• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.32-47
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• 1995

The coefficient of determination R/sup 2/, as the proprtation of by explained by a set of independent variavles x/sub 1/, x/sub 2, .cdots., x/sub k/ through a linear regression model, is a very useful tool in linear regression analysis. Suppose R/sup 2//sub yx/ is the coefficient of determination when y is regressed only on x/sub i/ alone. If the independent variables are correlaated, the sum, R/sup 2//sub {yx/sub 1/}/ +R/sup 2//sub {yx/sub 2/}/+.cdots.R/sup 2//sub {yx/sub k/}/, is not equal to R/sup 2/sub {yx/sub 1/x/sub 2/.cots.x/sub k/}/, where R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ is the coefficient of determination when y is regressed simultaneously on x/sub 1/, x/sub 2/,.cdots., x/sub k/. In this paper it is discussed that under what conditions the sum is greater than, equal to, or less than R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/, and then the proofs for these conditions are given. Also illustrated examples are provided. In addition, we will discuss about inequality between R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ and the sum, R/sup 2//sub {yx/sub 1/}/+R/sup 2//sub {yx/sub 2/}/+.cdots.+R/sup 2//sub {yx/sub k/}/.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.661-668
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• 2006

There have been some controversies on the use of the coefficient of determination for linear no-intercept model. One definition of the coefficient of determination, $R^2={\sum}\;{\widehat{y^2}}\;/\;{\sum}\;y^2$, is being widely accepted only for linear no-intercept models though Kvalseth (1985) demonstrated some possible pitfalls in using such $R^2$. Main objective of this note is to report that $R^2$ is not a desirable measure of fit for the no-intercept linear model. In fact it is found that mean square error(MSE) could replace $R^2$ efficiently in most cases where selection of no-intercept model is at issue.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.145-154
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• 2005

There have been some controversies on the use of the coefficient of determination for linear no-intercept model. One definition of the coefficient of determination, $R^2=\sum\;{y}{^{\hat{2}}/\sum\;{y^2}$, is being widely accepted only for linear no-intercept models though Kvalseth(1985) demonstrated some possible pitfalls in using such $R^2$. Main objective of this article is to provide a cautionary notice for use of the $R^2$ by pointing out its tricky aspects by means of empirical simulations.

• International journal of advanced smart convergence
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• v.13 no.1
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• pp.206-211
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• 2024

This study used a total of 205,565 datasets of 'voltage', 'current', '℃', and 'time(s)' to systematically analyze the properties and performance of solid electrolytes. As a method for characterizing solid electrolytes, a linear regression model, one of the machine learning models, is used to visualize the relationship between 'voltage' and 'current' and calculate the regression coefficient, mean squared error (MSE), and coefficient of determination (R^2). The regression coefficient between 'Voltage' and 'Current' in the results of the linear regression model is about 1.89, indicating that 'Voltage' has a positive effect on 'Current', and it is expected that the current will increase by about 1.89 times as the voltage increases. MSE found that the mean squared error between the model's predicted and actual values was about 0.3, with smaller values closer to the model's predictions to the actual values. The coefficient of determination (R^2) is about 0.25, which can be interpreted as explaining 25% of the data.

• Journal of Korean Society of Transportation
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• v.31 no.2
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• pp.60-68
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• 2013

This study developed plural gravity models and their application method in order to increase the accuracy of trip distribution estimation. The developed method initially involves utilizing the coefficient of determination ($R^2$) to set the target level. Afterwards, the gravity model is created, and if the gravity model's coefficient of determination is satisfactory in regards to the target level, the model creation is complete and future trip distribution estimation is calculated. If the coefficient of determination is not on par with the target level, the zone pair with the largest standardized residual is removed from the model until the target level is obtained. In respect to the model, the removed zone pairs are divided into positive(+) and negative(-) sides. In each of these sides, gravity models are made until the target level is reached. If there are no more zone pairs to remove, the model making process concludes, and future trip distribution estimation is calculated. The newly developed plural gravity model and application method was adopted for 42 zone pairs as a case study. The existing method of utilizing only one gravity model exhibited a coefficient of determination value ($R^2$) of 51.3%, however, the newly developed method produced three gravity models, and exhibited a coefficient of determination value ($R^2$) of over 90%. Also, the accuracy of the future trip distribution estimation was found to be higher than the existing method.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.117-127
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• 1991

Coefficient of determination $R^2$ is most frequently used descriptive measure in practical use of linear regression analysis. But there have been controversies on defining this measure in the cases of linear regression without the intercept, weighted linear regression and robust linear regression. Several authors such as Kvalseth(1985) and Willet and Singer(1988) proposed many variations of $R^2$ to meet the situations. However, theire measures are not satisfactory due to the lack of a universal principle. In this study, we propose a unfied approach to defining the coefficient of determination $R^2$ using the concept of likelihood distance. This new measure is in good accordance with typical $R^2$ in linear regression and, moreover, can be applied to nonlinear regression models and generalized linear models such as logit and log-linear models.

• Korean Journal of Animal Reproduction
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• v.17 no.4
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• pp.347-356
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• 1994

A simpled and sensitive microplate enzyme immunoassay(EIA) was developed for the determination of progesterone concentration in serum, based on progesterone monoclonal antibody as anti-progesterone, horseradish peroxidase(HRP) as enzyme-label and tetramethylbenzidine(TMB) as substrate. The assay has a sensitivity of 5 pg-120pg/well and intra- and inter-assay coefficients of variation for progesterone standard curve (1.0ng~10.0ng/ml) were ranged 2.5~9.9% and 1.7.8.0%, respectively, determination coefficient of the regressio equation of our standard curve(R2=0.990$\pm$0.007) were high, and this is the same level as that of commercial kit(Hormonost Bio-Lab, Germany, R2=0.98~0.99). The progesterone concentration of serum determined by both kits (Work & Bio-Lab) were significantly correlated (r=0.95, P<0.01) although a little higher value were resulted in our kit than that of commercial kit. It generally is these results indicated that the microplate-EIA can be cused for the determination of progesterone in serum, as well as, for the determination of the early pregnancy diagnosis.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.29 no.1
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• pp.33-42
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• 1999

Geometrically standardized dental radiographs were taken. We prepared Digital Cu-Equivalent Image Analyzing System for quantitative assessment of mandible bone. Images of radiographs were digitized by means of Quick scanner and personal Mcquintosh computer. NIH image as software was used for analyzing images. A stepwedge composed of 10 steps of 0.1mm copper foil in thickness was used for reference material. This study evaluated the effects of step numbers of copper wedge adopted for calculating equation. kVp and exposure time on the coefficient of determination(r²)of the equation for conversion to Cu-equivalent image and the coefficient of variation and Cu-Eq value(mm) measured at each copper step and alveolar bone of the mandible. The results were as follows: 1. The coefficients of determination(r²) of 10 conversion equations ranged from 0.9996 to 0.9973(mean=0.9988) under 70kVp and 0.16 sec. exposure. The equation showed the highest r was Y=4.75614612-0.06300524x +0.00032367x² -0.00000060x³. 2. The value of r² became lower when the equation was calculated from the copper stepwedge including 1.0mm step. In case of including 0mm step for calculation. the value of r showed variability. 3. The coefficient of variation showed 0.11, 0.20 respectively at each copper step of 0.2, 0.1mm in thickness. Those of the other steps to 0.9 mm ranged from 0.06 to 0.09 in mean value. 4. The mean Cu-Eq value of alveolar bone was 0.14±0.02mm under optimal exposure. The values were lower than the mean under the exposures over 0.20sec. in 60kVp and over 0.16sec. in 70kVp. 5. Under the exposure condition of 60kVp 0.16sec.. the coefficient of variation showed 0.03. 0.05 respectively at each copper-step of 0.3, 0.2mm in thickness. The value of r² showed over 0.9991 from both 9 and 10 steps of copper. The Cu-Eq value and the coefficient of variation was 0.14±0.01mm and 0.07 at alveolar bone respectively. In summary. A clinical application of this system seemed to be useful for assessment of quantitative assessment of alveolar provided high coefficient of determination is obtained by the modified adoption of copper step numbers and the low coefficient of variation for the range of Cu-Equivalent value of alveolar bone from optimal kVp and exposure time for each x-ray machine.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.155-162
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• 2017

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination $R^2$ and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in $R^2$ and F-statistic.

• Korean Journal of Remote Sensing
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• v.29 no.6
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• pp.657-662
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• 2013

The comparison between $CO_2$ volume mixing ratios observed by GOSAT and TCCON from September 2009 through November 2012 was performed at Tsukuba and Saga, two downwind sites in East Asia. The temporal trends of $CO_2$ values obtained from GOSAT show good agreement with those observed by TCCON at these two by the TCCON, showing a coefficient of determination ($R^2$) of 0.65. The regression slop we obtained was 0.92, showing a small bias of GOSAT $CO_2$ values compared to those observed by TCCON. However, we found the higher correlation in fall and winter than that in spring and summer. The $CO_2$ volume mixing ratios observ sites. The $CO_2$ volume mixing ratios observed by GOSAT are also in good agreement with those measured ed by GOSAT are in good agreement with those measured by the TCCON at those two sites in fall and winter, showing a coefficient of determination ($R^2$) of 0.66 where as the correlation of determination obtained between GOSAT and TCCON was only 0.27 in spring and summer.