Abstract
When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linear regression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer’s rule and matrix and propose the Cramer’s rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation.
Highlights
Regression analysis is an important branch of statistics
The equation deformation method can solve the unknown parameters of one-dimensional linear regression, can it solve the unknown parameters of multiple linear regression equation? Let’s go ahead and derive it
On the basis of the uncertainty theory, we proposed an equation deformation method to solve the unknown parameters of linear regression equation by using the expected value
Summary
Regression analysis is an important branch of statistics. It is a kind of statistical method to study the relationship between response variables and explanatory variables. Yao and Liu [8] puts forward a point estimation method for solving unknown parameters of uncertain regression equation through the principle of least square method in 2018, which is a method of processing imprecisely observed data. The least squares estimate can solve the parameters of linear uncertain regression equation, but it needs some advanced mathematics foundation. 3.1 Equation deformation method for one-dimensional linear regression model we always assumed that (xi , ỹi ), i = 1, 2, · · · , n be a set of imprecisely observed data, where xi , ỹi are independent uncertain variables with regular uncertainty distributions Φi , Ψi , i = 1, 2, · · · , n, respectively. Based on the uncertainty theory, we proposed an equation deformation method for solving unknown parameters.
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