• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.63-68
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• 1998

This paper proposes fuzzy regression analysis with non-symmetric fuzzy coefficients. By assuming non-symmetric triangular fuzzy coefficients and applying the quadratic programming fomulation, the center of the obtained fuzzy regression model attains more central tendency compared to the one with symmetric triangular fuzzy coefficients. For a data set composed of crisp inputs-fuzzy outputs, two approximation models called an upper approximation model and a lower approximation model are considered as the regression models. Thus, we also propose an integrated quadratic programming problem by which the upper approximation model always includes the lower approximation model at any threshold level under the assumption of the same centers in the two approximation models. Sensitivities of Weight coefficients in the proposed quadratic programming approaches are investigated through real data.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.445-449
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• 2005

Yen et al. [Fuzzy Sets and Systems 106 (1999) 167-177] calculated the fuzzy membership function for the output to find the non-symmetric triangular fuzzy number coefficients of a linear regression model for all given input-output data sets. In this note, we show that the result they obtained in their paper is invalid.

• Journal of Ocean Engineering and Technology
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• v.37 no.5
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• pp.198-204
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• 2023

In response to the complexity and time demands of conventional methods for estimating the hydrodynamic coefficients, this study aims to revolutionize ship maneuvering analysis by utilizing automatic identification system (AIS) data and the Support Vector Regression (SVR) algorithm. The AIS data were collected and processed to remove outliers and impute missing values. The rate of turn (ROT), speed over ground (SOG), course over ground (COG) and heading (HDG) in AIS data were used to calculate the rudder angle and ship velocity components, which were then used as training data for a regression model. The accuracy and efficiency of the algorithm were validated by comparing SVR-based estimated hydrodynamic coefficients and the original hydrodynamic coefficients of the Mariner class vessel. The validated SVR algorithm was then applied to estimate the hydrodynamic coefficients for real ships using AIS data. The turning circle test wassimulated from calculated hydrodynamic coefficients and compared with the AIS data. The research results demonstrate the effectiveness of the SVR model in accurately estimating the hydrodynamic coefficients from the AIS data. In conclusion, this study proposes the viability of employing SVR model and AIS data for accurately estimating the hydrodynamic coefficients. It offers a practical approach to ship maneuvering prediction and control in the maritime industry.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.589-597
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• 2021

In simple and multiple regression, there is a difference in the meaning of regression coefficients, and not only are the estimates of regression coefficients different, but they also have different signs. Understanding the relative contribution of explanatory variables in a regression model is an important part of regression analysis. In a standardized regression model, the regression coefficient can be interpreted as the change in the response variable with respect to the standard deviation when the explanatory variable increases by the standard deviation in a situation where the values of the explanatory variables other than the corresponding explanatory variable are fixed. However, the size of the standardized regression coefficient is not a proper measure of the relative importance of each explanatory variable. In this paper, the estimator of the regression coefficient in multiple regression is expressed as a function of the correlation coefficient and the coefficient of determination. Furthermore, it is considered in terms of the effect of an additional explanatory variable and additional increase in the coefficient of determination. We also explore the relationship between estimates of regression coefficients and correlation coefficients in various plots. These results are specifically applied when there are two explanatory variables.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.4
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• pp.45-61
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• 1988

The purpose of this study is to develop regression equations between annual specific sedi- ment of reservoirs and physiographic factors of watersheds. 122 irrigation reservoirs, which have irrigation areas equal to or larger than 200 ha, located in Korea except Cheju province are used in the analysis. Simple regression analyses between the specific annual sediment and each of the physical characteristic factors of the reservoirs are carried out at first. Then, multiple regression analyses between the annual specific sediment and the physical characteristic factors with high correlation coefficients in the simple regression analyses are made. The results obtained from this study are as follows : 1. The results of the sirnple regression analyses show that in each province the watershed area, the length of mainstream, the circumferential length of watershed have high cor- relation coefficients (R=0.814-0.986), and that drainage density, reservoir capacity per watershed area, drainage frequency, basin relief have low correlation coefficients (R=0. 387-0.955). 2. The purposed multiple regression equations between the annual specific sediment of reservoirs and three major characteritic factors of watersheds, namely, the watershed area, the circumferential length of watershed, and the length of mainstream, are proposed as given in Table 2. 3. The result of the simple regression analyses with respect to the reservoir elevation except Jeonnam province, which has very different characteristics comparing to other provinces, shows that watershed area, main stream length and circumferential length have high correlation coefficients (R=0.806-0.884) in low-elevation reservoirs and intermediate- elevation reservoirs, but low correlation coefficients (R=0.639-0.739) in high-elevation reservoirs. 4. With respect to the reservoir elevation, the proposed multiple regression equations bet- ween the annual specific sediment of reservoirs and the three major characteristic factors of watershed which have high correlation coefficients are proposed as given in Table 5.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.49-60
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• 2006

There are six approaches to constructing standardized coefficient for logistic regression. The standardized coefficient based on Kruskal's information theory is known to be the best from a conceptual standpoint. In order to calculate this standardized coefficient, the coefficient of determination based on entropy loss is used among many kinds of coefficients of determination for logistic regression. In this paper, this standardized coefficient is obtained by using four kinds of coefficients of determination which have the most intuitively reasonable interpretation as a proportional reduction in error measure for logistic regression. These four kinds of the sixth standardized coefficient are compared with other kinds of standardized coefficients.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.435-443
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• 2005

Coefficients of determination in logistic regression analysis are defined as various statistics, and their values are relatively smaller than those for linear regression model. These coefficients of determination are not generally used to evaluate and diagnose logistic regression model. Liao and McGee (2003) proposed two adjusted coefficients of determination which are robust at the addition of inappropriate predictors and the variation of sample size. In this work, these adjusted coefficients of determination are applied to variable selection method for logistic regression model and compared with results of other methods such as the forward selection, backward elimination, stepwise selection, and AIC statistic.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.541-548
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• 1997

In regression model with nested error structure interval estimations on regression coefficients in different stages are proposed. Ordinary least square estimators and generalized least square estimators of the regression coefficients in this model are derived for between and within group model. The confidence intervals are dervied by using independent idstributional properties between regression coefficient estimators and quadratic froms obtained from the model.

• Atmosphere
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• v.25 no.4
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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.

• Asian-Australasian Journal of Animal Sciences
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• v.31 no.10
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• pp.1542-1549
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• 2018

Objective: Because lactation periods in dairy cows lengthen with increasing total milk production, it is important to predict individual productivities after 305 days in milk (DIM) to determine the optimal lactation period. We therefore examined whether the random regression (RR) coefficient from 306 to 450 DIM (M2) can be predicted from those during the first 305 DIM (M1) by using a RR model. Methods: We analyzed test-day milk records from 85,690 Holstein cows in their first lactations and 131,727 cows in their later (second to fifth) lactations. Data in M1 and M2 were analyzed separately by using different single-trait RR animal models. We then performed a multiple regression analysis of the RR coefficients of M2 on those of M1 during the first and later lactations. Results: The first-order Legendre polynomials were practical covariates of RR for the milk yields of M2. All RR coefficients for the additive genetic (AG) effect and the intercept for the permanent environmental (PE) effect of M2 had moderate to strong correlations with the intercept for the AG effect of M1. The coefficients of determination for multiple regression of the combined intercepts for the AG and PE effects of M2 on the coefficients for the AG effect of M1 were moderate to high. The daily milk yields of M2 predicted by using the RR coefficients for the AG effect of M1 were highly correlated with those obtained by using the coefficients of M2. Conclusion: Milk production after 305 DIM can be predicted by using the RR coefficient estimates of the AG effect during the first 305 DIM.