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Regression - linear regression

2022-07-28 03:55:00 【Lu 727】

1、 effect

Linear regression is to use regression analysis in mathematical statistics , A statistical analysis method to determine the quantitative relationship between two or more variables , In linear regression analysis , Include only one independent variable and one dependent variable , And the relationship between them can be approximately expressed by a straight line , This kind of regression analysis is called univariate linear regression analysis . If the regression analysis includes two or more independent variables , And the relationship between dependent variable and independent variable is linear , It is called multiple linear regression analysis .

2、 Input / output description

Input : The independent variables X At least one or more quantitative or categorical variables , The dependent variable Y Quantitative variables are required .
Output : The result of model test goodness , Linear relationship between independent variable and dependent variable, etc .

3、 Case example

Through independent variables （ House age 、 Is there an elevator 、 Floor height 、 Room square ） Fitting the predicted dependent variable （ housing price ）

4、 Modeling steps

Generally speaking , Linear regression can be solved by least square method or gradient descent method , It can be calculated that for y=bx+a The straight line of . Take the least square method as an example , influence y There is often more than one factor , Suppose there is x1,x2,...,xk,k One factor , Generally, the following linear relation can be considered ：

Yes y And x1,x2,...,xk Simultaneous n Second independent observation n Group observations （xt1,xt2,...,xtk）,t=1,2,...,n（n>k+1）, They satisfy the relation ：

among , $\left ( \xi_{1}\cdots \xi _{n}\right )$ Unrelated are all related to $\xi$ Identically distributed random variables . In order to express the above formula with a matrix , Make $Y=X\beta +\xi$ .