NLS in R Programming Language

Nonlinear least squares (NLS) is a method to fit a function with parameters to a set of data that are not necessarily linearly related to the parameters. NLS is commonly used in many fields, such as statistics, engineering, and science.

R is a popular programming language for data analysis and statistical computing. It includes built-in functions for fitting models with nonlinear least squares.

Fitting a Model with NLS in R

To fit a model with NLS in R, you first need to define the function you want to fit. For example, suppose you have a set of data that you believe follows a quadratic relationship:

x <- c(1,2,3,4,5)              # independent variable
y <- c(2.1, 4.2, 6.5, 9.7, 12.5) # dependent variable

quadratic <- function(x, a, b, c){
  a * x^2 + b * x + c
}

The quadratic function takes three parameters: a, b, and c. These parameters determine the shape of the quadratic curve.

Next, you need to fit the model to the data using nls function:

nlsfit <- nls(y ~ quadratic(x, a, b, c), start = list(a = 1, b = 1, c = 1))

The nls function takes the response variable y, and the function to fit quadratic(x, a, b, c) as input. The start argument specifies the initial values of the parameters a, b, and c.

Finally, you can plot the data and the fitted curve:

plot(x, y)
lines(x, predict(nlsfit), col = "red")

Conclusion

NLS is a powerful tool for fitting models to data that do not follow linear relationships. R includes built-in support for NLS with the nls function, allowing you to easily fit a wide range of nonlinear models to your data.