Statistical Analysis of Fuzzy Linear Regression Model Based on Centroid Method

This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.

Determination of Compositions and Stability Constants of Holmium and Yttrium Complexes with Tribromoarsenazo by Linear Regression Method

According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.

Determination of Composition and Stability Constant of Praseodymium(Pr^(3+))Complex with Tribromoarsenazo(TBA)by Dual-Series Linear Regression Method

A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).

Analysis of the Invariance and Generalizability of Multiple Linear Regression Model Results Obtained from Maslach Burnout Scale through Jackknife Method

The purpose of this study was to examine the burnout levels of research assistants in Ondokuz Mayis University and to examine the results of multiple linear regression model based on the results obtained from Maslach Burnout Scale with Jackknife Method in terms of validity and generalizability. To do this, a questionnaire was given to 11 research assistants working at Ondokuz Mayis University and the burnout scores of this questionnaire were taken as the dependent variable of the multiple linear regression model. The variable of burnout was explained with the variables of age, weekly hours of classes taught, monthly average credit card debt, numbers of published articles and reports, gender, marital status, number of children and the departments of the research assistants. Dummy variables were assigned to the variables of gender, marital status, number of children and the departments of the research assistants and thus, they were made quantitative. The significance of the model as a result of multiple linear regressions was examined through backward elimination method. After this, for the five explanatory variables which influenced the variable of burnout, standardized model coefficients and coefficients of determination, and 95% confidence intervals of these values were estimated through Jackknife Method and the generalizability of the parameter estimation results of these variables on population was researched.

Development of a Quantitative Prediction Support System Using the Linear Regression Method

The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.

Imputing missing values using cumulative linear regression

The concept of missing data is important to apply statistical methods on the dataset. Statisticians and researchers may end up to an inaccurate illation about the data if the missing data are not handled properly. Of late, Python and R provide diverse packages for handling missing data. In this study, an imputation algorithm, cumulative linear regression, is proposed. The proposed algorithm depends on the linear regression technique. It differs from the existing methods, in that it cumulates the imputed variables;those variables will be incorporated in the linear regression equation to filling in the missing values in the next incomplete variable. The author performed a comparative study of the proposed method and those packages. The performance was measured in terms of imputation time, root-mean-square error, mean absolute error, and coefficient of determination (R^2). On analysing on five datasets with different missing values generated from different mechanisms, it was observed that the performances vary depending on the size, missing percentage, and the missingness mechanism. The results showed that the performance of the proposed method is slightly better.

Linear Regression Analysis for Symbolic Interval Data

In the network technology era, the collected data are growing more and more complex, and become larger than before. In this article, we focus on estimates of the linear regression parameters for symbolic interval data. We propose two approaches to estimate regression parameters for symbolic interval data under two different data models and compare our proposed approaches with the existing methods via simulations. Finally, we analyze two real datasets with the proposed methods for illustrations.

Prediction of Link Failure in MANET-IoT Using Fuzzy Linear Regression

A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes guides a link failure.This link failure creates more data packet drops that can cause a long time delay.As a result,measuring accurate link failure time is the key factor in the MANET.This paper presents a Fuzzy Linear Regression Method to measure Link Failure(FLRLF)and provide an optimal route in the MANET-Internet of Things(IoT).This work aims to predict link failure and improve routing efficiency in MANET.The Fuzzy Linear Regression Method(FLRM)measures the long lifespan link based on the link failure.The mobile node group is built by the Received Signal Strength(RSS).The Hill Climbing(HC)method selects the Group Leader(GL)based on node mobility,node degree and node energy.Additionally,it uses a Data Gathering node forward the infor-mation from GL to the sink node through multiple GL.The GL is identified by linking lifespan and energy using the Particle Swarm Optimization(PSO)algo-rithm.The simulation results demonstrate that the FLRLF approach increases the GL lifespan and minimizes the link failure time in the MANET.

Robust Linear Regression Models:Use of a Stable Distribution for the Response Data

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Data-driven Power Flow Method Based on Exact Linear Regression Equations

Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and loads become intermittent and much more uncertain,and the topology also changes more frequently,which may result in significant state shifts and further make NRPF or FDPF difficult to converge.To address this problem,we propose a data-driven PF(DDPF)method based on historical/simulated data that includes an offline learning stage and an online computing stage.In the offline learning stage,a learning model is constructed based on the proposed exact linear regression equations,and then the proposed learning model is solved by the ridge regression(RR)method to suppress the effect of data collinearity.In online computing stage,the nonlinear iterative calculation is not needed.Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.

Ecological impact assessment method of highways in Tibetan Plateau:A Case study of Gonghe-Yushu Expressway

In recent years,the ecological environment along highways in Tibetan Plateau has been severely affected due to the rapid construction of highways.In order to solve the problems of multiple indicators and inconsistent criteria in the ecological impact assessment of highways,and to scientifically screen assessment indicators,the paper proposes a multi-round indicator screening method,which combines literature analysis,expert rating,and statistical analysis.Based on this screening method,normalized difference vegetation index,land surface temperature,elevation,and normalized difference soil index are screened out.Combined with multiple linear regression,an ecological impact assessment model is established and applied to ecological impact assessment of Gonghe-Yushu Expressway.The results show that the expressway construction is the first driving force for the deterioration of the ecological environment along the roadside,and its interference range on the desert grassland ecosystem is greater than that on the agroforestry system.The ecological environment within 150 m on both sides of the expressway should be protected.

EFFECTS OF A CLOUD FILTERING METHOD FOR FENGYUN-3C MICROWAVE HUMIDITY AND TEMPERATURE SOUNDER MEASUREMENTS OVER OCEAN ON RETRIEVALS OF TEMPERATURE AND HUMIDITY

For Microwave Humidity and Temperature sounder(MWHTS) measurements over the ocean, a cloud filtering method is presented to filter out cloud-and precipitation-affected observations by analyzing the sensitivity of the simulated brightness temperatures of MWHTS to cloud liquid water, and using the root mean square error(RMSE)between observation and simulation in clear sky as a reference standard. The atmospheric temperature and humidity profiles are retrieved using MWHTS measurements with and without filtering by multiple linear regression(MLR),artificial neural networks(ANN) and one-dimensional variational(1DVAR) retrieval methods, respectively, and the effects of the filtering method on the retrieval accuracies are analyzed. The numerical results show that the filtering method can improve the retrieval accuracies of the MLR and the 1DVAR retrieval methods, but have little influence on that of the ANN. In addition, the dependencies of the retrieval methods upon the testing samples of brightness temperature are studied, and the results show that the 1DVAR retrieval method has great stability due to that the testing samples have great impact on the retrieval accuracies of the MLR and the ANN, but have little impact on that of the 1DVAR.

滑坡在役防治工程缺陷分类和健康评价方法

为快速评估常见在役滑坡防治工程的运行状态并采取科学有效的维护手段,笔者在三峡库区、汶川震区和川东地区实地调查了160余处抗滑挡墙、抗滑桩和格构锚固工程,获取了上述三类滑坡防治工程表征损伤的第一手资料,总结分析了其变形破坏模式及特征,定义了滑坡防治工程缺陷的概念,定性地提出了缺陷程度分级标准。在统计分析滑坡防治工程损伤特征基础上,选取了墙身滑移距离、墙身沉陷位移、墙身倾斜程度、墙身裂缝密度、桩体倾斜程度、桩体剪切程度、桩体裂缝密度、格梁最大裂缝宽度、单根格构梁裂缝率和受损格构变形区比例等10个控制指标作为其缺陷分类指标,结合多元线性回归法,对单体工程结构进行综合量化评分评定,进而建立了半定量的滑坡防治工程健康评价方法。

基于一元线性回归模型的供水网络中水表读数虚高问题研究

为了定量研究供水网络中总表漏水程度和分表读数虚高程度,根据水量平衡分析法的原理,结合大数据分析技术,建立了一元线性回归方程,回归常数代表总表漏水量程度,回归系数代表分表读数虚高程度。通过针对2021年某高校供水管网的实证研究表明,总表日均漏水量为15.5958吨,分表读数虚高率为1.07%。该方法对供水管网漏损率的精准评估等问题的解决提供了新的思路和方法。

一种基于线性回归的雷达航迹跟踪算法

针对雷达航迹跟踪过程中精度与实时性难兼顾的问题,提出了一种基于线性回归的雷达航迹跟踪算法。线性回归作为一种简单有效的建模方法,可用于预测与推断,与雷达航迹跟踪模型一致。工程实践数据表明,该算法对目标运行轨迹拟合度高,跟踪精度高,实用性强。

基于二次指数平滑和多元线性回归的宁波市港口物流需求预测分析

随着经济全球化的发展,港口作为物流发展的重要环节,港口物流需求已经成为港口资源配置规划和进出口贸易的重要依据。为对宁波市港口物流需求进行科学合理的预测,文章借助SPSS等数据分析软件,使用二次指数平滑和多元线性回归分别对其物流需求进行预测,通过对比两种预测方法的精度,最后发现,二次指数平滑法的预测精确度要优于多元线性回归法,并通过二次指数平滑法预测宁波市未来五年的港口物流需求量。

基于最小二乘法线性回归的火炮身管寿命预测

为直观地判断火炮身管寿命,提出一种基于最小二乘法线性回归的预测方法。根据靶场身管参数试验数据分析火炮身管内径、药室长、弯曲度随射弹数增加的变化规律;利用最小二乘法线性回归建立火炮身管磨损量与射弹数的关系式;对某型火炮身管寿命进行预测。结果表明:该方法能够较为准确地预测出火炮身管寿命且算法简单,便于推广使用,可为火炮射击、退役报废等提供重要参考。

基于有效积温法改进婺源油菜花期预报模型

基于1995-2022年婺源油菜观测资料和气象资料,分别以油菜现蕾、抽薹为起点,利用多元线性回归方法对基于有效积温法的油菜花期预报模型进行改进,建立了基于有效积温法模拟预报的普花期与实际日期误差天数的气象因子模型,以提高婺源花期预报模型的精确度。利用模拟精度、均方根误差(RMSE)和相对误差(RE)对改进前后的模拟效果进行对比和评价。结果表明:(1)以0℃为有效积温阈值,以平均有效积温值为有效积温指标对油菜普花期进行初步预报,随普花期临近预报精度提高。(2)相关分析表明,气温是影响油菜普花期的主要气象因子,以2月中旬平均气温、最高气温和最低气温为自变量,以基于有效积温法模拟预报的普花期与实际日期的误差天数为因变量,建立的气象因子改进模型具有统计学意义且通过显著性检验。(3)分别对改进前后的预报模型进行检验和评价,两种方法建立的预报模型效果均较好,气象因子改进模型的模拟结果更优,提高了油菜普花期预报的准确度。以抽薹为起点的气象因子改进预报模型在油菜普花期预报方面精确度最高,可有效应用于油菜普花期预报。