• Communications for Statistical Applications and Methods
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• v.20 no.2
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• pp.129-136
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• 2013

Linear regression is the most basic statistical model for exploring the relationship between a numerical response variable and several explanatory variables. Logistic regression secures the role of linear regression for the dichotomous response variable. In this paper, we propose a biplot-type display of the multivariate data guided by the linear regression and/or the logistic regression. The figures show the directional flow of the response variable as well as the interrelationship of explanatory variables.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.495-500
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• 2009

Two diagnostic plots, added variable plot and partial residual plot, are proposed when a new explanatory variable is linearly added to constrained regressions. They are useful for investigating the effect of adding an explanatory variable to the constrained regression. They visually give an overall impression of the strength of linear relationship between response variable and added variable. A numerical example is provided for illustration.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.403-410
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• 2014

Binary logistic regression analysis is a statistical technique that explains binary response variable by quantitative or qualitative explanatory variables. In the binary logistic regression model, the probability that the response variable equals, say 1, one of the binary values is to be explained as a transformation of linear combination of explanatory variables. This is one of big barriers that non-statisticians have to overcome in order to understand the model. In this study, an educational tool is developed that explains the need of the binary logistic regression analysis using Excel VBA. More precisely, this tool explains the problems related to modeling the probability of the response variable equal to 1 as a linear combination of explanatory variables and then shows how these problems can be solved through some transformations of the linear combination.

• The Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.335-346
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• 2022

Profile control chart aims to detect a change in the functional relationship of multivariate characteristics in the statistical process control. In monitoring two variables, a linear profile is of interest composed of the intercept and slope of one variable (response variable) against the other (explanatory variable). The previous studies on monitoring of the linear profile mostly assume that the explanatory variables are the same for all profiles. However, there are also cases where they vary depending on profiles. This paper intends to extend the monitoring method to where explanatory variables are different for each profile. We compare the new method's performance through simulation and apply it to monitoring a network intrusion using NSL-KDD data.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.195-204
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• 2007

In order to represent multiple regression data, an alternative graphical method, called as SSR Plot, is proposed by using geometrical description methods. This plot uses the relation that the sum of sqaures for regression (SSR) of two explanatory variables is known as the sum of the SSR of one variable and the increase in the SSR due to the addition of other variable to the model that already contains a variable. This half circle shaped SSR plot contains vectors corresponding explanatory variables. We might conclude that some explanatory variables corresponding to vectors which locate near the horisontal axis do affect the response variable. Also, for the regression model with two explanatory variables, a magnitude of the angle between two vectors can be identified for suppression.

• Physical Therapy Rehabilitation Science
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• v.11 no.2
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• pp.181-188
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• 2022

Objective: The purpose of this study to investigate the correlations among the motor function, balance, and gait velocity and the strength that could explain the variation of gait velocity of chronic stroke survivors. Design: This was a cross-sectional cohort study. Methods: Thirty hemiplegic stroke survivors hospitalized in an inpatient rehabilitation center were participated. The muscle tone of ankle plantarflexor and muscle strength of ankle dorsiflexor were measured respectively with modified Ashworth scale (MAS) and hand-held dynamometer. And the motor recovery and function with Fugl-Meyer assessment (FMA), balance with Berg balance scale (BBS) and timed up and go (TUG) test were measured. Gait velocity was measured with GAITRite. The correlation among motor function, muscle tone, muscle strength, balance, and gait were analyzed. In addition, the strength of the relationship between the response (gait velocity) and the explanatory variables was analyzed. Results: The gait velocity had positive correlations with FMA, muscle strength, and BBS, and negative correlation with MAS and TUG. Regression analysis showed that TUG (𝛽=-0.829) was a major explanatory variable for gait velocity. Conclusions: Our results suggest that gait velocity had correlations with muscle strength, MAS, FMA, BBS, and TUG. The tests and measurements affecting the variation of gait velocity the greatest were TUG, followed by FMA, BBS, muscle strength, and MAS. This study shows that TUG would be a possible assessment tool to determine the variation of gait velocity in stroke rehabilitation.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.4
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• pp.366-370
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• 2013

Regression Analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper introduce Theil's method to find a fuzzy regression model which explain the relationship between explanatory variable and response variables. Theil's method is a robust method which is not sensive to outliers. Theil's method use medians of rate of increment based on randomly chosen pairs of each components of ${\alpha}$-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. We propose an example to show Theil's estimator is robust than the Least squares estimator.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.61-74
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• 1995

These days, many kinds of graphical methods have been developed, and it is possible to get information directly from data. Especially, R-code (Cook and Weisberg, 1994) make it possible to draw various kinds of two and three dimensional plots, and to rotate the axis of the plots. But the maximum dimensional of the plot is three, so we can not draw plot of one response variable with more than three explanatory variables. Li(1991, 1992) has developed a method to reduce the dimension of the explanatory variables, so it is possible to draw lower dimensional plots to get information of the full explanatory variables. One of the dimension reduction method developed by Li is pHd. In this paper, we have tried to apply the pHd method for the model with multivariate response.