x_=(x 1+x2+x3+...+xn)/n

y_=(y 1+y2+y3+...+yn)/n？

Second, calculate the numerator and denominator respectively: (choose one of the two formulas)

Molecule = (x1y1+x2y2+x3y3+...+xnyn)-NX _ y _

Denominator = (x12+x2 2+x3 2+...+xn2)-n * x _ 2

Third: calculation? b？ : ? B= molecule? / ? denominator

The parameter b is estimated by the least square method, assuming that it obeys the normal distribution, and the partial derivatives of A and B are obtained respectively and equal to zero, then the solution of the equations is

Where is the sample variance of the observed value. Linear equation is called linear regression equation about, and the corresponding straight line is called regression straight line. By the way, it will be used in the future. Here is the sample variance of the observed value.

Find the average value of x and y first. x，Y

Then use the formula to solve: b = (x1y1+x2y2+... xnyn-nxy)/(x1+x2+... xn-nx).

Then substitute the average value of x and y into a=Y-bX.

Find a and substitute it into the general formula y=bx+a to get the linear regression equation.

(X is the average value, and Y is the average value of Yi)

Extended data

According to the type of relationship between independent variables and dependent variables, analysis can be divided into linear regression analysis and nonlinear regression analysis. If the regression analysis contains only one independent variable and one dependent variable, and the relationship between them can be approximately expressed by a straight line, this regression analysis is called unary linear regression analysis.

If regression analysis contains two or more independent variables, and there is a linear relationship between dependent variables and independent variables, it is called multivariate linear regression analysis.

References:

Baidu encyclopedia linear regression equation