• Restorative Dentistry and Endodontics
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• v.44 no.1
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• pp.11.1-11.8
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• 2019

In the previous sections, simple linear regression (SLR) 1 and 2, we developed a SLR model and evaluated its predictability. To obtain the best fitted line the intercept and slope were calculated by using the least square method. Predictability of the model was assessed by the proportion of the explained variability among the total variation of the response variable. In this session, we will discuss four basic assumptions of regression models for justification of the estimated regression model and residual analysis to check them.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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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.

• Atmosphere
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• v.24 no.4
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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.

• KIEAE Journal
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• v.15 no.5
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• pp.13-20
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• 2015

Purpose: In order to upgrade the energy performance of existing building, energy audit stage should be implemented first because it is useful method to find where the problems occur and know how much time and cost consumption for retrofit. In overseas researches, three levels of audit is proposed whereas there are no standards for audit in Korea. Besides, most studies use dynamic simulation in detail like audit level 3 even though the level 2 can save time and cost than level 3. Thus, this paper focused on audit level 2 and proposed the audit method with the simple linear regression analysis model. Method: Two parameters were considered for the simple regression analysis, which were the monthly electric use and the mean outdoor temperature data. The former is a dependent variable and the latter is a independent variable, and the building's energy performance profile was estimated from the regression analysis method. In this analysis, we found the abnormal point in cooling season and the more detailed analysis were conducted about the three heat source equipments. Result: Comparing with real and predicted models, the total consumption of predicted model was higher than real value as 23,608 kWh but it was the results that was reflected the compulsory control in 2013. Consequently, it was analyzed that the revised model could save the cooling energy as well as reduce peak electric use than before.

• Korean Journal of Veterinary Research
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• v.53 no.2
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• pp.73-76
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• 2013

The aim of this study was to produce a simple and inexpensive technique for estimating the obturator foramen area (OFA) from young calves based on the hypothesis that OFA can be extrapolated from simple linear measurements. Three linear measurements - dorsoventral height, craneocaudal width and total perimeter of obturator foramen - were obtained from 55 bovine hemicoxae. Different algorithms for determining OFA were then produced with a regression analysis (curve fitting) and statistical analysis software. The most simple equation was OFA ($mm^2$) = [3,150.538 + ($36.111^*CW$)] - [147,856.033/DH] (where CW = craneocaudal width and DH = dorsoventral height, both in mm), representing a good nonlinear model with a standard deviation of error for the estimate of 232.44 and a coefficient of multiple determination of 0.846. This formula may be helpful as a repeatable and easily performed estimation of the obturator foramen area in young bovines. The area of the obturator foramen magnum can thus be estimated using this regression formula.

• Nuclear Engineering and Technology
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• v.54 no.5
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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 the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.17-29
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• 1995

Recently, neural network models have been employed as an alternative to regression analysis for point estimation or function fitting in various field. Thus far, however, no theoretical or empirical guides seem to exist for selecting the tool which the most suitable one for a specific function-fitting problem. In this paper, we evaluate performance of three major function-fitting techniques, regression analysis and two neural network models, back-propagation and linear-Hebbian-learning neural networks. The functions to be fitted are simple linear ones of a single independent variable. The factors considered are size of noise both in dependent and independent variables, portion of outliers, and size of the data. Based on comutational results performed in this study, some guidelines are suggested to choose the best technique that can be used for a specific problem concerned.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.539-556
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• 2019

This paper derive a method to solve change point regression problems via a process for obtaining consequential results using properties of a difference-based intercept estimator first introduced by Park and Kim (Communications in Statistics - Theory Methods, 2019) for outlier detection in multiple linear regression models. We describe the statistical properties of the difference-based regression model in a piecewise simple linear regression model and then propose an efficient algorithm for change point detection. We illustrate the merits of our proposed method in the light of comparison with several existing methods under simulation studies and real data analysis. This methodology is quite valuable, "no matter what regression lines" and "no matter what the number of change points".

• Journal of Veterinary Clinics
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• v.27 no.4
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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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• v.17 no.2
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.