Uncertain linear regression model and its application

Guo, Haiying; Wang, Qianqian; Gao, Zhichao

doi:10.1007/s10845-014-1022-4

Cited by 24 publications

(11 citation statements)

References 10 publications

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“…Finally, Taguchi design of experiments has been used combined mostly with linear or quadratic regression models 11 . The commonly used Multiple Regression Analyses are based on many different regression models [23][24][25][26][27][28] . Many efforts have been made in order to achieve a highly accurate multiple regression model 25,[27][28][29] .…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective Curing Cycle Optimization for Glass Fabric/Epoxy Composites Using Poisson Regression and Genetic Algorithm

et al. 2018

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In this study, a multi-parameter design of experiments, using Taguchi method, has been conducted in order to investigate the optimum curing conditions for glass fabric/epoxy laminated composites, followed by a statistical analysis and genetic algorithm optimization. Heating rate a, temperature T 1 and duration h 1 were treated as independent variables in a L 25 Taguchi orthogonal array addressing five levels each. Tensile load and flexural strength were examined as pre-selected quality objectives. The results of the analysis of variance performed showed that the significant parameters for both tensile and flexural strength were temperature and duration, at a 95% confidence level. The estimation of the curing parameters for optimum tensile and flexural performance was achieved with an error considerably lower than 1%. The Poisson regression analysis was introduced to achieve a highly accurate regression model, with R 2 greater than 97% for both optimization criteria. Finally, these two regression models were converted into a two-fold function for maximizing both criteria, and used as fitness function for a multi-objective optimization genetic algorithm.

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Section: Introductionmentioning

confidence: 99%

Multi-Objective Curing Cycle Optimization for Glass Fabric/Epoxy Composites Using Poisson Regression and Genetic Algorithm

et al. 2018

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“…It was assumed that the model receives as input crisp data and the output will be in terms of uncertain variables. Furthermore, an uncertain linear regression model was studied by Guo et al (2017) and it was applied to predict China's GDP. Apart from these, for situations in which the data gathered from experts' knowledge is of imprecise form, Guo et al (2011) came out with an uncertain regression model with an intrinsic error structure driven by uncertain canonical process.…”

Section: Introductionmentioning

confidence: 99%

A Regression Model Based on Uncertain Set

Li¹,

Wang²,

Sampath³

et al. 2017

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Traditional regression analysis is a method of statistical data analysis based on probability theory. Regression models play crucial roles in various branches of statistics including design of experiments, econometrics etc. In regression models, the dependent variable is assumed to be of stochastic nature where randomness enters via errors. Further, the independent variables are assumed to be of deterministic nature. The regression coefficients which explain the interdependency between the variables are assumed to be crisp quantities. Whenever, difficulty arises in expressing the values taken by the dependent variable in terms of crisp quantities, traditional regression models become irrelevant. This paper provides a framework for dealing with such situations on using the notion of uncertain sets of various forms. In this paper, a solution for this problem obtained via linear programming technique is introduced along with an illustrative example.

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“…To estimate the unknown parameters in the uncertainty distribution, Liu [6] proposed a principle of least squares in 2010. With the further study of uncertain statistics, Wang and Peng [15] puts forward the method of moments to estimate the unknown parameters, Guo, Wang and Gao [16] proposed an uncertain linear regression model in 2014. 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.…”

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A new uncertain linear regression model based on equation deformation

2021

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When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimate 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 examples show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation. Keywords equation deformation method • least squares estimate • linear regression model • uncertainty theory 1 IntroductionRegression analysis is an important branch of statistics. It is a kind of statistical method to study the relationship between response variables and explanatory variables. Regression analysis is also one of the most commonly used and

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Uncertain linear regression model and its application

Cited by 24 publications

References 10 publications

Multi-Objective Curing Cycle Optimization for Glass Fabric/Epoxy Composites Using Poisson Regression and Genetic Algorithm

Multi-Objective Curing Cycle Optimization for Glass Fabric/Epoxy Composites Using Poisson Regression and Genetic Algorithm

A Regression Model Based on Uncertain Set

A new uncertain linear regression model based on equation deformation

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