scholarly journals A new uncertain linear regression model based on equation deformation

2021 ◽  
Author(s):  
Shuai Wang ◽  
Yufu Ning ◽  
Hongmei Shi
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Equation ◽  
Elementary Transformation ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Unknown Parameters ◽  
Deformation Method ◽  
Cramer’S Rule

Abstract 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.

A new uncertain linear regression model based on slope mean

2021 ◽  
pp. 1-10
Author(s):  
Shuai Wang ◽  
Yufu Ning ◽  
Hongmei Shi ◽  
Xiumei Chen
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Expected Value ◽  
Regression Equation ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Unknown Parameters ◽  
Average Value ◽  
Least Squares Estimate ◽  
Model Based

The least squares estimate can fully consider the given data and minimize the sum of squares of the residuals, and it can solve the linear regression equation of the imprecisely observed data effectively. Based on the least squares estimate and uncertainty theory, we first proposed the slope mean model, which is to calculate the slopes of expected value and each given data, and the average value of these slopes as the slope of the linear regression equation, substituted into the expected value coordinates, and we can get the linear regression equation. Then, we proposed the deviation slope mean model, which is a very good model and the focus of this paper. The idea of the deviation slope mean model is to calculate the slopes of each given data deviating from the regression equation, and take the average value of these slopes as the slope of the regression equation. Substituted into the expected value coordinate, we can get the linear regression equation. The deviation slope mean model can also be extended to multiple linear regression equation, we transform the established equations into matrix equation and use inverse matrix to solve unknown parameters. Finally, we put forward the hybrid model, which is a simplified model based on the combination of the least squares estimation and deviation slope mean model. To illustrate the efficiency of the proposed models, we provide numerical examples and solve the linear regression equations of the imprecisely observed data and the precisely observed data respectively. Through analysis and comparison, the deviation slope mean model has the best fitting effect. Part of the discussion, we are explained and summarized.

scholarly journals Prediction of Carcass Meat Percentage in Young Pigs Using Linear Regression Models and Artificial Neural Networks

2016 ◽  
Vol 16 (1) ◽  
pp. 275-286 ◽  
Author(s):  
Magdalena Szyndler-Nędza ◽  
Robert Eckert ◽  
Tadeusz Blicharski ◽  
Mirosław Tyra ◽  
Artur Prokowski
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Performance Testing ◽  
Regression Equations ◽  
Young Pigs ◽  
Marquardt Algorithm ◽  
Artificial Neural

Abstract One of the approaches to improving performance testing of pigs is to look for mathematical solutions to increase the accuracy of calculations. This is mainly done through improvement of linear regression equations based on current data on performance tested pigs in Poland. The advances in computer technology and the improvements in mathematical analysis have made it possible to use artificial neural networks (ANNs) for prediction of carcass meat percentage in young pigs. The aim of the study was to compare the potential for live estimation of carcass meat percentage in pigs using two computational methods: linear regression equations and ANNs. The experiment used 654 gilts of six breeds, which were subjected to performance testing and slaughter analysis at the Pig Performance Testing Station (SKURTCh). The collected data were used to train ANNs to estimate carcass meat percentage in young pigs. Training was performed using the Levenberg- Marquardt algorithm. Next, meatiness estimated by ANNs was compared with the results obtained using linear modelling. It is concluded that based on the fattening and slaughter performance test results of live pigs, artificial neural networks (SSN23) are significantly more accurate in estimating carcass meat percentage in young pigs compared to the three-variable linear regression model 1. The difference in meatiness estimation between SSN23 and the four-variable linear regression model 2 was statistically non-significant in most of the breeds except Duroc and Pietrain, where the meatiness of young animals was estimated more accurately by the linear regression model.

ARMA Model and Wavelet-Based ARMA Model Application

2011 ◽  
Vol 121-126 ◽  
pp. 1799-1803 ◽  
Author(s):  
Wei Wei ◽  
Hao Ma
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Arma Model ◽  
Optimal Model ◽  
Unknown Parameters ◽  
Model Application ◽  
Partially Linear ◽  
Modeling Theory ◽  
Partial Linear

This article discusses some of the linear regression model from the modeling theory, focusing on the modeling method of selecting the optimal model, choose the best bandwidth criteria. Then, given some of the partial linear regression model from the estimates and the partial residual nuclear smooth estimates, and estimate the model using the partial residual in the unknown parameters and to estimate the unknown function. Finally, the establishment of the Shanghai Index and Shenzhen Component Index Partially linear regression model.

Note on Cognitive Factors Related to Factor B of the 16 Pf Test

1971 ◽  
Vol 29 (3_suppl) ◽  
pp. 1075-1077 ◽  
Author(s):  
Joseph J. Fleishman ◽  
Bernard J. Fine
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Regression Equation ◽  
Cognitive Factors ◽  
Cognitive Tests ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Factor B ◽  
Enlisted Men ◽  
Selection Of

A selection of 21 tests from the French, Ekstrom, and Price battery of cognitive tests and the Cattell 16 PF Test were administered to 54 Army enlisted men. Product-moment correlations and multiple linear regression equations were computed between 16 PF Factor B scores (considered a measure of intelligence) and the 21 cognitive tests. The multiple linear regression equation indicated that 70% of the variance of Factor B scores could be accounted for by the selected cognitive tests.

scholarly journals THE RELIABILITY OF FORECASTS IN TRANSPORTATION

Transport ◽  
2002 ◽  
Vol 17 (6) ◽  
pp. 219-222
Author(s):  
Mindaugas Mazūra ◽  
Olga Fadina
Keyword(s):  
Linear Regression ◽  
Correlation Analysis ◽  
Mathematical Models ◽  
Nonlinear Regression ◽  
Empirical Data ◽  
Turnover Rate ◽  
Regression Equation ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Linear And Nonlinear

Major problems of forecasting the economic characteristics of transportation (i.e. the amount of freight and passengers carried, the turnover rate of freight and passengers, etc. in transportation as a whole and in particular areas using various transport facilities) are demonstrated. Methods for predicting the development of transportation based on multidimensional regression and correlation analysis and realizing mathematical models for choosing linear and nonlinear regression equations, more accurately approximating the empirical data, are presented. The research conducted has demonstrated that the most reliable forecasts may be made when the methods of choosing the proper non-linear regression equation described in Section 2 of the present paper are used.

scholarly journals Oat yield through panicle components and growth regulator

2017 ◽  
Vol 21 (4) ◽  
pp. 261-266
Author(s):  
Anderson Marolli ◽  
José A. G. da Silva ◽  
Rubia D. Mantai ◽  
Ana P. Brezolin ◽  
Maria E. Gzergorczick ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Grain Yield ◽  
Multiple Linear Regression ◽  
Growth Regulator ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
N Fertilizer ◽  
Regression Equations ◽  
Very High

ABSTRACT The growth regulator modifies the expression of lodging and panicle components in oat plants, with reflexes in yield. The objective of this study was to define the optimal dose of growth regulator in oat for a maximum lodging of 5%. In addition, this study aimed to identify potential variables of the panicle to compose the multiple linear regression model and the simulation of grain yield in conditions of use of the regulator under low, high and very high fertilization with nitrogen. The study was conducted in 2011, 2012 and 2013 in a randomized block design with four replicates in a 4 x 3 factorial scheme, for growth regulator doses (0, 200, 400 and 600 mL ha-1) and N-fertilizer doses (30, 90 and 150 kg ha-1), respectively. The growth regulator doses of 395, 450 and 560 mL ha-1 are efficient, with maximum oat lodging of 5%, under low, high and very high nitrogen fertilization, respectively. The grain weight per panicle and panicle harvest index are potential variables to compose the multiple linear regression model. Multiple linear regression equations are efficient in the simulation of oat grain yield under the conditions of use of growth regulator, regardless of the N-fertilizer dose.

scholarly journals RESEARCH ON GPS HEIGHT FITTING BASED ON LINEAR REGRESSION MODEL

2020 ◽  
Vol XLII-3/W10 ◽  
pp. 1189-1195
Author(s):  
K. Y. Yang ◽  
L. L. Liu ◽  
L. K. Huang
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Estimation Method ◽  
Regression Equation ◽  
Accuracy Evaluation ◽  
Gps Survey ◽  
Level Measurement ◽  
Fourth Level ◽  
Fitting Model

Abstract. This paper mainly expounds the parameter estimation method, the outlier diagnosis and the establishment of the optimal regression equation in the linear regression model theory, the analysis of the principle of the polynomial fitting model, the derivation of the algorithm process, and the research on the accuracy evaluation method.The GPS survey area is fitted and calculated. The fitting model is analyzed and compared in detail. The better parameter values and regression equation models of the planar region are estimated. The fitting accuracy meets the requirements of the fourth level measurement, which can be used in actual engineering. Replace the fourth level measurement in the application.

Physico-Chemical Analysis of Groundwater and Effect of Climatic Change in Angul-Talcher Area

2018 ◽  
Vol 6 (12) ◽  
pp. 26
Author(s):  
Aliva Bera ◽  
D.P. Satapathy
Keyword(s):  
Water Resources ◽  
Linear Regression ◽  
Regression Model ◽  
Climatic Change ◽  
Linear Regression Model ◽  
Ann Model ◽  
Quality Of Water ◽  
Physico Chemical ◽  
Simulation Based

In this paper, the linear regression model using ANN and the linear regression model using MS Excel were developed to estimate the physico-chemical concentrations in groundwater using pH, EC, TDS, TH, HCO3 as input parameters and Ca, Mg and K as output parameters. A comparison was made which indicated that ANN model had the better ability to estimate the physic-chemical concentrations in groundwater. An analytical survey along with simulation based tests for finding the climatic change and its effect on agriculture and water bodies in Angul-Talcher area is done. The various seasonal parameters such as pH, BOD, COD, TDS,TSS along with heavy elements like Pb, Cd, Zn, Cu, Fe, Mn concentration in water resources has been analyzed. For past 30 years rainfall data has been analyzed and water quality index values has been studied to find normal and abnormal quality of water resources and matlab based simulation has been done for performance analysis. All results has been analyzed and it is found that the condition is stable. 

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