• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.787-797
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• 2002

Partial residual plots, augmented partial residual plots and CERES plots are basic diagnostic tools for dealing with curvature as a function of specific predictors in regression problem. However, it is known that these plots can miss a curve or show a false curve in some cases such as predictors are related each other. Dynamic display of these plots is developed and applied. Examples demonstrate that dynamic plots are useful for obtaining additional Information on the curvature.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.73-81
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• 2000

The variance inflation factor can be expressed by the square of the ratio of t-statistics associated with slopes of partial regression and partial residual plots. Disagreement of two sides in the interpretation can be occurred, and we analyze it with some illustrations.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.311-317
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• 2001

It is necessary to check the linearity of selected covariates in regression diagnostics. There are various graphical methods using residual plots such as partial residual plots, augmented partial residual plots and combining conditional expectation and residual plots. In this paper, we propose the modified pseudolikelihood ratio test statistics based on these residual plots to test linearity of selected covariate. These test statistics which measure the distance between the nonparametric and parametric models are derived as a ratio of quadratic forms. The approximate distribution of these statistics is calculated numerically by using three moments. The power comparison of these statistics is given.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.529-537
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• 2004

This article concerns dynamic graphical methods for visualizing a curvature in regression problem in which some predictors enter nonlinearly. A sequence of augmented partial residual plot or partial residual plot updated by the change of linear combination of two predictors are constructed. Examples demonstrate that the suggested methods can be used to reduce the dimension of explanatory variables as well as to capture a curvature.

• 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.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.521-531
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• 2002

Various diagnostic techniques for identifying influential observations are mostly based on the deletion of a single observation. While such techniques can satisfactorily identify influential observations in many cases, they will not always be successful because of some mask effect. It is necessary, therefore, to develop techniques that examine the potentially influential effects of a subset of observations. The partial regression plots can be used to examine an influential observation for a single parameter in multiple linear regression. However, it is often desirable to detect influential observations for a subset of regression parameters when interest centers on a selected subset of independent variables. Thus, we propose a diagnostic measure which deals with detecting influential observations on a subset of regression parameters. In this paper, we propose a measure M, which can be effectively used for the detection of influential observations on a subset of regression parameters in multiple linear regression. An illustrated example is given to show how we can use the new measure M to identify influential observations on a subset of regression parameters.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.1-12
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• 2000

We explore the structure and usefulness of CERES plot as a basic tool for dealing with curvature as a function of the new predictor in nonlinear regression. If a predictor has a nonlinear effect and there are nonlinear relationships among the predictors the partial residual plot and augmented partial residual plot are not able to display the correct functional form of the predictor. Unlike these plots the CERES plot can show the correct from. In situations where nonlinearity exists in two predictors we extend the idea of CERES plot to three dimensions, This is illustrated by simulated data.

• 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.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.24.2-24.2
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• 2008

We have examined the relative contributions of representative space weather proxies (geomagnetic aa index) to global warming (Global temperature anomaly) and compared them with that of green house effect characterized CO2 content from 1868 to 2005. For this we used Hadcrut3 temperature anomaly (Ta) data, aa index taken at two anti-podal subauroral stations (Canberra Australia and hartland England), and the CO2 data come from historical ice core records. From the comparison between Ta and aa index, we found several interesting results: (1) the linear correlation coefficient between two parameters increases until 1990 and then decreases rapidly, and (2) the scattered plots between two parameters shows different patterns before and after 1990. A partial correlation of Ta and two quantities (aa, CO2) also shows that the geomagnetic effect (aa index) is dominant until about 1990 and the CO2 effect becomes much more important after then. These results imply that the green house effect become very important since at least 1990. For a further analysis, we simply assume that Ta (total) = Ta (aa) + Ta (CO2) and made a linear regression between Ta and aa index from 1868 to 1990. A linear model is then made from the linear regression between energy consumption (a proxy of CO2 effect) and Ta (total) - Ta (aa) since 1990. This linear model makes it possible to predict the temperature anomaly in 2030, about 1 degree higher than the present temperature, which is much larger than in the previous century.

• KSBB Journal
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• v.21 no.1 s.96
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• pp.59-67
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• 2006

2D spectrofluorometer produces many spectral data during fermentation processes. The fluorescence spectra are analyzed using chemometric methods such as principal component analysis (PCA), principal component regression (PCR) and partial least square regression (PLS). Analysis of the spectral data by PCA results in scores and loadings that are visualized in score-loading plots and used to monitor a few fermentation processes by S. cerevisae and recombinant E. coli. Two chemometric models were established to analyze the correlation between fluorescence spectra and process variables using PCR and PLS, and PLS was found to show slightly better calibration and prediction performance than PCR.