Nonlinear Regression Analysis: Friedman1 Benchmark Dataset This analysis explores nonlinear regression modeling using the Friedman1 benchmark dataset, a simulated dataset designed to evaluate machine learning algorithms on complex nonlinear relationships. The true data-generating function is y = 10·sin(π·X1·X2) + 20·(X3-0.5)² + 10·X4 + 5·X5 + ε, where only five of ten predictors (X1-X5) are informative, while the remaining five (X6-X10) are pure noise. Across Exercises 7.2 and 7.5, we trained and evaluated multiple regression models including Linear Regression, GLMNET, K-Nearest Neighbors, Multivariate Adaptive Regression Splines (MARS), Support Vector Machines (SVM), and Random Forest. MARS emerged as the optimal model with a test set RMSE of 1.159 and R² of 0.946, representing a 56.6% improvement over the best linear model (RMSE = 2.670). Remarkably, MARS achieved perfect feature selection accuracy (100%), correctly identifying all five informative predictors while completely excluding all noise variables—a capability that distinguishes it from linear approaches which assigned non-zero importance to spurious predictors. The analysis demonstrates that MARS's adaptive basis functions not only capture complex nonlinear patterns including multiplicative interactions (X1·X2) and quadratic relationships (X3²) but also perform automatic variable selection, making it particularly valuable for high-dimensional datasets where distinguishing signal from noise is critical. These findings validate MARS as a powerful tool for nonlinear regression that combines predictive accuracy with interpretability through its piecewise linear structure and transparent feature selection mechanism.

Informe de simulación en R sobre capacidad de proceso, estación de reproceso y sistema de transporte.

This report explores Nobel Prize data retrieved directly from the official Nobel Prize API. Using R, the analysis extracts and transforms JSON data to answer key questions about laureate distribution, average age at award, and global trends across countries and continents.