• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.473-478
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• 2002

A test for a single outlier in multivariate regression with linear constraints on regression coefficients using a mean shift model is derived. It is shown that influential observations based on case-deletions in testing linear hypotheses are determined by two types of outliers that are mean shift outliers with or without linear constraints, An illustrative example is given.

• Communications for Statistical Applications and Methods
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• 제28권2호
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• pp.189-204
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• 2021

In a regression analysis, a single best model is usually selected among several candidate models. However, it is often useful to combine several candidate models to achieve better performance, especially, in the prediction viewpoint. Model combining methods such as stacking and Bayesian model averaging (BMA) have been suggested from the perspective of averaging candidate models. When the candidate models include a true model, it is expected that BMA generally gives better performance than stacking. On the other hand, when candidate models do not include the true model, it is known that stacking outperforms BMA. Since stacking and BMA approaches have different properties, it is difficult to determine which method is more appropriate under other situations. In particular, it is not easy to find research papers that compare stacking and BMA when regression model assumptions are violated. Therefore, in the paper, we compare the performance among model averaging methods as well as a single best model in the linear regression analysis when standard linear regression assumptions are violated. Simulations were conducted to compare model averaging methods with the linear regression when data include outliers and data do not include them. We also compared them when data include errors from a non-normal distribution. The model averaging methods were applied to the water pollution data, which have a strong multicollinearity among variables. Simulation studies showed that the stacking method tends to give better performance than BMA or standard linear regression analysis (including the stepwise selection method) in the sense of risks (see (3.1)) or prediction error (see (3.2)) when typical linear regression assumptions are violated.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.319-325
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• 2001

In this note, we propose a simple fuzzy linear regression model for fuzzy input-output data based on Tanaka's approach. Then an LP-based method to derived the satisfying solution of the decision making is developed.

• 대기
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• 제24권4호
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• pp.491-502
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• 2014

As a part of the KIAPS (Korea Institute of Atmospheric Prediction Systems) Package for Observation Processing (KPOP), we have developed the modules for Advanced Microwave Sounding Unit-A (AMSU-A) pre-processing and its bias correction. The KPOP system calculates the airmass bias correction coefficients via the method of multiple linear regression in which the scan-corrected innovation and the thicknesses of 850~300, 200~50, 50~5, and 10~1 hPa are respectively used for dependent and independent variables. Among the four airmass predictors, the multicollinearity has been shown by the Variance Inflation Factor (VIF) that quantifies the severity of multicollinearity in a least square regression. To resolve the multicollinearity, we adopted simple linear regression and Principal Component Regression (PCR) to calculate the airmass bias correction coefficients and compared the results with those from the multiple linear regression. The analysis shows that the order of performances is multiple linear, principal component, and simple linear regressions. For bias correction for the AMSU-A channel 4 which is the most sensitive to the lower troposphere, the multiple linear regression with all four airmass predictors is superior to the simple linear regression with one airmass predictor of 850~300 hPa. The results of PCR with 95% accumulated variances accounted for eigenvalues showed the similar results of the multiple linear regression.

• Corrosion Science and Technology
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• 제19권6호
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• pp.302-309
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• 2020

This study aimed to predict the pitting corrosion characteristics of AL-6XN super-austenitic steel using multiple linear regression. The variables used in the model are degree of sensitization, temperature, and pH. Experiments were designed and cyclic polarization curve tests were conducted accordingly. The data obtained from the cyclic polarization curve tests were used as training data for the multiple linear regression model. The significance of each factor in the response (critical pitting potential, repassivation potential) was analyzed. The multiple linear regression model was validated using experimental conditions that were not included in the training data. As a result, the degree of sensitization showed a greater effect than the other variables. Multiple linear regression showed poor performance for prediction of repassivation potential. On the other hand, the model showed a considerable degree of predictive performance for critical pitting potential. The coefficient of determination (R2) was 0.7745. The possibility for pitting potential prediction was confirmed using multiple linear regression.

• 대기
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• 제25권4호
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• pp.669-683
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• 2015

In this study, we investigated the prediction skills of four multiple linear regression methods for monthly air temperature over South Korea. We used simulation results from four regional climate models (RegCM4, SNURCM, WRF, and YSURSM) driven by two boundary conditions (NCEP/DOE Reanalysis 2 and ERA-Interim). We selected 15 years (1989~2003) as the training period and the last 5 years (2004~2008) as validation period. The four regression methods used in this study are as follows: 1) Homogeneous Multiple linear Regression (HMR), 2) Homogeneous Multiple linear Regression constraining the regression coefficients to be nonnegative (HMR+), 3) non-homogeneous multiple linear regression (EMOS; Ensemble Model Output Statistics), 4) EMOS with positive coefficients (EMOS+). It is same method as the third method except for constraining the coefficients to be nonnegative. The four regression methods showed similar prediction skills for the monthly air temperature over South Korea. However, the prediction skills of regression methods which don't constrain regression coefficients to be nonnegative are clearly impacted by the existence of outliers. Among the four multiple linear regression methods, HMR+ and EMOS+ methods showed the best skill during the validation period. HMR+ and EMOS+ methods showed a very similar performance in terms of the MAE and RMSE. Therefore, we recommend the HMR+ as the best method because of ease of development and applications.

• Nuclear Engineering and Technology
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• 제54권5호
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• pp.1902-1908
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• 2022

In many of the complex systems modeled in the field of nuclear engineering, it is often useful to use linear regression-based analyses to analyze relationships between model parameters and responses of interests. In cases where the response of interest is calculated by a simulation which uses Monte Carlo methods, there will be some uncertainty in the responses. Further, the reduction of this uncertainty increases the time necessary to run each calculation. This paper presents some discussion on how the Monte Carlo error in the response of interest influences the error in computed linear regression coefficients. A mathematical justification is given that shows that when performing linear regression in these scenarios, the error in regression coefficients can be largely independent of the Monte Carlo error in each individual calculation. This condition is only true if the total number of calculations are scaled to have a constant total time, or amount of work, for all calculations. An application with a simple pin cell model is used to demonstrate these observations in a practical problem.

• Journal of information and communication convergence engineering
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• 제21권1호
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• pp.62-67
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• 2023

This paper proposes an imputation method using a bidirectional k-nearest components search based local linear regression method. The bidirectional k-nearest-components search method selects components in the dynamic range from the missing points. Unlike the existing methods, which use a fixed-size window, the proposed method can flexibly select adjacent components in an imputation problem. The weight values assigned to the components around the missing points are calculated using local linear regression. The local linear regression method is free from the rank problem in a matrix of dependent variables. In addition, it can calculate the weight values that reflect the data flow in a specific environment, such as a blackout. The original missing values were estimated from a linear combination of the components and their weights. Finally, the estimated value imputes the missing values. In the experimental results, the proposed method outperformed the existing methods when the error between the original data and imputation data was measured using MAE and RMSE.

• 한국임상수의학회지
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• 제27권4호
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• pp.427-434
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• 2010

Correlation is a technique used to measure the strength or the degree of closeness of the linear association between two quantitative variables. Common misuses of this technique are highlighted. Linear regression is a technique used to identify a relationship between two continuous variables in mathematical equations, which could be used for comparison or estimation purposes. Specifically, regression analysis can provide answers for questions such as how much does one variable change for a given change in the other, how accurately can the value of one variable be predicted from the knowledge of the other. Regression does not give any indication of how good the association is while correlation provides a measure of how well a least-squares regression line fits the given set of data. The better the correlation, the closer the data points are to the regression line. In this tutorial article, the process of obtaining a linear regression relationship for a given set of bivariate data was described. The least square method to obtain the line which minimizes the total error between the data points and the regression line was employed and illustrated. The coefficient of determination, the ratio of the explained variation of the values of the independent variable to total variation, was described. Finally, the process of calculating confidence and prediction interval was reviewed and demonstrated.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.519-524
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• 2003

We suggest a method of identifying outliers, using local influence, in regression when linear constraints are imposed on the regression coefficients. An example is given for illustration.