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 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.

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 PENGARUH TINGKAT PENDIDIKAN, MOTIVASI, DAN KOMPENSASI TERHADAP KINERJA PEGAWAI DI BRI CABANG SEMARANG AHMAD YANI

2019 ◽  
Vol 11 (02) ◽  
pp. 31-47
Author(s):  
Sopi Sopi ◽  
Zumrotun Nafi'ah
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Industrial Revolution ◽  
Employee Performance ◽  
Science And Technology ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Improve Performance ◽  
Independent Variables ◽  
Life Education

Education, motivation and compensation are important things that can improve performance. This study aims to explain whether there is an influence of education, motivation and compensation on employee performance. So that through the results of this study it is expected to be a reference for leaders in managing the organization. In this study there are three independent variables namely education, motivation and compensation and one dependent variable is employee performance. At present it is in the era of industrial revolution 4.0, which is marked by; big data / giant data, internet of think, labor knowledge, and long life education. Since the beginning of the life of mankind to an infinite period, it is largely determined by the mastery of science and technology. Science and technology can not be separated from the progress of education level. Education is the base of all changes both individually, as well as countries. Employee performance is determined by the education that is owned, as high as education, the higher the performance and vice versa. The population in this study are BRI CAB employees, SEMARANG A-YANI, 60 people and all of them are sampled. The results of the analysis using SPSS 23 program statistical tools obtained multiple linear regression equation Y = 0.505 X1 + 0.175 X2 + 0.408 X3 The results of multiple linear regression equations show that there is a positive and significant influence between education on employee performance at BRI CAB. A YANI SEMARANG (t count test 6.314> t table 0.05), motivation towards employee performance at BRI CAB. A YANI SEMARANG (tcount 2,160> t table 0,05), and compensation for employee performance at BRI CAB. A YANI SEMARANG (t test 5.108> ttable 0.05). While together (simultaneously) the influence of education, motivation and compensation has an effect on and significant on the performance of employees at BRI CAB. A YANI SEMARANG (count = 44,692> ftabel = 0.05). The influence of the two research variables is very strong with a correlation value of 69.0% for employee performance at BRI CAB. A YANI SEMARANG is influenced by the motivation and compensation education of the remaining 31.0% of the employees' performance at BRI CAB. A YANI SEMARANG is influenced by other variables that affect employee performance.

scholarly journals Relationship between Cognitive Style and Habits of Mind

2019 ◽  
Vol 2 (1) ◽  
pp. 23
Author(s):  
Hayatun Nufus ◽  
Rezi Ariawan
Keyword(s):  
Linear Regression ◽  
Cognitive Style ◽  
Significance Test ◽  
Regression Equation ◽  
Coefficient Of Determination ◽  
Habits Of Mind ◽  
Linear Regression Equation ◽  
Research Subjects ◽  
Analysis Technique ◽  
The Relationship

This research is a correlational study that examines the relationship between cognitive style and habits of mind. The research subjects involved 4th semester students in the Department of Mathematics Education at the Faculty of Tarbiyah and Teacher Training of UIN Suska Riau which consisted of students with heterogeneous academic abilities. Cognitive style data was collected using the GEFT question instrument with test techniques. Habits of mind data were collected using a questionnaire instrument with a questionnaire distribution technique. The data analysis technique begins with the Pearson Product Moment correlation test which is continued with the significance test and the calculation of the magnitude of the relationship that occurs using the coefficient of determination. Because the data is positively correlated, it continues with determining the linear regression equation. The results showed that there was a significant weak correlation between cognitive style and habits of mind with a relationship score of 6% and a linear regression equation y '= 36.35 + 0.31 x.

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

Coronal Suture Pathology and Synostotic Progression in Rabbits with Congenital Craniosynostosis

1996 ◽  
Vol 33 (5) ◽  
pp. 369-378 ◽  
Author(s):  
Mark P. Mooney ◽  
Timothy D. Smith ◽  
Annie M. Burrows ◽  
Herbert L. Langdon ◽  
Cynthia E. Stone ◽  
...  
Keyword(s):  
Linear Regression ◽  
Inbred Strain ◽  
Rabbit Model ◽  
Regression Equation ◽  
Histologic Examination ◽  
Coronal Suture ◽  
Linear Regression Equation ◽  
Cross Sectional ◽  
High Tension ◽  
Single Focus

The purpose of the present study was to describe coronal suture pathology and cross sectional synostotic progression in an inbred strain of rabbits with congenital craniosynostosis. Calvaria from 102 perinatal rabbits (39 unaffected; 63 bilateral or unilateral synostosis) were collected at fetal days 21 (n = 12), 25 (n = 20), 27 (n = 22), 30 (term) (n = 32), and 3 days post-term (n = 16) for gross morphologic and histologic examination. Synostotic foci, the extent of relative bony bridging, and suture morphology were evaluated qualitatively and quantitatively. Of the 204 coronal sutures examined, 91 sutures were synostosed, and 113 were patent. All synostosed sutures showed similar foci by day 25, which originated as bony bridges in the middle of each suture on the ectocortic surface. Bony bridging width increased significantly (p < .001) from day 25 through 3 days post-term, and was best described by a linear regression equation. Osteogenic front areas of synostosed sutures were up to 2.5 times greater than patent sutures in term fetuses. Findings demonstrate that coronal suture synostosis in the congenital rabbit model (1) begins early during suture morphogenesis (before 25 days of gestation); (2) consistently radiates from a single focus corresponding to a normal interdigitating region (i.e., a high-tension environment); (3) varies in onset and rate as evidenced by low R2 value between age and extent of bony bridging; and (4) is the result of early hyperostosis of the osteogenic fronts and sutural agenesis. A number of possible pathogenetic mechanisms are discussed.

scholarly journals Comparison of Regression Equation and Friedewald’s Formula with Direct Measurement of Low-density Lipoprotein Cholesterol in Bangladeshi Population

2013 ◽  
Vol 6 (1) ◽  
pp. 143-152
Author(s):  
M. Saiedullah ◽  
N. Chowdhury ◽  
M.A.H. Khan ◽  
S. Hayat ◽  
S. Begum ◽  
...  
Keyword(s):  
Linear Regression ◽  
Low Density Lipoprotein ◽  
Density Lipoprotein ◽  
Regression Equation ◽  
Lipoprotein Cholesterol ◽  
Low Density ◽  
Regression Equations ◽  
Validation Group ◽  
Low Density Lipoprotein Cholesterol ◽  
Bangladeshi Population

Friedewald’s formula (FF) is the most widely used formula in clinical practice to calculate low-density lipoprotein cholesterol (LDLC) from total cholesterol (TC), triglyceride (TG) and high-density lipoprotein cholesterol (HDLC). But this formula frequently underestimates LDLC. The aim of this study was to derive a regression equation (RE) to abolish the underestimation and to compare the performance of RE and FF in Bangladeshi population. RE was derived from 531 lipid profiles (equation derivation group) for the calculation of LDLC by multiple linear regression analysis. The RE was then used to calculate LDLC in another 952 subjects (equation validation group). LDLC calculated by RE and FF were compared with measured LDLC by appropriate statistical analyses. In equation validation group, measured LDLC, LDLC calculated by RE and FF were 2.97±0.81, 2.91±0.80 and 2.72±0.93 mmol/L respectively. Precision (r) was 0.9525 for RE and 0.9193 for FF. Passing & Bablok linear regression equations against measured LDLC were y = 0.9792x + 0.007 for RE and y = 1.1412x – 0.6781 for FF. Accuracy within ±12% of measured LDLC was 79% and 57% for RE and FF, respectively. The derived RE is more accurate than FF for the calculation of LDLC in Bangladeshi population.  Keywords: Lipoprotein cholesterol; Friedewald’s formula; Bangladeshi population.  © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  doi: http://dx.doi.org/10.3329/jsr.v6i1.14864 J. Sci. Res. 6 (1), 143-152 (2014)

Sign in / Sign up

Export Citation Format

Share Document