Journal articles: 'Regression coefficient function'

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Khammar, Amir Hamzeh, Mohsen Arefi, and Mohammad Ghasem Akbari. "Quantile Fuzzy Varying Coefficient Regression based on kernel function." Applied Soft Computing 107 (August 2021): 107313. http://dx.doi.org/10.1016/j.asoc.2021.107313.

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Li, Meng, and Hong-Wei Sun. "Asymptotic analysis of quantile regression learning based on coefficient dependent regularization." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 04 (July 2015): 1550018. http://dx.doi.org/10.1142/s0219691315500186.

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In this paper, we consider conditional quantile regression learning algorithms based on the pinball loss with data dependent hypothesis space and ℓ2-regularizer. Functions in this hypothesis space are linear combination of basis functions generated by a kernel function and sample data. The only conditions imposed on the kernel function are the continuity and boundedness which are pretty weak. Our main goal is to study the consistency of this regularized quantile regression learning. By concentration inequality with ℓ2-empirical covering numbers and operator decomposition techniques, satisfied error bounds and convergence rates are explicitly derived.

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Cao, MingXiang, and DaoJiang He. "Linearly admissible estimators on linear functions of regression coefficient under balanced loss function." Communications in Statistics - Theory and Methods 48, no. 11 (March 14, 2019): 2700–2706. http://dx.doi.org/10.1080/03610926.2018.1472788.

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Bae, M. S., and S. R. Ha. "Nonlinear regression approach to evaluate nutrient delivery coefficient." Water Science and Technology 53, no. 2 (January 1, 2006): 271–79. http://dx.doi.org/10.2166/wst.2006.061.

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Implementation of the Korean Total Maximum Daily Load Act calls for new tools to quantify nutrient losses from diffuse sources at a river basin district scale. In this study, it was elucidated that the nonlinear regression model (NRM) reduces the uncertainty of the boundary conditions of the water quality model. The NRM was proposed to analyse the delivery coefficients of surface waters and retention coefficients of pollutants. Delivery coefficient of pollution load was considered as a function of two variables: the watershed form ratio, Sf, which is a measurable geomorphologic variable and the retention coefficient, ϕ, which is an empirical constant representing the basin-wide retarding capacity of pollutant wash-off. This model was applied on the Geum River, one of the major basins in South Korea. The QUAL2E was used to simulate stream water quality using NRM. In this paper, we elucidate the possibility to use a nonlinear regression model for delivery and retention of nutrients in a drainage basin characterized as both data-rich and data-poor, and the magnitude of the nutrient loads and sources has been uncertain for a long time. Keywords Delivery coefficient; diffuse pollution; pollution load runoff; retention coefficient

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Wei, Laisheng. "EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL." Acta Mathematica Scientia 16 (1996): 22–33. http://dx.doi.org/10.1016/s0252-9602(17)30814-7.

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Guo, Luo, Zhihai Ma, and Lianjun Zhang. "Comparison of bandwidth selection in application of geographically weighted regression: a case study." Canadian Journal of Forest Research 38, no. 9 (September 2008): 2526–34. http://dx.doi.org/10.1139/x08-091.

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A forest plot with a clustered spatial pattern of tree locations was used to investigate the impacts of different kernel functions (fixed vs. adaptive) and different sizes of bandwidth on model fitting, model performance, and spatial characteristics of the geographically weighted regression (GWR) coefficient estimates and model residuals. Our results indicated that (i) the GWR models with smaller bandwidths fit the data better, yielded smaller model residuals across tree sizes, significantly reduced spatial autocorrelation and heterogeneity for model residuals, and generated better spatial patterns for model residuals; however, smaller bandwidth sizes produced a high level of coefficient variability; (ii) the GWR models based on the fixed spatial kernel function produced smoother spatial distributions for the model coefficients than those based on the adaptive kernel function; and (iii) the GWR cross-validation or Akaike’s information criterion (AIC) optimization process may not produce an “optimal” bandwidth for model fitting and performance. It was evident that the selection of spatial kernel function and bandwidth has a strong impact on the descriptive and predictive power of GWR models.

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Cao, Mingxiang, Xingzhong Xu, and Daojiang He. "Linearly admissible estimators of stochastic regression coefficient under balanced loss function." Statistics 48, no. 2 (February 6, 2013): 359–66. http://dx.doi.org/10.1080/02331888.2013.766794.

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Karunamuni, R. J., and L. Wei. "On empirical Bayes estimation of multivariate regression coefficient." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–18. http://dx.doi.org/10.1155/ijmms/2006/51695.

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We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression modelY=Xβ+ε, whereYis anm-vector of observations,Xis a knownm×kmatrix,βis an unknownk-vector, andεis anm-vector of unobservable random variables. The problem is squared error loss estimation ofβbased on some “previous” dataY1,…,Ynas well as the “current” data vectorYwhenβis distributed according to some unknown distributionG, whereYisatisfiesYi=Xβi+εi,i=1,…,n. We construct a new empirical Bayes estimator ofβwhenεi∼N(0,σ2Im),i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.

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DU, JIANG, ZHONGZHAN ZHANG, and ZHIMENG SUN. "VARIABLE SELECTION FOR PARTIALLY LINEAR VARYING COEFFICIENT QUANTILE REGRESSION MODEL." International Journal of Biomathematics 06, no. 03 (May 2013): 1350015. http://dx.doi.org/10.1142/s1793524513500150.

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In this paper, we propose a variable selection procedure for partially linear varying coefficient model under quantile loss function with adaptive Lasso penalty. The functional coefficients are estimated by B-spline approximations. The proposed procedure simultaneously selects significant variables and estimates unknown parameters. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, we show that the proposed procedure can be as efficient as the Oracle estimator, and derive the optimal convergence rate of the functional coefficients. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed variable selection procedure.

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Hu, Guikai, Qingguo Li, and Ping Peng. "Minimax estimator of regression coefficient in normal distribution under balanced loss function." Linear Algebra and its Applications 436, no. 5 (March 2012): 1228–37. http://dx.doi.org/10.1016/j.laa.2011.08.013.

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Ishola, Taiwo Abass, Olatayo Timothy Olabisi, and Adesanya Kazeem Kehinde. "Parameter Estimation of Fractional Trigonometric Polynomial Regression Model." JOURNAL OF UNIVERSITY OF BABYLON for pure and applied sciences 27, no. 1 (May 13, 2019): 519–26. http://dx.doi.org/10.29196/jubpas.v27i1.2208.

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Trigonometric Polynomial Regression is a form of non-linear regression in which the relationship between the outcome variable and risk variable is Fractional modeled as 1/nth degree polynomial regression by combining the function of cos(nx) and sin(nx) on the value of natural numbers. The model was used to analyze the relationship between three continuous and periodic variables. Coefficients of the model were estimated using the Maximum Likelihood Estimate (MLE) method. From the results, the model obtained indicated that an increased in body mass index will increase the level of blood pressure while age may or may not have an influence on the blood pressure level. The values of the Coefficient of variation showed the variation in the dependent variable was well explained by the independent variables and the value of the adjusted coefficient of determination showed the model had a good fit with a high level of predictive power.

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Shi, Xiaoxia, and Peter C. B. Phillips. "NONLINEAR COINTEGRATING REGRESSION UNDER WEAK IDENTIFICATION." Econometric Theory 28, no. 3 (November 25, 2011): 509–47. http://dx.doi.org/10.1017/s0266466611000648.

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An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite-sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.

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Hu, Guikai, and Ping Peng. "All admissible linear estimators of a regression coefficient under a balanced loss function." Journal of Multivariate Analysis 102, no. 8 (September 2011): 1217–24. http://dx.doi.org/10.1016/j.jmva.2011.04.003.

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Hu, Guikai, Qingguo Li, and Shenghua Yu. "Linear minimax prediction of finite population regression coefficient under a balanced loss function." Communications in Statistics - Theory and Methods 45, no. 24 (February 2, 2016): 7197–209. http://dx.doi.org/10.1080/03610926.2014.978945.

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Acal, Christian, Manuel Escabias, Ana M. Aguilera, and Mariano J. Valderrama. "COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression." Mathematics 9, no. 11 (May 28, 2021): 1237. http://dx.doi.org/10.3390/math9111237.

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The aim of this paper is the imputation of missing data of COVID-19 hospitalized and intensive care curves in several Spanish regions. Taking into account that the curves of cases, deceases and recovered people are completely observed, a function-on-function regression model is proposed to estimate the missing values of the functional responses associated with hospitalized and intensive care curves. The estimation of the functional coefficient model in terms of principal components’ regression with the completely observed data provides a prediction equation for the imputation of the unobserved data for the response. An application with data from the first wave of COVID-19 in Spain is developed after properly homogenizing, registering and smoothing the data in a common interval so that the observed curves become comparable. Finally, Canonical Correlation Analysis is performed on the functional principal components to interpret the relationship between hospital occupancy rate and illness response variables.

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Park, Geon Yong. "Diffusion coefficient calculated by complementary error function for the sublimation diffusion of disperse dye." Journal of Engineered Fibers and Fabrics 14 (January 2019): 155892501986659. http://dx.doi.org/10.1177/1558925019866592.

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In order to find a simple and reliable method for the calculation of the diffusion coefficient, the correlation equation of concentration and distance in the form of complementary error function was derived from solving an ordinary differential equation of the diffusion equation. A disperse dye in paste was treated at 170°C–190°C for 3–4 h for the sublimation diffusion into polyethylene terephthalate using a film roll method. Quadratic regression analysis on the profile of dye concentration–distance was used to determine the surface concentration. The diffusion coefficient of each layer was calculated by obtaining the variable value of the complementary error function from the ratio of the mean dye concentration of each layer to the surface concentration. From linear regression analysis on the Arrhenius plot of the logarithm of the diffusion coefficient versus the reciprocal of absolute temperature, the correlation coefficient for the diffusion of 3 h was 0.9978 and that of 4 h was 0.9991. Thus, it was expected that the diffusion coefficients determined by the equation of complementary error function adopted in this experiment were reliable. The activation energy of diffusion for 3 h was 30.5 kcal mol−1 and that for 4 h was 27.4 kcal mol−1.

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Qi, Qing Lan, and Shao Xiong Zhang. "Nonlinear Regression Analysis for Programming and Engineering Application." Advanced Materials Research 846-847 (November 2013): 1080–83. http://dx.doi.org/10.4028/www.scientific.net/amr.846-847.1080.

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Aiming at the calculating the flow of cutthroat flume in Hydraulic Engineering, the test data is processed through the nonlinear regression analysis program which is based on the principle of least square method. With 33 equations of various functions including linear, power function curve and exponential curve to be selected as the mathematical model, the regression analysis is taken through 33 equations. Comparing the regression coefficient from analysis, the optimal mathematical model is selected as the empirical formula, which has great significance in guiding the practical engineering.

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Tomović, Slavko. "Forecasting of a technical product state using the regression function and the variation coefficient." Vojnotehnicki glasnik 45, no. 1 (1997): 85–94. http://dx.doi.org/10.5937/vojtehg9701085t.

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Kumar, M., N. K. Tiwari, and S. Ranjan. "Kernel function based regression approaches for estimating the oxygen transfer performance of plunging hollow jet aerator." Journal of Achievements in Materials and Manufacturing Engineering 2, no. 95 (August 1, 2019): 74–84. http://dx.doi.org/10.5604/01.3001.0013.7917.

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Purpose: To evaluate the capability of various kernels employed with support vector regression (SVR) and Gaussian process regression (GPR) techniques in estimating the volumetric oxygen transfer coefficient of plunging hollow jets. Design/methodology/approach: In this study, a data set of 81 observations is acquired from laboratory experiments of hollow jets plunging on the surface of water in the tank. The jet variables: jet velocity, jet thickness, jet length, and water depth are varied accordingly and the values of volumetric oxygen transfer coefficient is computed. An empirical relationship expressing the oxygenation performance of plunging hollow jet aerator in terms of jet variables is formulated using multiple nonlinear regression. The performance of this nonlinear relationship is compared with various kernel function based SVR and GPR models. Models developed with the training data set (51 observations) are checked on testing data set (24 observations) for performance comparison. Sensitivity analysis is carried out to examine the influence of jet variables in effecting the oxygen transfer capabilities of plunging hollow jet aerator. Findings: The overall comparison of kernels yielded good estimation performance of Radial Basis Function kernel (RBF) and Pearson VII Function kernel (PUK) using the SVR technique which is followed by nonlinear regression, and other kernel function based regression models. Research limitations/implications: The results of the study pertaining to the performance of kernels are based on the current experimental conditions and the estimation potential of the regression models may fluctuate beyond the selection of current data range due to datadependant learning of the soft computing models. Practical implications: Volumetric oxygen transfer coefficient of plunging hollow jets can be predicted precisely using SVR model by employing RBF as kernel function as compared to empirical correlation and other kernel function based regression models. Originality/value: The comparative analysis of kernel functions is conducted in this study. In previous studies, the predictive modelling approaches are implemented in simulating the aeration properties of cylindrical solid jets only, while this paper simulates the volumetric oxygen transfer coefficient of diverging hollow jets with the jet variables by utilizing polynomial, normalized polynomial, PUK, and RBF kernels in SVR and GPR.

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Clark, Robert G., and Margo Barr. "A blended link approach to relative risk regression." Statistical Methods in Medical Research 27, no. 11 (March 13, 2017): 3325–39. http://dx.doi.org/10.1177/0962280217698174.

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A binary health outcome may be regressed on covariates using a log link, rather than more typical link functions such as the logit. This allows the exponentiated regression coefficient for each covariate to be interpreted as a relative risk conditional on the remaining covariates. Relative risks are simpler to interpret than the odds ratios which arise with a logit link. There are practical and conceptual challenges in log-link binary regression, mainly due to the requirement that probabilities are less than or equal to 1. Viable probabilities are now usually achieved by the imposition of a constraint on the parameter space, but the log link function is still more work to apply in practice. We propose instead a new smooth link function which is equal to the log up to a cutoff and a linearly scaled logit function above the cutoff. The new approach is conceptually clearer, simpler to implement and generally less biased, and it retains the relative risk interpretation for all but the highest risk individuals. Alternative binary regressions are compared using a simulation study and a diabetic retinopathy dataset.

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Zhang, Shangfeng, Jiani Zhu, Qi Fang, Yaoxin Liu, Siwa Xu, and Ming-Hsueh Tsai. "Solving the Time-Varying Cobb-Douglas Production Function Using a Varying-Coefficient Quantile Regression Model." Journal of Advanced Computational Intelligence and Intelligent Informatics 23, no. 5 (September 20, 2019): 831–37. http://dx.doi.org/10.20965/jaciii.2019.p0831.

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The output elasticity estimated by the traditional Cobb-Douglas production function is a fixed constant that describes developed countries with relative stable factor shares well. While the fixed constant fails to describe developing countries with changing factor shares during economic transitional periods, such as China. In this paper, we construct a time-varying elasticity production function model and extend the Cobb-Douglas production function to a time-varying elasticity Cobb-Douglas production function. The semi-parametric varying-coefficient quantile model, together with the local polynomial and the two-phase methods, is used for the estimation of the time-varying elasticity of the capital coefficient and the labor force. Empirical research on Chinese economic growth shows that the time-varying elasticity of capital is declining and the time-varying elasticity of the labor force is increasing gradually.

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Wu, Yunfeng, Xin Luo, Fang Zheng, Shanshan Yang, Suxian Cai, and Sin Chun Ng. "Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression." Mathematical Problems in Engineering 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/913897.

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This paper presents a novel adaptive linear and normalized combination (ALNC) method that can be used to combine the component radial basis function networks (RBFNs) to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error) and the better fidelity (characterized by normalized correlation coefficient) of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.

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A. Rady, El Houssainy, and Ahmed Amin El-Sheikh. "The Distribution of the Coefficient of determination in Linear Regression Model: A Review." Journal of University of Shanghai for Science and Technology 23, no. 09 (September 6, 2021): 126–27. http://dx.doi.org/10.51201/jusst/21/08481.

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In this article, we review the different studies about the coefficient of determination in linear regression models and make a highlight about the inferences and the density function of the coefficient of determination which presented under the most common assumption when the error terms obey the normal distributions, and also analyzed the certain effects of departures from normality of the error term

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Phan, Binh Thi Thanh, and Manh Van Luong. "Load forecasting by regression model based on fuzzy rules." Science and Technology Development Journal 17, no. 1 (March 31, 2014): 30–36. http://dx.doi.org/10.32508/stdj.v17i1.1267.

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The forecasting models by traditional regression function have the crisp functions such as Y=f(x1, x2 ,….,xn) or logY=f(logx1, logx2 ,….,logxn). Here f has the linear form and xi are the factors such as GDP, temperature, industrial output, population… But these models are able to be used only when the linear correlation existed (expressed by the correlation coefficient). This paper introduced the regression model based on the fuzzy Takagi-Sugeno rules. These rules are built by using the subtractive clustering. The model is used for the general case, even when there are no the crisp function f. Examining shows that the good results are obtained in the case of traditional correlation such as linear or linear by logarithm. The results are also satisfactory for the case of unknown correlation. The electricity consumption forecasting due to the temperature factor for one substation of HochiMinh city was carried out.

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Yu, Yan Hua, Li Xia Song, and Kun Lun Zhang. "Fuzzy C-Regression Models." Applied Mechanics and Materials 278-280 (January 2013): 1323–26. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.1323.

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Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

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Zhang, Qi, Jun Hai Ma, and Yan Wang. "Study on Forecasting of Gold Price Based on Varying-Coefficient Regression Model." Key Engineering Materials 467-469 (February 2011): 1398–403. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.1398.

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U.S. dollar index, oil prices, silver prices, DOW index, OECD leading index and the CRB index are selected and varying-coefficient regression model which has dynamic response to the various variables influence is applied to predict the gold price and improve the prediction accuracy in this paper. In addition, the weighted least squares is adopted as an estimation of the parameters, corrects the traditional least squares method defect which assumes the sample data weights equal points to the prediction, making sample weights larger closer with prediction points. In the choice of weighting function, the paper uses cross validation to gain smoothing parameter. In the last, we predicted the 12 months gold prices from January 2010 December 2010 applies varying-coefficient regression model.

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Bakoyannis, Giorgos, Ying Zhang, and Constantin T. Yiannoutsos. "Semiparametric regression and risk prediction with competing risks data under missing cause of failure." Lifetime Data Analysis 26, no. 4 (January 25, 2020): 659–84. http://dx.doi.org/10.1007/s10985-020-09494-1.

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Abstract The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.

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Zhou, Yang, and Di-Rong Chen. "Optimal rate for prediction when predictor and response are functions." Analysis and Applications 18, no. 04 (June 6, 2020): 697–714. http://dx.doi.org/10.1142/s0219530520500037.

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In functional data analysis, linear prediction problems have been widely studied based on the functional linear regression model. However, restrictive condition is needed to ensure the existence of the coefficient function. In this paper, a general linear prediction model is considered on the framework of reproducing kernel Hilbert space, which includes both the functional linear regression model and the point impact model. We show that from the point view of prediction, this general model works as well even the coefficient function does not exist. Moreover, under mild conditions, the minimax optimal rate of convergence is established for the prediction under the integrated mean squared prediction error. In particular, the rate reduces to the existing result when the coefficient function exists.

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Namba, Akio, and Kazuhiro Ohtani. "Risk performance of a pre-test ridge regression estimator under the LINEX loss function when each individual regression coefficient is estimated." Journal of Statistical Computation and Simulation 80, no. 3 (March 2010): 255–62. http://dx.doi.org/10.1080/00949650802605739.

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Korohoda, Przemysław, and Joanna Grabska-Chrząstowska. "Logistic Regression Realized with Artificial Neuron and Estimation Formulas." Image Processing & Communications 17, no. 4 (December 1, 2012): 265–74. http://dx.doi.org/10.2478/v10248-012-0055-6.

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Abstract In the paper an experiment is described, that was designed and conducted to verify hypothesis that artificial neuron with sigmoidal activation function can efficiently solve the task of logistic regression in the case when the explaining variable is one-dimensional, and the explained variable is binomial. Computations were performed with 12 sets of statistical parameters, assumed for the generation of 65356 sets of data in each case. Comparative analysis of the obtained results with use of the reference values for the regression coefficients indicated that the investigated neuron can satisfactory perform the task, with efficiency similar to that obtained with classical logistic regression algorithm, when the teaching sets of input data, corresponding with output values 0 and 1, do not allow for simple separation. Moreover, it has been discovered that the simple formulas estimating the statistical distributions parameters from the samples, offer statistically superior assessment of the regression coefficient parameters.

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Parsian, Monireh, Somayeh Kamali Igoli, and Khadijehi Abolmaali Alhossein. "The Effect of Family Function on Social Adjustment and Self-Regulation of High School Students." International Journal of Psychological Studies 12, no. 3 (August 31, 2020): 50. http://dx.doi.org/10.5539/ijps.v12n3p50.

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This paper examines the family function on social adjustment and self-regulation of high school students. The research method is descriptive-correlational. The statistical population consists of all second-high school girl students in the city of Ghaemshahr. 110 female students were randomly selected as the research sample size. The results showed that there is a significant difference between family function and social adjustment and self-regulation of high school students at the error level of less than 0.01 and confidence level of 0.99. Based on regression analysis, family function variables (with a coefficient of 0.46) and social adjustment (with a coefficient of 0.44) had the highest coefficient of standardized regression, respectively, on the dependent variable of student self-regulation.

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Masha, Luke, James Stone, Danielle Stone, Jun Zhang, and Luo Sheng. "Pulmonary Catherization Data Correlate Poorly with Renal Function in Heart Failure." Cardiorenal Medicine 8, no. 3 (2018): 183–91. http://dx.doi.org/10.1159/000487203.

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Background: The mechanisms of renal dysfunction in heart failure are poorly understood. We chose to explore the relationship of cardiac filling pressures and cardiac index (CI) in relation to renal dysfunction in advanced heart failure. Objectives: To determine the relationship between renal function and cardiac filling pressures using the United Network of Organ Sharing (UNOS) pulmonary artery catherization registry. Methods: Patients over the age of 18 years who were listed for single-organ heart transplantation were included. Exclusion criteria included a history of mechanical circulatory support, previous transplantation, any use of renal replacement therapy, prior history of malignancy, and cardiac surgery, amongst others. Correlations between serum creatinine (SCr) and CI, pulmonary capillary wedge pressure (PCWP), pulmonary artery systolic pressure (PASP), and pulmonary artery diastolic pressure (PADP) were assessed by Pearson correlation coefficients and simple linear regression coefficients. Results: Pearson correlation coefficients between SCr and PCWP, PASP, and PADP were near zero with values of 0.1, 0.07, and 0.08, respectively (p < 0.0001). A weak negative correlation coefficient between SCr and CI was found (correlation coefficient, –0.045, p = 0.027). In a subgroup of young patients unlikely to have noncardiac etiologies, no significant correlations between these values were identified. Conclusion: These findings suggest that, as assessed by pulmonary artery catherization, none of the factors – PCWP, PASP, PADP, or CI – play a prominent role in cardiorenal syndromes.

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Stratton, H. H., P. J. Feustel, and J. C. Newell. "Regression of calculated variables in the presence of shared measurement error." Journal of Applied Physiology 62, no. 5 (May 1, 1987): 2083–93. http://dx.doi.org/10.1152/jappl.1987.62.5.2083.

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To test hypotheses regarding relations between meaningful parameters, it is often necessary to calculate these parameters from other directly measured variables. For example, the relationship between O2 consumption and O2 delivery may be of interest, although these may be computed from measurements of cardiac output and blood O2 contents. If a measured variable is used in the calculation of two derived parameters, error in the measurement will couple the calculated parameters and introduce a bias, which can lead to incorrect conclusions. This paper presents a method of correcting for this bias in the linear regression coefficient and the Pearson correlation coefficient when calculations involve the nonlinear and linear combination of the measured variables. The general solution is obtained when the first two terms of a Taylor series expansion of the function can be used to represent the function, as in the case of multiplication. A significance test for the hypothesis that the regression coefficient is equal to zero is also presented. Physiological examples are provided demonstrating this technique, and the correction methods are also applied in simulations to verify the adequacy of the technique and to test for the magnitude of the coupling effect. In two previous studies of O2 consumption and delivery, the effect of coupled error is shown to be small when the range of O2 deliveries studied is large, and measurement errors are of reasonable size.

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Clarke, Allan J., and Stephen Van Gorder. "On Fitting a Straight Line to Data when the “Noise” in Both Variables Is Unknown*." Journal of Atmospheric and Oceanic Technology 30, no. 1 (January 1, 2013): 151–58. http://dx.doi.org/10.1175/jtech-d-12-00067.1.

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Abstract In meteorology and oceanography, and other fields, it is often necessary to fit a straight line to some points and estimate its slope. If both variables corresponding to the points are noisy, the slope as estimated by the ordinary least squares regression coefficient is biased low; that is, for a large enough sample, it always underestimates the true regression coefficient between the variables. In the common situation when the relative size of the noise in the variables is unknown, an appropriate regression coefficient is plus or minus the ratio of the standard deviations of the variables, the sign being determined by the sign of the correlation coefficient. For this case of unknown noise, the authors here obtain the probability density function (pdf) for the true regression coefficient divided by the appropriate regression coefficient just mentioned. For the case when the number of data is very large, a simple analytical expression for this pdf is obtained; for a finite number of data points the relevant pdfs are obtained numerically. The pdfs enable the authors to provide tables for confidence intervals for the true regression coefficient. Using these tables, the end result of this analysis is a simple practical way to estimate the true regression coefficient between two variables given their standard deviations, the sample correlation, and the number of independent data.

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Li, Gang, Jan Zrimec, Boyang Ji, Jun Geng, Johan Larsbrink, Aleksej Zelezniak, Jens Nielsen, and Martin KM Engqvist. "Performance of Regression Models as a Function of Experiment Noise." Bioinformatics and Biology Insights 15 (January 2021): 117793222110203. http://dx.doi.org/10.1177/11779322211020315.

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Background: A challenge in developing machine learning regression models is that it is difficult to know whether maximal performance has been reached on the test dataset, or whether further model improvement is possible. In biology, this problem is particularly pronounced as sample labels (response variables) are typically obtained through experiments and therefore have experiment noise associated with them. Such label noise puts a fundamental limit to the metrics of performance attainable by regression models on the test dataset. Results: We address this challenge by deriving an expected upper bound for the coefficient of determination ( R2) for regression models when tested on the holdout dataset. This upper bound depends only on the noise associated with the response variable in a dataset as well as its variance. The upper bound estimate was validated via Monte Carlo simulations and then used as a tool to bootstrap performance of regression models trained on biological datasets, including protein sequence data, transcriptomic data, and genomic data. Conclusions: The new method for estimating upper bounds for model performance on test data should aid researchers in developing ML regression models that reach their maximum potential. Although we study biological datasets in this work, the new upper bound estimates will hold true for regression models from any research field or application area where response variables have associated noise.

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Hillier, Grant. "EXACT PROPERTIES OF THE CONDITIONAL LIKELIHOOD RATIO TEST IN AN IV REGRESSION MODEL." Econometric Theory 25, no. 4 (August 2009): 915–57. http://dx.doi.org/10.1017/s026646660809035x.

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For a simplified structural equation/IV regression model with one right-side endogenous variable, we derive the exact conditional distribution function of Moreira's (2003) conditional likelihood ratio (CLR) test statistic. This is used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of this function are provided for practical use. The analogous functions are also obtained for the case of testing more than one right-side endogenous coefficient, but in this case for a similar test motivated by, but not generally the same as, the likelihood ratio test. Next, the exact power functions of the CLR test, the Anderson-Rubin test, and the Lagrange multiplier test suggested by Kleibergen (2002) are derived and studied. The CLR test is shown to clearly conditionally dominate the other two tests for virtually all parameter configurations, but no test considered is either inadmissable or uniformly superior to the other two. The unconditional distribution function of the likelihood ratio test statistic is also derived using the same argument. This shows that both exactly, and under Staiger/Stock weak-instrument asymptotics, the test based on the usual asymptotic critical value is always oversized and can be very seriously so when the number of instruments is large.

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Shi, Liping, Qinghe Zhang, Shihui Zhang, Chao Yi, and Guangxu Liu. "Electromagnetic Response Prediction of Reflectarray Antenna Elements Based on Support Vector Regression." Applied Computational Electromagnetics Society 35, no. 12 (February 15, 2021): 1519–24. http://dx.doi.org/10.47037/2020.aces.j.351210.

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In this letter, support vector regression (SVR) is used to predict the electromagnetic (EM) response of a complex shaped reflectarray (RA) unit cell. The calculation of the scattering coefficients of passive RA elements with periodic intervals is firstly transformed into a regression estimation problem, and then an analysis model is established by SVR to quickly predict the EM response of the unit cells. To this end, the full-wave (FW) simulation software is used to obtain a set of random samples of the scattering coefficient matrix of the RA antenna unit cell, which is used for SVR training. Under the same conditions, the radial basis function network (RBFN) is also used to predict the EM response of the elements, and the comparison results show the effectiveness and accuracy of the proposed method.

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Ugwuanyi, HK, FO Okafor, and JC Ezeokonkwo. "ASSESSMENT OF TRAFFIC FLOW ON ENUGU HIGHWAYS USING SPEED DENSITY REGRESSION COEFFICIENT." Nigerian Journal of Technology 36, no. 3 (June 30, 2017): 749–57. http://dx.doi.org/10.4314/njt.v36i3.13.

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In an attempt to estimate the operating speeds and volume of traffic on highway lanes as a function of predicted demands, speed-density models were estimated using data from highway sites. Speed, flow and volume are the most important elements of the traffic flow. In this study, the speed-density regression models are compared using five highways in relation to their correlation coefficient based on the daily traffic flow data obtained from the roads. The traffic flow data were collected by hourly traffic count on each road. The coefficient of correlation (R) proved to have the best fit with a higher confidence and less variation for a two-lane highway than a one-lane highway. The space-mean speed (u) and density (k) relationship for the two-lane highways are; u, Â and uÂ whereas the space-mean speed (u) and density (k) relationship for the one-lane highways are; u = Â respectively. This research provides practical application for speed estimation, construction, maintenance and optimization of the highways using the speed-density models which will enhance traffic monitoring, traffic control management, traffic forecasting and model calibration.Â http://dx.doi.org/10.4314/njt.v36i3.13

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LUCENA, Leandro Ricardo Rodrigues de, Juliana De Souza PEREIRA, and Maurício Luiz de Mello Vieira LEITE. "Growth curve Nopalea cochenillifera in fractionation function of cladodes using power regression model." REVISTA BRASILEIRA DE BIOMETRIA 36, no. 3 (September 26, 2018): 578. http://dx.doi.org/10.28951/rbb.v36i3.238.

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In this work we evaluate the growth length of bud of Nopalea cochenillifera using five different forms of crops through power regression model. The adjusted models showed very similar estimates of lengths observed independent using of planting method. The power regression models showed coefficient of determination of model high 99.65% (treatment 1), 99.82% (treatment 2), 99.26% (treatment 3), 99.93% (treatment 4) and 99.34% (treatment 5). The power regression model proved effective to model the growth length of Nopalea cochenillifera of bud can generate strategies and plans for future plantings, as well useful information as: appropriate crop management, increased plant growth period and pest control.

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Katipamula, S., T. A. Reddy, and D. E. Claridge. "Multivariate Regression Modeling." Journal of Solar Energy Engineering 120, no. 3 (August 1, 1998): 177–84. http://dx.doi.org/10.1115/1.2888067.

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An empirical or regression modeling approach is simple to develop and easy to use compared to detailed hourly simulations of energy use in commercial buildings. Therefore, regression models developed from measured energy data are becoming an increasingly popular method for determining retrofit savings or identifying operational and maintenance (O&M) problems. Because energy consumption in large commercial buildings is a complex function of climatic conditions, building characteristics, building usage, system characteristics and type of heating, ventilation, and air conditioning (HVAC) equipment used, a multiple linear regression (MLR) model provides better accuracy than a single-variable model for modeling energy consumption. Also, when hourly monitored data are available, an issue which arises is what time resolution to adopt for regression models to be most accurate. This paper addresses both these topics. This paper reviews the literature on MLR models of building energy use, describes the methodology to develop MLR models, and highlights the usefulness of MLR models as baseline models and in detecting deviations in energy consumption resulting from major operational changes. The paper first develops the functional basis of cooling energy use for two commonly used HVAC systems: dual-duct constant volume (DDCV) and dual-duct variable air volume (DDVAV). Using these functional forms, the cooling energy consumption in five large commercial buildings located in central Texas were modeled at monthly, daily, hourly, and hour-of-day (HOD) time scales. Compared to the single-variable model (two-parameter model with outdoor dry-bulb as the only variable), MLR models showed a decrease in coefficient of variation (CV) between 10 percent to 60 percent, with an average decrease of about 33 percent, thus clearly indicating the superiority of MLR models. Although the models at the monthly time scale had higher coefficient of determination (R2) and lower CV than daily, hourly, and HOD models, the daily and HOD models proved more accurate at predicting cooling energy use.

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Lu, Wei, James G. Ramsay, and James M. Bailey. "Reliability of Pharmacodynamic Analysis by Logistic Regression." Anesthesiology 99, no. 6 (December 1, 2003): 1255–62. http://dx.doi.org/10.1097/00000542-200312000-00005.

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Background Many pharmacologic studies record data as binary, yes-or-no, variables with analysis using logistic regression. In a previous study, it was shown that estimates of C50, the drug concentration associated with a 50% probability of drug effect, were unbiased, whereas estimates of gamma, the term describing the steepness of the concentration-effect relationship, were biased when sparse data were naively pooled for analysis. In this study, it was determined whether mixed-effects analysis improved the accuracy of parameter estimation. Methods Pharmacodynamic studies with binary, yes-or-no, responses were simulated and analyzed with NONMEM. The bias and coefficient of variation of C50 and gamma estimates were determined as a function of numbers of patients in the simulated study, the number of simulated data points per patient, and the "true" value of gamma. In addition, 100 sparse binary human data sets were generated from an evaluation of midazolam for postoperative sedation of adult patients undergoing cardiac surgery by random selection of a single data point (sedation score vs. midazolam plasma concentration) from each of the 30 patients in the study. C50 and gamma were estimated for each of these data sets by using NONMEM and were compared with the estimates from the complete data set of 656 observations. Results Estimates of C50 were unbiased, even for sparse data (one data point per patient) with coefficients of variation of 30-50%. Estimates of gamma were highly biased for sparse data for all values of gamma greater than 1, and the value of gamma was overestimated. Unbiased estimation of gamma required 10 data points per patient. The coefficient of variation of gamma estimates was greater than that of the C50 estimates. Clinical data for sedation with midazolam confirmed the simulation results, showing an overestimate of gamma with sparse data. Conclusion Although accurate estimations of C50 from sparse binary data are possible, estimates of gamma are biased. Data with 10 or more observations per patient is necessary for accurate estimations of gamma.

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Sangh, Neeraj. "Static Systematic Risk Profile of Nifty 100 Stocks: A Year on Year Analysis of Beta." GIS Business 12, no. 5 (September 22, 2017): 75–83. http://dx.doi.org/10.26643/gis.v12i5.3346.

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Beta Coefficient, as a measurement statistic of systematic risk of securities, was initially explained by Sharpe as a slope of simple linear regression function using rate of return on a market index as independent variable and a securitys rate of return as dependent variable. National Stock Exchange (NSE), the leading stock exchange of India, practice this ordinary least square (OLS) regression based single index market model for disseminating beta coefficients of prominent NIFTY 100 stocks. OLS regression based index model presumes that beta coefficients of securities should remain stable for accuracy of predicted returns. Brenner and Smidt (1977) emphasized the importance of having accurate beta forecast mainly because of (i) understanding risk-return relationships in capital market theory and (ii) extensive usage of beta in making investment decisions. The objective of this paper is to examine year on year stability of beta coefficients of NIFTY 100 index stocks.

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Chakraborty, Antik, Anirban Bhattacharya, and Bani K. Mallick. "Bayesian sparse multiple regression for simultaneous rank reduction and variable selection." Biometrika 107, no. 1 (November 23, 2019): 205–21. http://dx.doi.org/10.1093/biomet/asz056.

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Summary We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra-high-dimensional settings where the number of predictors can grow subexponentially relative to the sample size. A one-step post-processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection, with default choices of tuning parameters. We additionally provide an estimate of the rank using a novel optimization function achieving dimension reduction in the covariate space. We exhibit the performance of the proposed methodology in an extensive simulation study and a real data example.

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Hu, Guikai, and Ping Peng. "Admissibility for linear estimators of regression coefficient in a general Gauss–Markoff model under balanced loss function." Journal of Statistical Planning and Inference 140, no. 11 (November 2010): 3365–75. http://dx.doi.org/10.1016/j.jspi.2010.05.004.

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Jirásková, Eva, Jiří Kulhánek, Taťjana Nevěčná, and Oldřich Pytela. "Construction and Chemometric Analysis of Acidity Function in Perchloric Acid." Collection of Czechoslovak Chemical Communications 64, no. 8 (1999): 1253–61. http://dx.doi.org/10.1135/cccc19991253.

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Four 2,6-disubstituted anilines with CH3, Cl, and NO2 substituents have been synthesized and, together with four commercial substances of the same type, subjected to spectrophotometry to find the concentration ratios of the protonated and non-protonated forms in aqueous perchloric acid of 0.02-10.55 mol dm-3 concentration. By a procedure devised earlier, the acidity function has been constructed and the pKa values calculated. The Principal Component Analysis was applied to the acidity function obtained and on other eight acidity functions of perchloric acid were taken from literature. It was found that the first principal component explained 99.78% of variability, which indicated high degree of similarity of the said functions irrespective of the indicator type and solvent used. The regression dependences acidity function values on the first principle component are very close, the regression coefficient expressing the measure of sensitivity of the indicator to the acidifying medium. The pKa values obtained agree well with the literature data.

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Pham, Huong T. T., and Hoa Pham. "On the existence of posterior mean for Bayesian logistic regression." Monte Carlo Methods and Applications 27, no. 3 (May 18, 2021): 277–88. http://dx.doi.org/10.1515/mcma-2021-2089.

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Abstract Existence conditions for posterior mean of Bayesian logistic regression depend on both chosen prior distributions and a likelihood function. In logistic regression, different patterns of data points can lead to finite maximum likelihood estimates (MLE) or infinite MLE of the regression coefficients. Albert and Anderson [On the existence of maximum likelihood estimates in logistic regression models, Biometrika 71 1984, 1, 1–10] gave definitions of different types of data points, which are complete separation, quasicomplete separation and overlap. Conditions for the existence of the MLE for logistic regression models were proposed under different types of data points. Based on these conditions, we propose the necessary and sufficient conditions for the existence of posterior mean under different choices of prior distributions. In this paper, a general wide class of priors, which are informative priors and non-informative priors having proper distributions and improper distributions, are considered for the existence of posterior mean. In addition, necessary and sufficient conditions for the existence of posterior mean for an individual coefficient is also proposed.

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Margahana, Helisia. "THE INFLUENCE OF MOTIVATION AND DIRECTION FUNCTION ON EMPLOYEE WORK DISCIPLINE IN THE DEPARTMENT OF TOURISM AND CULTURE OF SOUTH OKU DISTRICT." DIA Jurnal Ilmiah Administrasi Publik 18, no. 1 (June 18, 2020): 210–21. http://dx.doi.org/10.30996/dia.v18i1.4127.

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This research study aims to partially and jointly analyze the influence of Motivation, Guidance Function on employee work discipline, and to analyze the most dominant variables in influencing employee work discipline at the Office of Tourism and Culture of South OKU Regency. Results of regression analysis and the correlation between motivation and discipline Employee employment shows a regression model ? = 3.987 + 0.958X1 + e with a correlation coefficient of 0.900. The results of the regression analysis and the correlation between direction on employee work discipline show the regression model ? = 16,805 + 0.665X2 + e with a correlation coefficient of 0.825. The results of multiple regression analysis and the correlation between motivation and direction together on work discipline show the regression model ? = 2.817 + 0.675X1 + 0.300X2 + e with a correlation coefficient of 0.937 at the 95% confidence level, it is found that motivation and direction can simultaneously predict employee work discipline. Motivation and direction simultaneously have a strong positive effect with work discipline of 86.9% and have a significant effect. The effect of motivation and direction simultaneously on the work discipline of the employees of the South OKU Regency Tourism and Culture Office is 2,817, so if there is an increase in motivation and direction together then this will increase the work discipline of the OKU Regency Tourism and Culture Office employees South with significant .. This research was conducted on 28 respondents with the analytical method used is path analysis using SPSS software.

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Burger, T., H. J. Ploss, J. Kuhn, S. Ebel, and J. Fricke. "Diffuse Reflectance and Transmittance Spectroscopy for the Quantitative Determination of Scattering and Absorption Coefficients in Quantitative Powder Analysis." Applied Spectroscopy 51, no. 9 (September 1997): 1323–29. http://dx.doi.org/10.1366/0003702971941999.

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A three-flux approximation of the equation of radiative transfer is used to separately determine the effective specific scattering and absorption coefficients of powder mixtures from hemispherical reflectance and transmittance measurements. For a two-component mixture of lactose and paracetamol, it is demonstrated how the knowledge of the separately known scattering coefficient can be used to improve partial least-squares regression (PLS) calibrations of diffuse reflectance data pretreated by multiplicative scatter correction (MSC). Furthermore it is shown that the measured specific absorption coefficient of the investigated mixtures is not generally a linear function of the constituents concentration, a result which might be caused by the mixing procedure of the samples. With the use of the absorption coefficient, it is demonstrated that artificial neural networks are superior to PLS calibrations when modeling a nonlinear relation.

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Queiroz, Douglas Santos, and Daniela Franco Vieira. "DETERMINAÇÃO DE COEFICIENTE DE EXPANSÃO TÉRMICA DO BIODIESEL E SEUS IMPACTOS NO SISTEMA DE MEDIÇÃO VOLUMÉTRICO." Eclética Química Journal 35, no. 4 (January 22, 2018): 107. http://dx.doi.org/10.26850/1678-4618eqj.v35.4.2010.p107-111.

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The purpose of this study was to determine the coefficient of thermal expansion of the biodiesel from the experimental data of density as a function of temperature. For this, we used some fundamentals of thermodynamics. The value obtained for the coefficient of thermal expansion after the linear regression for biodiesel was 8.49 × 10-4 ° C-1, with a correlation coefficient equal to 0.9978

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Mello-Román, Jorge Daniel, Adolfo Hernández, and Julio César Mello-Román. "Improved Predictive Ability of KPLS Regression with Memetic Algorithms." Mathematics 9, no. 5 (March 1, 2021): 506. http://dx.doi.org/10.3390/math9050506.

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Kernel partial least squares regression (KPLS) is a non-linear method for predicting one or more dependent variables from a set of predictors, which transforms the original datasets into a feature space where it is possible to generate a linear model and extract orthogonal factors also called components. A difficulty in implementing KPLS regression is determining the number of components and the kernel function parameters that maximize its performance. In this work, a method is proposed to improve the predictive ability of the KPLS regression by means of memetic algorithms. A metaheuristic tuning procedure is carried out to select the number of components and the kernel function parameters that maximize the cumulative predictive squared correlation coefficient, an overall indicator of the predictive ability of KPLS. The proposed methodology led to estimate optimal parameters of the KPLS regression for the improvement of its predictive ability.

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Journal articles on the topic 'Regression coefficient function'

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