The focus of this article
In the previous lessons, we learned the difference and connection between linear regression model and nonlinear regression model. A polynomial nonlinear regression model is a type of regression model used to fit nonlinear data. Unlike linear regression models, polynomial nonlinear regression models can accommodate more complex data patterns by increasing the degree of the polynomial. In this article, we will introduce the principles, application scenarios, and modeling methods of polynomial nonlinear regression models.
Polynomial Nonlinear Regression Model
A polynomial nonlinear regression model is a polynomial-based regression model that assumes that the relationship between the independent variable and the dependent variable can be described by a polynomial function. A polynomial function is a function of the form y = a0 + a1*x + a2*x^2 + ... + an*x^n, where y is the dependent variable, x is the independent variable, a0, a1, a2, ..., an is the coefficient of the polynomial, n is the degree of the polynomial.
If there is only one feature in the polynomial and the high-order term of this feature is called unit polynomial regression , if there are multiple multiple features and high-order terms of these features, then this is called multiple linear regression .
Application scenarios of polynomial nonlinear regression model
Multinomial nonlinear regression models are suitable for situations where there is a nonlinear relationship between the independent variable and the dependent variable. In the real world, many problems can be modeled by polynomial nonlinear regression models, such as:
- Natural sciences: Experimental data in the fields of physics and chemistry usually contain nonlinear relationships, and polynomial nonlinear regression models can be used to fit these data to obtain mathematical expressions of physical or chemical laws.
- Field of economics: Some empirical laws in economics can also be described by polynomial nonlinear regression models, such as economic growth models, consumption models, etc.
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