What is the formula of linear regression equation?
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The formula of linear regression equation is shown in the following figure:
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.
Extended materials:
Linear regression equation is one of the statistical analysis methods to determine the interdependent quantitative relationship between two or more variables by regression analysis in mathematical statistics.
Linear regression models often adopt least square approximation fitting, but other fitting methods may also be adopted, such as minimizing "fitting defects" in other specifications (such as minimum absolute error regression) or minimizing the penalty of least square loss function in regression. On the contrary, the least square approximation can be used to fit these nonlinear models. Therefore, although the least square method and linear model are closely related, they cannot be equated.
References:
Baidu Encyclopedia-Linear Regression Equation
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The formula of linear regression equation is shown in the following figure:
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.
Extended data
Linear regression equation is one of the statistical analysis methods to determine the interdependent quantitative relationship between two or more variables by regression analysis in mathematical statistics. Linear regression is also the first type of regression analysis that has been strictly studied and widely used in practical applications. According to the number of independent variables, it can be divided into univariate linear regression analysis equation and multivariate linear regression analysis equation.
In statistics, linear regression equation is a regression analysis that uses least square function to model the relationship between one or more independent variables and dependent variables. The function is a linear combination of one or more model parameters called regression coefficients. The case with only one independent variable is called simple regression, and the case with multiple independent variables is called multiple regression. Conversely, this should be distinguished by multiple linear regression predicted by multiple related dependent variables rather than a single scalar variable. )
Refer to Baidu Encyclopedia-Linear Regression Equation
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Original publisher: Deputy Director Lu.
Linear regression equation Linear regression proves that the simplest correlation between formula variables is linear correlation. Assuming that there is a linear correlation between the random variable * and the variable, the points (,) obtained from the experimental data will be scattered around a straight line. Therefore, it can be considered that the type of regression function is linear, that is, the parameters and b are estimated by least square method, assuming that they obey normal distribution, and the partial derivatives of a and b are obtained respectively, which are equal to zero. Linear regression proves that the formula 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, which is the sample variance of the observed value. Solve with the formula: b= linear regression equation. The formula of linear regression equation A is a general formula. The linear regression equation y=bx+a crosses the fixed point (x pull, y pull).