A type of regression analysis called nonlinear regression involves fitting data to a model before expressing the result as a mathematical function. It is conducted as Y=f(X,β)+ϵ, where: X is a vector of P predictors; β is a vector of k parameters, and F (-) is the known regression function. Simple linear regression establishes a straight-line relationship between two variables (X and Y) (y=mx+b), whereas nonlinear regression establishes a nonlinear (curved) relationship between the two variables.
The general rule is to test whether linear regression can fit the specific kind of curve in the data by using it first. People may need to use nonlinear regression if they are unable to get a satisfactory fit using linear regression. Because linear regression is easy to use and understand, more information is available for people to utilize in evaluating the model (Kim et al., 2020). Although linear regression can model curves, it is somewhat limited in the types of angles that it can fit, and occasionally it is unable to fit the particular curve in the data. Nonlinear regression may fit a much wider variety of curves, but it can be more challenging to interpret the results of the independent variable analysis and find the best fit. Furthermore, p-values cannot be calculated for the parameter estimations, and R-squared is invalid for nonlinear regression.
Nonlinear regression can be utilized to forecast population growth over time. Although there appears to be a connection between time and population increase, it is nonlinear, necessitating the use of a nonlinear regression model, as shown by a scatter diagram of changing demographics data over time (Kim et al., 2020). Future population increase predictions and projections for seasons that were not monitored can both be made using a logistic population growth model. In the corporate world, linear regressions can be used to analyze patterns and generate estimations or forecasts. For instance, by performing a linear assessment of the sales data with monthly sales, a corporation might anticipate sales in the upcoming months if its sales have been rising gradually every month for the past several years.
Reference
Kim, Y. J., Lee, S. J., Jin, H. S., Suh, I. A., & Song, S. Y. (2020). Comparison of linear and nonlinear statistical models for analyzing determinants of residential energy consumption. Energy and Buildings, 223. Web.