An Improved Volumetric Estimation Using Polynomial Regression

Abstract

The polynomial regression (PR) technique is used to estimate the parameters of the dependent variable having a polynomial relationship with the independent variable. Normality and nonlinearity exhibit polynomial characterization of power terms greater than 2. Polynomial Regression models (PRM) with the auxiliary variables are considered up to their third order interactions. Preliminary, multicollinearity between the independent variables is minimized and statistical tests involving the Global, Correlation Coefficient, Wald, and Goodness-of-Fit tests, are carried out to select significant variables with their possible interactions. Comparisons between the polynomial regression models (PRM) are made using the eight selection criteria (8SC). The best regression model is identified based on the minimum value of the eight selection criteria (8SC). The use of an appropriate transformation will increase in the degree of a statistically valid polynomial, hence, providing a better estimation for the model.