The Least Squares Method is a widely used mathematical technique for finding the best-fitting model to a set of data points. It is often used in both linear and nonlinear regression analysis to estimate the parameters of a model that minimizes the sum of the squared differences between the observed data and the predicted values from the model. The goal is to find the parameters that make the model as close as possible to the actual data.
Linear Least Squares Method:
In linear regression, the model is represented by a linear equation
Nonlinear Least Squares Method:
In cases where the relationship between the variables is nonlinear, a more complex model is used. The nonlinear least squares method aims to estimate the parameters of a nonlinear model that minimizes the sum of the squared differences between the observed data and the model’s predictions.
The nonlinear least squares method involves iteratively adjusting the parameters
to minimize the sum of squared differences. This is often done using optimization techniques such as the Gauss-Newton method or the Levenberg-Marquardt algorithm. The process continues until the model fits the data as closely as possible.