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.

Consumer Behavioural Buying Patterns on the Demand for Detergents Using Hierarchically Multiple Polynomial Regression Model

Publisher Summary If the eigenvalues are known approximately, the convergence of the power method can largely be improved by increasing the quotient |λ 1 /λ 2 |. The most simple case is that of adding to all eigenvalues the same constant c . If all eigenvalues are positive, one subtracts (λ 2 + λ n )/2. Knowing for instance that a four-rowed matrix has approximately the eigenvalues—12; 6; 4; 1, one subtracts 3,5 and has the new approximate eigenvalues—8,5; 2,5; 0,5; − 2, 5. Therefore, the quotient λ 1 /λ 2 has increased from 12/6 = 2 to 8,5/2,5 = 3,4. As is well known the eigenvectors remain unchanged. When λ 1 > 0, but the other eigenvalues are partially 2 and the first negative eigenvalue from all eigenvalues. In many cases, this is the best choice and in every case, it will improve the relation. This chapter discusses the use of polynomials and quadratic transformations.

E. Bodewig

Papers

The use of polynomials