• Journal of the Korean Statistical Society
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• v.9 no.1
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• pp.61-77
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• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.219-225
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• 1998

The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.703-712
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• 2003

This paper deals with the strong consistency of the asymmetric least squares for the nonlinear censored regression models which includes dependent variables cut off midway by any of external conditions, and provide the sufficient conditions which ensure the strong consistency of proposed estimators of the censored regression models. One example is given to illustrate the application of the main result.

• Journal of Information Technology Applications and Management
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• v.24 no.1
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• pp.25-32
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• 2017

For repairable software systems, the Mean Time Between Failure (MTBF) is used as a measure of software system stability. Therefore, the evaluation of software reliability requirements or reliability characteristics can be applied MTBF. In this paper, we want to compare MTBF in terms of parameter estimation using Makeham life distribution. The parameter estimates used the least square method which is regression analyzer method and the maximum likelihood method. As a result, the MTBF using the least square method shows a non-decreased pattern and case of the maximum likelihood method shows a non-increased form as the failure time increases. In comparison with the observed MTBF, MTBF using the maximum likelihood estimation is smallerd about difference of interval than the least square estimation which is regression analyzer method. Thus, In terms of MTBF, the maximum likelihood estimation has efficient than the regression analyzer method. In terms of coefficient of determination, the mean square error and mean error of prediction, the maximum likelihood method can be judged as an efficient method.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.886-890
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• 2007

Machine fault prognosis techniques have been considered profoundly in the recent time due to their profit for reducing unexpected faults or unscheduled maintenance. With those techniques, the working conditions of components, the trending of fault propagation, and the time-to-failure are forecasted precisely before they reach the failure thresholds. In this work, we propose an approach of Least Square Regression Tree (LSRT), which is an extension of the Classification and Regression Tree (CART), in association with one-step-ahead prediction of time-series forecasting technique to predict the future conditions of machines. In this technique, the number of available observations is firstly determined by using Cao's method and LSRT is employed as prognosis system in the next step. The proposed approach is evaluated by real data of low methane compressor. Furthermore, the comparison between the predicted results of CART and LSRT are carried out to prove the accuracy. The predicted results show that LSRT offers a potential for machine condition prognosis.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.4
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• pp.121-131
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• 2020

This study aims to investigate the interplay between education and local roads on Foreign Direct Investment (FDI) in the Philippines, using economic growth as an instrument. The study used the quantitative research design applying both descriptive and inferential statistics. A combination of Two Stage Least Square Regression Model and three approaches in Panel Regression Model such as Pooled Least Square, Fixed Effect Model, and Random Effect Model were utilized in order to study the effects of education and local roads on foreign direct investment of the Philippines. Based on Fixed Effect regression results, higher education graduates and local road investments, as conditioned by economic growth, were significant factors in order to increase the foreign direct investment in the Philippines. Accordingly, a unit increase in higher education graduates, as conditioned by economic growth, leads to 8.758 unit increases in the foreign direct investment. While, a unit increased in local road investments, as conditioned by economic growth, leads to a 0.002 decrease in foreign direct investment. The regression results of the study suggest that the Foreign Direct Investment in the regions such as CAR, I, II, IV-B, V, VIII, IX, X, XI, XII, XIII, and ARMM are higher compared to Region IV-A.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.235-245
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• 2000

In this paper, we consider the Regression Quantiles Estimators in nonlinear regression models. This paper provides the sufficient conditions for strong consistency and asymptotic normality of proposed estimation and drives asymptotic relative efficiency of proposed estimatiors with least square estimation. We give some examples and results of Monte Carlo simulation to compare least square and regression quantile estimators.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.571-575
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• 2003

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input--output data using shape preserving operations for least-squares fitting. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using mixed nonlinear program.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.73-77
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• 2004

종속변수와 독립변수 사이의 통계적인 관계를 설명하기 위해 사용되는 회귀모형을 분석하는 방법을 회귀분석이라 한다. 독립변수와 종속변수가 퍼지수인 퍼지회귀모형을 추정하기 위해 최소전대편차추정량을 제시하고. 예제를 이용하여 퍼지최소절대편차회귀모형과 퍼지최소자 승회귀모형의 효율성을 평가한다.