The focus of this article
In the previous courses, we learned the univariate linear regression model and the multivariate linear regression model. Whether it is univariate linear regression or multivariate linear regression, both are the same and both are linear. In this article we will learn the difference and connection between linear regression model and nonlinear regression.
Basic Differences About Models
Linear regression : Linear regression means that the index of each variable is 1, and its shape is a straight line or a hyperplane. A linear regression model assumes that the relationship between the dependent variable and the independent variable is linear. The form of the linear regression model is: y = β0 + β1x1 + β2x2 + ... + βnxn, where y represents the dependent variable, x1, x2, ..., xn represent the independent variables, β0, β1, β2, ..., βn represents the coefficient of the model.
Nonlinear regression : The form of the nonlinear regression model can be any nonlinear function, such as polynomial function (at least one variable has an index other than 1), exponential function, logarithmic function, etc. Its form is a curved form. Nonlinear regression models assume that the relationship between the dependent variable and the independent variable is nonlinear.
Fitting ability
The linear regression model is suitable for the case where the relationship between the dependent variable and the independent variable is linear, and the data fitting effect for the nonlinear relationship is poor. The fitting ability of the linear regression model is limited by the linear assumption, and it cannot fit complex nonlinear relationships well.
The nonlinear regression model is suitable for situations where the relationship between the dependent variable and the independent variable is nonlinear, and can better fit the data of the nonlinear relationship. The fitting ability of the nonlinear regression model is strong, and it can more accurately describe the complex relationship between the dependent variable and the independent variable.
parameter learning
The parameter estimation of the linear regression model can be carried out by the method of least squares, that is, by minimizing