• Communications for Statistical Applications and Methods
• /
• 제9권2호
• /
• pp.473-478
• /
• 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
• /
• 제20권2호
• /
• pp.129-136
• /
• 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.

• Journal of the Korean Statistical Society
• /
• 제7권2호
• /
• pp.105-108
• /
• 1978

Freund, Vail, and Ross, Goldberger and Jochems and Goldberger have given some results for the stepwise estimation of the parameters of a univariate regression model, D.G. Kabe gave similar results for a multivariate linear regression model. We give here alternative derivation of some results derived by D.G. Kabe.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.479-485
• /
• 2003

The influence of observations on the Wilks' lambda test of a linear hypothesis in multivariate regression is investigated using the local influence method. The perturbation scheme of case-weights is considered. A numerical example is given to show the effectiveness of the local influence method in identifying the influential observations.

• 한국식품과학회지
• /
• 제51권3호
• /
• pp.227-236
• /
• 2019

Antioxidant activity in water and ethanol extracts of dried Lycium chinense fruit, as a result of the total phenolic and tannin content, was measured using a number of chemical and biochemical assays for radical scavenging and inhibition of lipid peroxidation, with the analysis being extended by applying a bootstrapping statistical method. Previous statistical analyses mostly provided linear correlation and regression analyses between antioxidant activity and increasing concentrations of phenolics and tannins in a concentration-dependent mode. The present study showed that multiple component or multivariate analysis by applying multiple regression analysis or regression planes proved more informative than linear regression analysis of the relationship between the concentration of individual components and antioxidant activity. In this paper, we represented the multivariate analysis of antioxidant activities of both phenolic and tannin contents combined in the water and ethanol extracts, which revealed the hidden observations that were not evident from linear statistical analysis.

• Communications for Statistical Applications and Methods
• /
• 제28권5호
• /
• pp.553-562
• /
• 2021

Directional regression (DR; Li and Wang, 2007) is well-known as an exhaustive sufficient dimension reduction method, and performs well in complex regression models to have linear and nonlinear trends. However, the extension of DR is not well-done upto date, so we will extend DR to accommodate multivariate regression and large p-small n regression. We propose three versions of DR for multivariate regression and discuss how DR is applicable for the latter regression case. Numerical studies confirm that DR is robust to the number of clusters and the choice of hierarchical-clustering or pooled DR.

• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.165-172
• /
• 1998

This paper considers a linear regression model with censored data where each error term follows a multivariate normal distribution. In this paper we consider the diffuse prior distribution for parameters of the linear regression model. With censored data we derive the full conditional densities for parameters of a multiple regression model in order to obtain the marginal posterior densities of the relevant parameters through the Gibbs Sampler, which was proposed by Geman and Geman(1984) and utilized by Gelfand and Smith(1990) with statistical viewpoint.

• Communications for Statistical Applications and Methods
• /
• 제1권1호
• /
• pp.33-40
• /
• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• 한국가스학회지
• /
• 제11권3호
• /
• pp.13-18
• /
• 2007

다변량 통계 분석법(Multivariate statistical analysis method)의 대표적 방법인 다중 선형 회귀법(Multiple linear regression. MLR)을 이용하여 2성분계 혼합물의 인화점을 회귀 분석하고 예측하였다. 가연성 물질의 인화점에 대한 예측은 실제 화학 공정 설계에서 화재 및 폭발 위험성을 판단하는 중요한 부분 중의 하나이다. 본 연구에서는 순수 성분의 물성 자료만을 이용하여 2성분계 혼합물의 인화점 실험 자료에 대해 다중 선형 회귀법(MLR)을 수행하였고, 이를 이용하여 새로운 혼합물에 대한 인화점을 예측하였다. 2성분계 혼합물의 인화점에 대한 MLR의 회귀 성능과 새로운 혼합물에 대한 예측 성능을 알아보기 위해, 기존의 인화점 추정 방법인 Raoult의 법칙과 Van Laar식에 의한 추정값과 비교해 보았다.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2000년도 추계학술발표회 논문집
• /
• pp.187-191
• /
• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.