Linear Regression Parameters Research Articles

Confidence ellipses for simple regression parameters with Quasi-associated random errors

The work presented in this paper introduces a novel methodology for constructing confidence regions for linear regression parameters using ellipses, particularly in cases where the random errors are quasi-associated. Linear regression is widely employed in statistical analysis to predict a dependent variable using one or more independent variables. Traditionally, it is assumed that random errors in regression models follow a normal distribution. However, this assumption may not hold in many practical applications where errors exhibit dependencies. Thus, this study focuses on quasi-associated random variables, which include both positively and negatively associated variables.We derive exponential inequalities that allow the construction of confidence ellipses for least squares estimates of model parameters. This approach is applied to a Keynesian consumption function, which models the relationship between consumption and national income. Using data on monthly per capita income in Africa over 12 years, we demonstrate the effectiveness of our method in estimating regression parameters when the random errors are quasi-associated. The findings show that this technique can improve the accuracy of statistical models used in fields such as economics and engineering, especially in cases where the traditional assumptions of regression analysis are not met.

Estimating the parameters of simple nested piecele-linear regression with a linear component

Subject of research: the problem of estimating the parameters of a simple nested piecewise linear regression with a linear component. Purpose of research: to apply an effective linear-Boolean programming apparatus to solve this problem. Methods and objects of research: the object of research is the minimization of approximation errors of simple nested piecewise linear regression with a linear component, methods – linear regression analysis and mathematical programming apparatus. Main results of research: an approach to determining parameter estimates for simple nested piecewise linear regression with a linear component is described using the least modulus method, which allows us to reduce this problem to a linear-Boolean programming problem. A numerical example has been solved.

Bayesian Regression Analysis using Median Rank Set Sampling

Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.

INTERVAL MODEL FOR ASSESSING THE PURITY OF NUCLEAR STRUCTURAL METALS BY MICROHARDNESS

The article considers the possibilities of evaluating the purity of Zr-1%Nb zirconium alloy samples – the main structural material of the thermal neutron reactors active zones with a water coolant – according to the microhardness of the metal. The correctness of the application of interval regression analysis is shown, if there is uncertainty, incompleteness of information, measurement errors in the experimental data for determining the oxygen content in metal samples and its microhardness. The method of estimating parameters of interval linear regression is presented.

Identification of Photovoltaic Array Model Parameters by Robust Linear Regression Methods

The aim of this paper is to propose an approach for photovoltaic (PV) sources modeling based on robust least squares linear regression (LSR) parameter identification method. On the basis of experimental data of solar irradiance, cell temperature and voltage and currents at maximum power points for a given PV array, correlation functions among the considered quantities are defined. By implementing these functions in a Matlab® Simulink model, accurate I-V characteristics for the considered array are obtained, managing only the solar irradiance. The method is validated comparing the computed and the experimental maximum power points (MPPs). Its effectiveness is proven to be better with respect of parameter identification methods based on discrete approaches and standard LSR method

Multiple Regression Model as Interpolation Through the Points of Weighted Means

A well-known property of the multiple linear regression is that its plane goes through the point of the mean values of all variables, and this feature can be used to find the model's intercept. This work shows that a regression by n predictors also passes via n additional points of the specific weighted mean values. Thus, the regression is uniquely defined by all these n+1 multidimensional points of means, and approximation of observations by the theoretical model collapses to the interpolation function going through the knots of the weighted means. This property is obtained from the normal system of equations which serves for finding the linear regression parameters in the ordinary least squares approach. The derived features can be applied in nonlinear modeling for adjusting the model parameters so that the fitted values would go through the same reference points of means, that can be useful in applied regression analysis. Numerical examples are discussed. The found properties reveal the essence of regression function as hyperplane going through special points of mean values, which makes regression models more transparent and useful for solving and interpretation in various applied statistical problems.

ВЫЧИСЛЕНИЕ ПАРАМЕТРОВ ПРОСТОЙ ФОРМЫ ВЛОЖЕННОЙ КУСОЧНО-ЛИНЕЙНОЙ РЕГРЕССИИ МЕТОДОМ СМЕШАННОГО ОЦЕНИВАНИЯ

The article describes an algorithm for calculating numerical estimates of the parameters of a simple nested piecewise linear regression using mixed estimation. The algorithm aims at simultaneous identifi cation using methods of least modules and antirobust estimation, both of which operate on certain subsamplings from the initial sampling. The approach comes to solving the problem of linear Boolean programming. A numerical problem has been solved.

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Variational estimation method is a deterministic approximation technique which involves Bayesian framework while giving a point estimate instead of the usual Bayesian interval estimation. The linear regression model, which has always been a popular model, can benefit from the implementation of variational estimation method. In this paper, the theoretical basis on why variational method can reduce overfitting in linear regression is reviewed. Based on the review, in theory, variational method is more robust to overfitting than MLE. This paper also performed a simulation study. The simulation is done in a manner such that the simulation represents the situation of predicting for new or hidden data. The simulation starts from generating random explanatory data and generates the appropriate response data based on linear regression equation. Then, the randomly generated data is used to estimate the linear regression parameters. The simulation is performed to compare the parameters estimation results from variational method with the method of MLE. The comparison is done using the estimation values and the squared differences between true parameters value and the estimates. Empirical findings show that both methods have relatively close estimate values. It can be seen as the simulation study concludes that both variational and ML yield rather close parameters estimates for simple linear regression case. The estimates closeness gets more obvious as the sample size grows. The study also found that Variational method has performs better in terms of parameters estimation in linear regression when the sample size is small or the data has large variance.

Implementing a New Scale Technique in the M-Estimation Method to Estimate Parameters of Multiple Linear Regression: Simulation Study

The goal of this study is to develop a new technique for estimating the parameters of a multiple linear regression by using M-estimation based on scale estimator to handle the influence of outlier values. In order to get new estimators, the root mean square error (RMSE) criterion is used to check the efficiency between the new technique and the classical method. The research showed that the new technique (M-estimation based on scale estimator) yields more accurate parameter estimates than the traditional approach (OLS) in all simulated cases.

Subgroup detection based on partially linear additive individualized model with missing data in response

Based on partially linear additive individualized model, a fusion-penalized inverse probability weighted least squares method is proposed to detect the subgroup for missing data in response. Firstly, the B-spline technique is used to approximate the unknown additive individualized functions and then an inverse probability weighted quadratic loss function is established with fusion penalty on the difference of subject-wise B-spline coefficients. Secondly, minimization of such quadratic loss function leads to the estimation of linear regression parameters and individualized B spline coefficients. With a proper tuning parameter, some differences in penalty term are shrunk into zero and thus the corresponding subjects will be clustered into the same subgroup. Thirdly, a clustering method is developed to automatically determine the subgroup membership for the subjects with missing data. Fourthly, large sample properties of resulting estimates are given under some regular conditions. Finally, numerical studies are presented to illustrate the performance of the proposed subgroup detection method.

Soybean and grapevine rusts accelerate the defoliation rates of host plants

AbstractGrapevine leaf rust (GLR) and soybean rust (SBR), caused by Neophysopella tropicalis and Phakopsora pachyrhizi, respectively, may lead to early defoliation of the host, depending on disease severity level. The rate of defoliation is an important parameter in mechanistic models aimed at simulating yield loss, but such knowledge is not available for these rust diseases. This work aimed to (i) relate the temporal dynamics of GLR and SBR to defoliation; and (ii) estimate the relative rates of defoliation and model their relationship with rust severities. Grapevine and soybean plants were inoculated in the field at increasing concentrations of urediniospore suspensions of the respective causal agent. Control plots of the vineyard and the soybean field were protected with sequential fungicide sprays to evaluate natural defoliation. Rust severity (proportion of area affected) of each leaf or leaflet was evaluated every three or four days on 1323 grapevine leaves and 655 soybean leaflets, respectively. The relative rates of defoliation were estimated as the slope parameters of linear regression of the Napierian logarithm of the number of alive leaves or leaflets over time. Defoliation rates in grapevine and soybean incremented logarithmically with the increase of rust severity. Defoliation rates on symptomless grapevine and soybean leaves were 0.018 and 0.05 day−1, respectively, while they averaged 0.033 day−1 on diseased grapevine leaves (rust severity between 5% and 12%), and 0.12 day−1 on diseased soybean leaflets (rust severity between 25% and 60%). Thus, a quantitative relationship was established between rust severity and defoliation on grapevine and soybean.

Using the Ellipsoid Method to Study Relationships in Medical Data

Deterioration of moral and psychological state on the background of a full–scale war is observed in many social groups. Timely detection of various types of pre–depressive states and appropriate therapy is a critically important task nowadays. In addition, an equally important task is to identify relationships between physical and psychological indicators of health. Establishing such regularities will allow detecting anxious states, avoiding direct profile testing of a patient. The article is devoted to construction of a mathematical apparatus for predicting psychological conclusions based on cardiological data. For this, a linear regression model and the ellipsoid method are used to determine its parameters with a criterion based on least moduli method (LMM), a feature selection procedure and a metric for assessing consistency of a data set. Material of the article is presented in 5 sections. Section 1 describes the ellipsoid method for finding parameters of linear regression with the least moduli method as a criterion in the power of p. Problem dimensions that can be successfully solved using the ellipsoid method on modern computers are indicated. The 2nd Section is devoted to Octave program emlmp, which implements the ellipsoid method, and the results of two computational experiments with its use. The obtained results demonstrate robustness of the obtained solutions when parameter p values are close to one. The 3rd Section describes mechanism of variable selection for the best prediction of psychological state of patients based on cardiological data. Variable selection was carried out using the Python Sequential Feature Selector procedure for predicting two psychological indicators – Beck's anxiety scale and psychologist's formalized conclusion. The 4th Section contains the results of a computational experiment using the emlmp program with LMM and least square method (LSM) criteria for predicting a psychologist’s formalized conclusion based on 84 selected patients and 22 parameters. Obtained solutions and forecasts for comparing criteria based on LMM and LSM are given. In the 5th Section, a metric for evaluation consistency of a data set is proposed, which allows to evaluate consistency for each parameter separately. A linear connection was found between 4 psychological parameters and the maximum accuracy of regression models with optimal number of parameters in specified models. Keywords: linear regression, convex function, ellipsoid method, least moduli method, data prediction, GNU Octave.

Application of artificial neural networks for characterisation of formability properties of sheet metals

Artificial neural network models were developed to estimate forming limit diagrams from tensile test results based on our own experiments and data from the literature for steel and aluminium sheet metals. Experimental data were obtained from tensile tests and Nakazima tests. The input parameters used in the models were yield strength, ultimate tensile strength, uniform elongation, elongation at fracture, anisotropy coefficient and hardening exponent or combinations of these. The forming limit curves were defined by the measured minor and major strains using seven standard test specimens. After training the artificial neural network, the difference between measured and predicted results was evaluated by linear regression parameters and by the absolute errors. For steel sheet data taken from the literature, the estimated outputs of ANN models were compared with the results of empirical formulae developed by different authors. It was found that there was a high correlation coefficient between predicted and measured values for models using neural networks, which gave better approximations than other linear and non-linear models.

Design of a linear regression model-based Internet exit anomaly detection method

Abstract Anomaly detection for Internet egress is to enhance the user experience of browsing the Internet. Firstly, the five functional modules of the system are described, and the pre-processing data module is used to extract the Internet topology data for Internet anomaly detection. The linear regression algorithm is also introduced in detail, including the definition of linear regression and its parameter estimation method and the optimization of linear regression parameters by variance and squared error. Finally, the performance evaluation of the anomaly detection system proposed in this paper is carried out to verify the system’s feasibility. From the performance evaluation, the detection rate of the system in this paper is 2.93 and 5.33 percentage points higher than that of SVM and SNN detection methods, respectively, and the false alarm rate is 2.85%. Regarding the impact of different packet lengths, the system in this paper is relatively stable when the packet length is 600, with an accuracy rate of 99.94% and a false alarm rate of only 1.93%. The above data show that the Internet egress anomaly detection system proposed in this paper can effectively detect the anomalies existing in the Internet egress and accurately grasp the data can timely deal with the abnormal nodes, thus improving the user browsing experience.

Training future psychologists to solve research tasks using regression analysis

Mathematical statistics methods are used in many fields of psychology and pedagogy as a tool necessary for processing research results of various nature.
 The skills of research activity are necessary for future bachelors studying in the specialty 053 Psychology, both when writing coursework and qualification papers, and in the future in professional activities or further studies in master's and postgraduate studies.
 The task of identifying the quantitative dependence between characteristics is most often found in psychological and pedagogical research.
 However, the question of the correctness, correctness of the use of certain methods of mathematical statistics in the processing of experimental data of psychological and pedagogical research, due to the specificity of the data itself, remains relevant, since the wrong choice of methods and criteria will contribute to the application of erroneous statistical procedures and the formulation of incorrect research conclusions. Therefore, a detailed study of methods, analysis and solution of research tasks is a necessary part of the process of training a competent psychologist.
 The training of bachelors in the specialty 053 Psychology at the Kharkiv State Academy of Physical Culture to solve research problems using regression analysis is carried out as part of the study of the discipline «Computer processing of experimental research data».
 The topic «Regression analysis» is studied in lectures and practical classes.
 The concepts of regression, regression model, forecasting are considered at the lecture. General characteristics of regression analysis methods and problems. Estimating the parameters of paired and multiple linear regression using the method of least squares.
 The article provides materials on the application of regression analysis, which can be used in the statistical analysis of a research experiment when performing coursework, qualification works for bachelors and masters, and dissertation works. The development of skills and abilities to solve applied research problems using the methods of mathematical statistics in practical classes is an integral part of the process of training future psychologists.

Influence of salinity on hydrogen isotope fractionation of n-alkanes in mangrove leaves and surface sediments: A comparison across various geomorphological settings

Increasing attention has recently been paid to hydrogen isotope ratios of mangrove lipids due to their potential for reconstructing past salinity and hydrology. This proxy is based on several observations that net 2H/1H fractionation, εn-alkane/water, between mangrove leaf waxes and surface water, increases with surface water salinity. However, the extent to which hydrogeomorphic conditions, on a regional scale, affect the hydrogen isotope fractionations of n-alkanes in mangrove trees and sediments is not yet understood. This study aimed to assess the robustness of negative εn-alkane/water – salinity for six mangrove species and adjacent surface sediments from the Zhanjiang mangrove across different hydrogeomorphic settings. The results indicated that a significant inverse relationship exists between εn-C31/water and εn-C33/water and salinity for all samples from the three fringe and basin/interior mangroves, with εn-C31/water decreasing by −2.57 ± 0.87 ‰ ppt−1 and εn-C33/water decreasing by −3.64 ± 1.14 ‰ ppt−1. These trends, as well as interspecific differences among mangrove species, could be attributed to biochemical changes in response to salt stress, such as using different proportions of amino acids and soluble carbohydrates as compatible solutes. In contrast, the relationship between sedimentary εn-alkane/water and salinity differed significantly across hydrogeomorphic conditions and land-use changes, possibly due to variations in hydrology and input of allochthonous organic matter. A comparison of fitted parameters of linear regressions among riverine, fringe, and interior mangroves suggests that the slop and intercept describing the linear relationship between sedimentary εC27–33/water of basin/interior mangroves and salinity are generally consistent with that of the corresponding mangrove trees. This suggests that the basin/interior mangroves and their sedimentary deposits may be better candidates for paleoenvironmental reconstruction using hydrogen isotope ratios of long-chain n-alkanes.

Plankton Community, Carbon-Nitrogen Ratios and Food Preference in Blind Feeding Phase of Litopenaeus vannamei

Litopenaeus vannamei is one of the largest commodities having a major impact on the global economy. Shrimp larvae have drastic changes in morphology and physiology which require extra maintenance. Feed management in early rearing using a blind feeding system which plankton as the main food. The relation between plankton and C/N needs to be investigated to optimize the growth of natural feed. The aims of the study were to analyze plankton community structure; the relationship between plankton to C/N and the environmental parameters; and determine the shrimp preferences of plankton. Data were collected at 3 points in 3 different ponds (PA, PB, PC) on day 8 and day 15 using a stratified sampling method with criteria (intensive system and blind feeding phase). Plankton density and C/N relationship were analyzed using Linear Regression, plankton and environmental parameters using Canonical Correspondence Analysis (CCA). Shrimp food preferences were analyzed descriptively in percentage. The results showed that diatoms and dinoflagellates dominated phytoplankton, and rotifers dominate zooplankton. C/N showed a positive correlation to protozoa, but a negative correlation to pennate diatoms and copepods. The most influential environmental factors for both phytoplankton and zooplankton density were temperature, C-organic, salinity, pH, alkalinity, and dissolved oxygen.

Road classification using 3D LiDAR sensor on vehicle

Road classification is essential in outdoor vehicle perception systems to evaluate driving scenarios. A light detection and ranging (LiDAR) sensor can provide accurate measurements of an environment composed of range, intensity, and angular information. This study proposes a weakly supervised learning algorithm for classifying road surface types based on laser measurements. The proposed algorithm first separates the laser points on the road surface based on the angular structure of the initial range measures obtained using 3D LiDAR in a noniterative manner. Then, a physical-data-driven model that represents the retroreflective nature of the different surface types is abstracted from the intensity measures and their factors. The linear regression parameters of the model are employed as feature descriptions of the road surface. The K-means method is used to classify the different road types. The learning process requires weak supervision at the training centroid stage and is robust to new road types. The classification performance was evaluated in different outdoor scenarios, and the classification accuracies exceeded 98%. The proposed algorithm outperforms similar existing methods, performs at the same frequency as that of LiDAR, and can be implemented in real time.

The Application of the Least Squares Method to Multicollinear Data

Regression analysis is an analysis that aims to determine whether there is a statistically dependent relationship between two variables, namely the predictor variable and the response variable. One of the methods for estimating multiple linear regression parameters is the Least Squares Method. Therefore, careful and meticulous analysis and selection of appropriate techniques are required to overcome the multicollinearity problem and ensure accurate and meaningful regression analysis results. Descriptive statistical table of response variables and predictor variables, where the average results are rounded. The regression equation using the OLS method is as follows: Y ̂=2,037+0.302X_1+0.206X_2+0.172X_3+0.342X_4. Therefore, it is important to use special techniques such as regularization or PCA to overcome the multicollinearity problem in the data before applying the least squares method. Thus, we can obtain more stable and accurate regression coefficient estimates and a more reliable linear regression model.

IoT-Based Reinforcement Learning Using Probabilistic Model for Determining Extensive Exploration through Computational Intelligence for Next-Generation Techniques.

Computing intelligence is built on several learning and optimization techniques. Incorporating cutting-edge learning techniques to balance the interaction between exploitation and exploration is therefore an inspiring field, especially when it is combined with IoT. The reinforcement learning techniques created in recent years have largely focused on incorporating deep learning technology to improve the generalization skills of the algorithm while ignoring the issue of detecting and taking full advantage of the dilemma. To increase the effectiveness of exploration, a deep reinforcement algorithm based on computational intelligence is proposed in this study, using intelligent sensors and the Bayesian approach. In addition, the technique for computing the posterior distribution of parameters in Bayesian linear regression is expanded to nonlinear models such as artificial neural networks. The Bayesian Bootstrap Deep Q-Network (BBDQN) algorithm is created by combining the bootstrapped DQN with the recommended computing technique. Finally, tests in two scenarios demonstrate that, when faced with severe exploration problems, BBDQN outperforms DQN and bootstrapped DQN in terms of exploration efficiency.