Linear regression often fails when real-world data shows saturation, exponential growth, or S-curves. Nonlinear regression addresses this by modeling curved relationships through functions like exponentials and logistics. In R, the nls() function implements nonlinear least squares, requiring analysts to specify the functional form and provide initial parameter estimates.

Historical roots trace back to Gauss and Legendre's least squares for astronomy. Today, self-starting models in R (e.g., Michaelis–Menten, Gompertz) automate initial guesses, making nonlinear regression accessible for biology, finance, and engineering. These methods are essential for accurate parameter estimation in pharmacokinetics, enzyme kinetics, and growth forecasting.

Choosing good starting values is critical for convergence in iterative optimization. Poor guesses can lead to local minima or model failure. Compared to linear models, nonlinear regression offers better interpretability for theory-driven relationships, though it requires domain knowledge to avoid overfitting. Future applications will likely integrate these models with machine learning for hybrid approaches.