What is regression?

Concept

Regression analysis is a mathematical model. When the dependent variable and the independent variable have a linear relationship, it is a special linear model. 

The simplest case is one- variable linear regression , which consists of an independent variable and a dependent variable that are roughly linearly related; the model is Y=a+bX+ε (X is the independent variable, Y is the dependent variable, and ε is the random error ) . 

It is usually assumed that the mean value of random error is 0, and the variance is σ^2 (σ^2﹥0, σ^2 has nothing to do with the value of X). If it is further assumed that random errors follow a normal distribution , it is called a normal linear model. Generally, if there are k independent variables and 1 dependent variable, the value of the dependent variable is divided into two parts: one part is affected by the independent variable, that is, expressed as its function, the function form is known and contains unknown parameters; the other part is Other unconsidered factors and random influence, namely random error.

When the function is a linear function with unknown parameters, it is called a linear regression analysis model; when the function is a nonlinear function with unknown parameters , it is called a nonlinear regression analysis model. When the number of independent variables is greater than 1, it is called multiple regression, and when the number of dependent variables is greater than 1, it is called multiple regression. 

Regression analysis content

The main contents of regression analysis are as follows:

① Starting from a set of data, determine the quantitative relationship between certain variables; that is, establish a mathematical model and estimate unknown parameters. Usually the least square method is used .

②Test the trustworthiness of these relations.

③In the relationship between multiple independent variables affecting one dependent variable, judge whether the independent variable’s influence is significant, and select the significant influence into the model, and eliminate the insignificant variables. Stepwise regression , forward regression and backward regression are usually used .

④ Predict or control a certain process by using the required relationship.

The application of regression analysis is very extensive, and the use of statistical software packages can make various algorithms more convenient.

Regression type

The main types of regression are: linear regression, curvilinear regression, binary logistic regression, and multiple logistic regression.