Polynomial parametric and non-parametric B-Splines regression models. An Engineering Application.

Abstract

A study of the polynomial parametric and nonparametric B-splines regression models applied to a simulation of an impact of a car against a bus body was performed. A non-experimental design, cross-sectional, and correlational was established. The R software was used and the following criteria were considered: the rejection of the nullity of the coefficients of the models through the Student's t-hypothesis test, the validity of the models using the Snedecor F-test of the ANOVA table, the goodness of fit, 95% confidence intervals, and compliance with the assumptions of normal distribution, non-autocorrelation and homoscedasticity of the residuals. The Wilcoxon nonparametric test was applied to select the appropriate regression model based on the lengths of the confidence intervals. The parametric polynomial regression models were fitted to curves with parabolic shape or curvature without abrupt changes, fitting better to the relationships of the vehicle impact simulation, whose explanatory variable is the speed of the impacting vehicle. While the nonparametric B-splines regression models provided a better fit to bell-shaped curves with more abrupt curvature changes.