Literature reviews revealed that multicollinearity always exists when model a deals with several independent variables. This phenomenon can cause the t statistic and the related probability-value to give a misleading impression of the importance of the independent variables. There are two approaches in tackling this issue. The common approach is correlation-coefficient based and the other is variance-based. Many softwares in the market have highlighted this phenomenon and offer options in minimising the effect. Currently, the variance-based approach is widely available in the software market. This is because it does not depend on the type of dependent variables. This variance-based approach via Variance Inflation Factor (VIF) quantifies the severity of multicollinearity in an ordinary least squares regression analysis. It provides an index that measures how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of collinearity. Thus, here, a novel approach is revealed in detailing the procedures to remove several variables due to multicollinearity effects. Ultimately, the insignificant variables are eliminated. It is found that when a very stringent criterion is set for multicollinearity, the process of elimination of variables becomes smooth and easy besides shortening the number of iteration.

Background: Market studies on consumer preferences on product items had shown that consumer's behavioural patterns and intentions are sources of business profit level. In the advent wave of global businesses, the behavioural buying patterns of consumers have to be studied and analysed. Hence, this research illustrated the procedures in getting the best polynomial regression model of the consumer buying patterns on the demand for detergent that had included interaction variables. Methods: The hierarchically multiple polynomial regression models involved were up to the third-order polynomial and all the possible models were also considered. The possible models were reduced to several selected models using progressive removal of multicollinearity variables and elimination of insignificant variables. To enhance the understanding of the whole concept in this study, multiple polynomial regressions with eight selection criteria (8SC) had been explored and presented in the process of getting the best model from a set of selected models. Results: A numerical illustration on the demand of detergent had been included to get a clear picture of the process in getting the best polynomial order model. There were two single independent variables: the "price difference" between the price offered by the enterprise and the average industry price of competitors' similar detergents (in US$) and advertising expenditure (in US$). Conclusion: In conclusion, the best cubic model was obtained where the parameters involved in the model were estimated using ordinary least square method.

EM Algorithm and Multiple Imputation are widely used methods in dealing with missing data. Although Multiple Imputation always be the favourite choice of researcher due to its accuracy and simple application, but the issue arises whether EM algorithm perform better with several times of imputation. Both methods will be tested using different number of imputations with the help of Amelia and Mice package in R software. The imputed data sets are compared using model averaging with Corrected Akaike Information Criteria (AICC ) as model selection Criterion. External validation and mean squared error of prediction (MSE(P)) are used to determine the best imputation method. Gateshead Millennium Study (GMS) data on children weight will illustrate the comparison between EM Algorithm and Multiple imputation. The results show that Multiple imputation performs slightly better compared to EM Algorithm.

The presence of outliers is an example of aberrant data that can have huge negative influence on statistical method under the assumption of normality and it affects the estimation. This paper introduces an alternative method as outlier treatment in time series which is interpolation. It compares two interpolation methods using performance indicator. Assuming outlier as a missing value in the data allows the application of the interpolation method to interpolate the missing value, thus comparing the result using the forecast accuracy. The monthly time series data from January 1998 until December 2015 of Malaysia Tourist Arrivals were used to deal with outliers. The results found that the cubic spline interpolation method gave the best result than the linear interpolation and the improved time series data indicated better performance in forecasting rather than the original time series data of Box-Jenkins model.

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