Linear Regression Parameters Research Articles

Estimasi Parameter Regresi Linear Menggunakan Regresi Kuantil

Regression analysis is a statistical analysis method for estimating the relationship between dependent variables (Y) and one or more independent variables (X) . As the purpose of this study is to theoretically examine the quantile regression method in estimating linear regression parameters. In regression analysis usually the method used to estimate parameters is the least square method with assumptions that must be met that normal assumption, homoskedasticity, no autocorrelation and non multicollinearity. Basically the least square method is sensitive to the assumptions of deviations in the data, so that the estimations results will be lees good if the assumptions are not fulfilled. Therefore, to overcome the limitations of the least square method developed a quantile regression method for estimating linear regression parameters. Based on the result of research that has been done shows that the estimation of linear regression parameters using the quantile regression method is obtained by minimazing the absolute number of errors through the simplex algorithm.

Statistical filtering of useful concrete creep data from imperfect laboratory tests

The reporting and evaluation of creep tests of concrete is complicated by the fact that creep is significant even for the shortest observable load durations. Compared to the strain after 0.1 s load duration, the strain at 2 h duration is typically 53% greater. Most experimenters have for decades been unaware of this fact. Consequently, the reported creep curves require correction by a time shift, which ranges from 0 to 2 h. This further implies a vertical shift of entire creep curve, important for all times up to structure lifetime. To filter out the errors, it is argued that, within an initial period during which the advance of hydration is negligible, which is normally about 1 day, the initial basic creep must follow a power law of the time. Creep test data from the literature are used to prove it. Corrections by time and deformation shifts are determined by minimization of the sum of squared deviations of the power law from the creep test data. For a fixed exponent n and time shift s, the optimization is reduced to linear regressions of two kinds, depending on whether the data are given in terms of either the compliance function or the creep coefficient. For both, the linear regression parameters depend nonlinearly on the chosen values of n and s. To avoid nonlinear optimization, which need not converge to the correct result, a set of many discrete values of n and s within their realistic ranges is selected and the (n, s) combination minimizing the objective function is obtained by a search. Enforcing a power law form of the initial creep curve is found to lead to better data fits. The optimum exponent n for the entire database is around 0.3, applicable to the time period cca (10 s, 1 day). After that, the exponent transits to about 0.1, and prior to that it is about 0.08. After filtering out the errors, the corrected database will allow better calibration of the general creep prediction model such as B3 or B4.

Uncertainty Quantification in Robust Inference for Irregularly Spaced Spatial Data Using Block Bootstrap

This paper deals with uncertainty quantification (UQ) for a class of robust estimators of population parameters of a stationary, multivariate random field that is observed at a finite number of locations s1,…, sn, generated by a stochastic design. The class of robust estimators considered here is given by the so-called M-estimators that in particular include robust estimators of location, scale, linear regression parameters, as well as the maximum likelihood and pseudo maximum likelihood estimators, among others. Finding practically useful UQ measures, both in terms of standard errors of the point estimators as well as interval estimation for the parameters is a difficult problem due to presence of inhomogeneous dependence among irregularly spaced spatial observations. Exact and asymptotic variances of such estimators have a complicated form that depends on the autocovariance function of the random field, the spatial sampling density, and also on the relative rate of growth of the sample size versus the volume of the sampling region. Similar complex interactions of these factors are also present in the sampling distributions of these estimators which makes exact calibration of confidence intervals impractical. Here it is shown that a version of the spatial block bootstrap can be used to produce valid UQ measures, both in terms of estimation of the standard error as well as interval estimation. A key advantage of the proposed method is that it provides valid approximations in very general settings without requiring any explicit adjustments for spatial sampling structures and without requiring explicit estimation of the covariance function and of the spatial sampling density.

Estimating Detection Limits in Chromatography from Calibration Data: Ordinary Least Squares Regression vs. Weighted Least Squares

It is necessary to determine the limit of detection when validating any analytical method. For methods with a linear response, a simple and low labor-consuming procedure is to use the linear regression parameters obtained in the calibration to estimate the blank standard deviation from the residual standard deviation (sres), or the intercept standard deviation (sb0). In this study, multiple experimental calibrations are evaluated, applying both ordinary and weighted least squares. Moreover, the analyses of replicated blank matrices, spiked at 2–5 times the lowest calculated limit values with the two regression methods, are performed to obtain the standard deviation of the blank. The limits of detection obtained with ordinary least squares, weighted least squares, the signal-to-noise ratio, and replicate blank measurements are then compared. Ordinary least squares, which is the simplest and most commonly applied calibration regression methodology, always overestimate the values of the standard deviations at the lower levels of calibration ranges. As a result, the detection limits are up to one order of magnitude greater than those obtained with the other approaches studied, which all gave similar limits.

PEMODELAN PERTUMBUHAN EKONOMI DI PROVINSI BANTEN MENGGUNAKAN MIXED GEOGRAPHICALLY WEIGHTED REGRESSION

Economic growth can be measured by amount of Gross Regional Domestic Product (GRDP). Based on official news of statistics BPS, Economic growth in Banten region has increase up to 5.59%. It supported by several sector, there are agriculture, business, industry and from various fields. Mixed Geographically Weighted Regression (MGWR) methods have been developed based on linear regression by giving spatial effect or location (longitude and latitude), the resulting model from Economic growth in Banten will be local or different based on each location. MGWR mixed method between linear regression and GWR, parameters in linear regression are global and GWR parameters are local. The results more specific because economic growth in Banten region assessed by location.Keywords: Banten, Economic growth, MGWR.

Uncertain multivariable regression model

Uncertainty theory provides an alternative to model human belief degree without the scope of probability theory. Supposing that a response variable is an uncertain variable, the simple uncertain regression has proposed. In many cases, the number of response variables is more than one. This paper proposes uncertain multivariable linear regression model which has multiple response variables. Firstly, this paper discusses generalized least squares estimate of simple uncertain linear regression model. Moreover, this paper introduces a least squares method to estimate unknown parameters of uncertain multivariable linear regression.

Application of Chosen Methods of Robust Estimation: Baarda’s and Huber’s in Search for Outliers in the Real Estate Market Modeling

Abstract In the article, an attempt was made to compile a dataset which was devoid of outliers, on the example of Cracovian apartment market. Robust estimation was the tool which was used, but only its two methods were considered: Baarda’s and Huber’s. Huber’s method belongs to the so-called active methods which means that it allows to eliminate gross errors during the estimation of the parameters of multiple linear regression where a unit price is called a dependent variable or forecasted one. Baarda’s method is a passive method which is based on statistical tests and allows, after determining the parameters of a multiple linear regression model, to indicate the observations which may be burdened with gross errors. Thus both mentioned algorithms differ from each other substantially. In this publication, Baarda’s and Huber’s methods were compared in the context of their effectiveness for the analyzed dataset, and as tools of preparing the data for further analysis. The results showed that Baarda’s method is more appropriate for the analyzed dataset than Huber’s algorithm, but it does not mean that the active method is worse.

Study on the biomass and size spectra of bio-particles in vermifilter biofilms

In biological processes of sludge treatment, the sludge yield is closely related to the energy dissipation of entire microbial system. The vermifilter (VF), a novel biofilter, works efficiently due to the introduction of earthworms, which modifies the energy flow pathway through the variations of microbial size structure. For a deep insight into the sludge reduction in the VF, the biomass size spectrum (BSS) was employed to map the energy dissipation in the VF. The results indicated that bio-particles in the size class of [31, 63] μm were reduced most in the excess sludge after the VF treatment. In biofilms, bio-particles in the size class of [31, 63] μm varied most with the filter depth and earthworm density. Eight biomass and size spectra (BSS) were established for all beds of the VF and BF (the control of the VF, without earthworms). The normalized BSS were all linear both in the VF and BF, and their linear regression parameters, the slopes (k) and intercepts (b), varied with the filter depth and the earthworm density. The k and b of the VF were both significantly different from those of the BF. According to the k, the productivity level of largest bio-particles was higher in the VF than in the BF. According to the b, bio-particles at the bottom of size structure could be taken faster in the VF than in the BF. At last, some improvement approaches with some tries were proposed to enhance the sludge treatment capacity of the VF.

Constructing a Switching Regression with Unknown Switching Points

Switching regression is considered in the case where switching points are unknown. A general method is described to estimate switching points and parameters of linear regression with switching. Examples of its use are given.

Estimated Total Albumin in Fresh Urine Samples Based on Correlation Between the Roche Immunoturbidimetric and an In-House HPLC Method.

Background: Many studies have reported higher values of urinary albumin measured by high performance liquid chromatography (HPLC) in comparison with immunochemical methods. The aims of our study were the implementation of the HPLC method for albuminuria, testing the hypothesis about coeluting proteins, comparison of albuminuria assessed by HPLC and immunoturbidimetric (IT) methods in diabetic and non-diabetic patient samples. Methods: We compared albuminuria assessed by HPLC with albuminuria assessed by the IT method in fresh urine samples of 636 diabetics and 456 non-diabetics. We investigated relationships between albuminuria and blood glycated hemoglobin HbA1c. Results: We found significant differences between the parameters of linear regressions between albuminuria determined using HPLC and IT among patients with and without DM, and even between patients with DM type 1 and type 2. We confirmed the underestimation of albuminuria assessed by IT. We did not reveal any significant correlation between blood glycated hemoglobin and any of the parameters derived from albuminuria. Conclusions: We excluded non-specificity of the HPLC method. Despite of a little bit lower analytical sensitivity of the HPLC method in comparison with IT method the diagnostic sensitivity of HPLC method is higher, because it measures the total albuminuria (immunoreactive plus immunounreactive). We developed three formulas (for nondiabetics, for diabetics type 1 and diabetics type 2) for the estimation of the total albuminuria from IT values. We also confirmed that albuminuria and HbA1c are independent biomarkers.

Stable estimation of autoregressive model parameters with exogenous variables on the basis of the generalized least absolute deviation method

The generalized least absolute deviation method is an alternative to the least squares method. Together with an appropriate choice of the loss function, it ensures the stability and efficiency of estimating the coefficients of autoregressive models. This paper is devoted to the previously considered methods for finding the parameters of linear regression and autoregressive models without exogenous variables extend to the problem of estimating the parameters of autoregressive models with exogenous variables.

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.

Comparison and bias estimation of isotope dilution mass spectrometry and HPLC for cholesterol: methodological comparison of two internationally accepted reference methods listed in JCTLM

Objective To evaluate the consistency and comparability of two kinds of cholesterol reference methods listed in the Joint Committee for Traceability in Laboratory Medicine (JCTLM). Methods 52 fresh frozen sera with cholesterol concentrations among 3-10 mmol/L were tested by isotope dilution liquid chromatography tandem mass spectrometry (ID-LC/MS/MS) and high performance liquid chromatography (HPLC). The precision and accuracy of the two methods were calculated, and then a series of analysis were conducted including plotting scatter plots and deviation graphs, testing outliers, selecting the best fitting regression models and calculating the regression equations and parameters, and so on. The results of the two methods were statistically analyzed to estimate the expected deviation at the level of medical decision of cholesterol and the 95% confidence range. Results For HPLC method, the CV of instrument measurement was 0.22% (0-0.49%), the total CV of samples measurement was 0.36% (0.02%-0.83%), and the average bias of the reference materials was 0.37% (-1.31%-0.14%). For ID-LC/MS/MS method, the CV of instrument measurement was 0.50% (0-1.51%), the total CV of samples measurement was 0.55% (0.03%-1.17%), and the average bias of the reference materials was 0.24% (-0.53%-0.14%). No outliers were found from the scatter plots and the statistical analysis and the linear regression were fitted to analyze the results of the two methods. The linear regression parameters of two methods for 52 fresh frozen human sera were as follows: the slope was 0.989 5, the standard error of slope was 0.003 4, the intercept was 0.063 4 mmol/L, the standard error of intercept was 0.019 9 mmol/L, the standard error of Y-estimate was 0.034 8 mmol/L, and the correlation coefficient was 0.999 7. Compared with the ID-LC/MS/MS method, the absolute deviation of fresh sera by HPLC method was 0.000 mmol/L (-0.083-0.076 mmol/L), with a relative deviation of 0.07% (-1.22-1.24%). T-test results showed no statistically significant difference between the two methods. The expected deviations at the cholesterol medicine decision level were within the range 95% confidence range, and the expected deviations were far less than the allowable error. Conclusions The HPLC method of cholesterol has good consistency and comparability with ID/MS method using the primary measurement principle. Because of more advantages of HPLC method such as less cost, more simple, requirement, and better precision, HPLC method is expected to play an important role in the process of standardization and traceability of serum cholesterol.(Chin J Lab Med, 2017, 40: 780-786) Key words: Cholesterol; Indicator dilution techniques; Chromatography, liquid; Tandem Mass spectrometry; Chromatography, high pressure liquid; Isotopes

Continuous Wavelet Transform Analysis of Surface Electromyography for Muscle Fatigue Assessment on the Elbow Joint Motion

Studying muscle fatigue plays an important role in preventing the risks associated with musculoskeletal disorders. The effect of elbow-joint angle on time-frequency parameters during a repetitive motion provides valuable information in finding the most accurate position of the angle causing muscle fatigue. Therefore, the purpose of this study is to analyze the effect of muscle fatigue on the spectral and time-frequency domain parameters derived from electromyography (EMG) signals using the Continuous Wavelet Transform (CWT). Four male participants were recruited to perform a repetitive motion (flexion and extension movements) from a non-fatigue to fatigue condition. EMG signals were recorded from the biceps muscle. The recorded EMG signals were then analyzed offline using the complex Morlet wavelet. The time-frequency domain data were analyzed using the time-averaged wavelet spectrum (TAWS) and the Scale-Average Wavelet Power (SAWP) parameters. The spectral domain data were analyzed using the Instantaneous Mean Frequency (IMNF) and the Instantaneous Mean Power Spectrum (IMNP) parameters. The index of muscle fatigue was observed by calculating the increase of the IMNP and the decrease of the IMNF parameters. After performing a repetitive motion from non-fatigue to fatigue condition, the average of the IMNF value decreased by 15.69% and the average of the IMNP values increased by 84%, respectively. This study suggests that the reliable frequency band to detect muscle fatigue is 31.10-36.19Hz with linear regression parameters of 0.979mV^2Hz^(-1) and 0.0095mV^2Hz^(-1) for R^2 and slope, respectively.

СОЦИОЛОГИЧЕСКИЙ АНАЛИЗ ДИНАМИКИ КОЭФФИЦИЕНТА ДЕТОРОЖДЕНИЙ В АЛТАЙСКОМ КРАЕ НА ОСНОВЕ МЕТОДА НЕЧЕТКОЙ ЛИНЕЙНОЙ РЕГРЕССИИ

Цель. Построение математической модели динамики изменения рождаемости в Алтайском крае в 2000–2016 годах, анализ динамики изменения коэффициентов рождаемости для нескольких возрастных категорий женщин детородного возраста.Методы и методология проведения работы. Вспомогательным элементом анализа служит построение линейных математических моделей динамики коэффициентов рождаемости с помощью метода нечеткой линейной регрессии на основе нечетких чисел. Нечеткая линейная регрессия рассматривается как альтернатива стандартной статистической линейной регрессии в случае коротких временных рядов и неизвестного закона распределения. Определены параметры нечеткой линейной и стандартной статистической регрессий для временных рядов коэффициентов рождаемости, используя построенный алгоритм на языке системы MatLab. Метод нечеткой линейной регрессии пока не используется в социологических исследованиях.Результаты. Делается вывод о социально-демографических изменениях в обществе, о высокой эффективности демографической политики руководства региона и страны и применимости метода нечеткой линейной регрессии для социологического анализа.

Spawning phenology of the white bream (Blicca bjoerkna) in the "Dnieper-Orylskiy" Nature Reserve in relation to seasonal temperature dynamic

Spawning phenology of the white bream (Blicca bjoerkna) in the "Dnieper-Orylskiy" Nature Reserve in relation to seasonal temperature dynamic

Effect of intravenous gadoxetate disodium and flip angle on hepatic proton density fat fraction estimation with six-echo, gradient-recalled-echo, magnitude-based MR imaging at 3T.

The aim of the study was to determine in patients undergoing gadoxetate disodium (Gx)-enhanced MR exams whether proton density fat fraction (PDFF) estimation accuracy of magnitude-based multi-gradient-echo MRI (MRI-M) could be improved by using high flip angle (FA) on post-contrast images. Thirty-one adults with known or suspected hepatic steatosis undergoing 3T clinical Gx-enhanced liver MRI were enrolled prospectively. MR spectroscopy (MRS), the reference standard, was performed before Gx to measure MRS-PDFF. Low (10°)- and high (50°)-flip angle (FA) MRI-M sequences were acquired before and during the hepatobiliary phase after Gx administration; MRI-PDFF was estimated in the MRS-PDFF voxel location. Linear regression parameters (slope, intercept, average bias, R 2) were calculated for MRS-PDFF as a function of MRI-PDFF for each MRI-M sequence (pre-Gx low-FA, pre-Gx high-FA, post-Gx low-FA, post-Gx high-FA) for all patients and for patients with MRS-PDFF<10%. Regression parameters were compared (Bonferroni-adjusted bootstrap-based tests). Three of the four MRI-M sequences (pre-Gx low-FA, post-Gx low-FA, post-Gx high-FA) provided relatively unbiased PDFF estimates overall and in the low-PDFF range, with regression slopes close to 1 and intercepts and biases close to zero. Pre-Gx high-FA MRI overestimated PDFF in proportion to MRS-PDFF, with slopes of 0.72 (overall) and 0.63 (low-PDFF range). Based on regression bias closest to 0, the post-Gx high-FA sequence was the most accurate overall and in the low-PDFF range. This sequence provided statistically significant improvements in at least two regression parameters compared to every other sequence. In patients undergoing Gx-enhanced MR exams, PDFF estimation accuracy of MRI-M can be improved by using high-FA on post-contrast images.

METODE REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO UNTUK ESTIMASI BAYESIAN DALAM MODEL REGRESI LINEAR PER POTONGAN

The method used to estimate the parameters of piecewise linear regression is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems are proposed the Reversible Jump MCMC Algorithm. Reversible Jump MCMC Algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of piecewise linear regression models.Bayes estimator for the parameters of piecewise linear regression models obtained by the Markov chain.

On-tree maturity control of peach cultivars: Comparison between destructive and nondestructive harvest indices

Optimal harvest maturity is required for flavorful peach. The supply chain often errs on the side of immature fruit with subsequent consumer dissatisfaction. Maturity indices used to determine harvest date of peach include nondestructive assessments of size and background color, and destructive measurements of flesh color, firmness and soluble solids content (SSC) . More recently an index related to the absorbance of chlorophyll (IAD) can be nondestructively assessed with a DA-meter. This application is particularly useful in red-skinned cultivars in which background color changes from green to yellow are not perceptible to the naked eye. The objective and nondestructive IAD was compared with objective and destructive assessments of firmness and SSC, as indices to make harvest decisions on peach orchards. Seven peach and five nectarine cultivars [Prunus persica (L.) Batsch] were studied. Fruits were assessed with a DA-meter and the resulting IAD values were related to firmness and SSC in several consecutive samplings during the maturity period for each cultivar. Pooling all sampling dates for each cultivar, significant positive linear regressions were observed between IAD and firmness, with coefficients of determination 0.11<R2<0.65. However, in each cultivar the linear regression parameters between IAD and firmness are different and changed in sequential samplings required for maturity control and in successive harvests. No significant relationship was observed between IAD and SSC in any cultivar. In conclusion, the DA-meter cannot replace firmness and SSC measurements during on-tree maturity control, which remain essential for sensory quality management in the supply chain. .

Quarterly Estimates of Regional GDP in Poland Application of Statistical Inference of Functions of Parameters

The article presents the application of a linear regression model to the problem of space-time disaggregation of the GDP of the Polish economy. In the approach described, the structural parameters of linear regression are subject to estimation, where the annual GDP of voivodships (regions of Poland at NUTS 2 level) or the rate of its changes represent the explained variable, while the annual domestic GDP or the rate of its changes is the explanatory variable. The authors propose to estimate the quarterly GDP and its changes in individual regions as functions of regression parameters. The study presents the results of GDP estimates and its changes in individual regions. Alternative approaches were subject to evaluation in terms of the level of statistical uncertainty associated with the estimation and in terms of the level of spatial diversity of the estimated values.