Non-Linear Data Modeling using Regression Techniques

Abstract

The purpose of this study is to use multiple linear and polynomial regression techniques to examine the relation between blood pressure (BP) and certain biochemical markers. For this study, 180 observations from a cross-sectional dataset were examined. Blood Urea (B. Urea), Creatinine, and body mass index (BMI) were the independent variables, while BP was the dependent variable. The ordinary least squares (OLS) method was first used and evaluated at a significance level of α = 0.01. The statistically significant predictive variables in the OLS model were B. Urea and BMI, with a coefficient of determination (R2 = 0.60) for the dependent variable. Furthermore, the multicollinearity test was performed, descriptive statistics for the variables were determined, and the normality of the data was tested. Finally, polynomial regression and Ridge regression were used to control the problem of high multicollinearity resulting from polynomial parts in third-order polynomial models. The main factor affecting BP variability in this method is B. Urea. We conclude, from comparing the results, that the polynomial method is more suitable, with an increase in the value of the coefficient of determination by (R2 = 0.70) and the significance of all combinations between two variables. Furthermore, the higher the degree of the polynomial model, the more complex and more difficult it is to interpret the results.