error. The result showed that the choices of variable selection were affected by the presence of multicollinearity as different variables were selected under Ridge and Least Square Regression for same level of P.

Making an appropriate decision in the selection of sustainable club from other clubs studied involves the use of right statistical approach, hence the need for stochastic and game theory analysis of English premier league scoreline. The following clubs Manchester United (MU), Chelsea (C), Arsenal (A), Manchester City (MC), Liverpool (LP), Tottenham (T) and Everton (E) were studied for both home and away matches for the period of 2010/2011 to 2019/2020 season. The optimal strategy and overall optimal strategy for MR G and MR B were obtained for each season and the 10 seasons respectively. The result showed that Manchester United has the highest probability (0.29) of being selected by MR B and Liverpool has the probability of 0.27 of being selected by MR G. The matrix of flow was also obtained when Manchester United played against Liverpool, given that Manchester United is home, as WWWLWWDWDD, and when Manchester United is away and Liverpool home, as WDLWLLDDWW. The two and four step transition matrix was also used to predict the future matches and their probabilities obtained given the probabilities of the previous game. The limiting distribution of the transition probability matrix obtained showed that Manchester United has a 67% chance of winning Liverpool while Liverpool has a 33% chance of winning Manchester United, this shows that Manchester United is stronger at home. Thus, the two most sustainable clubs out of the seven clubs studied are Manchester United and Liverpool.