• Communications for Statistical Applications and Methods
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• 제2권1호
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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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• 제17권2호
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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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• 한국데이터정보과학회 2005년도 춘계학술대회
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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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• 제13권1호
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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.

• 대한교통학회지
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• 제31권2호
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• pp.60-68
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• 2013

본 논문에서는 중력모형의 예측 정확도 향상을 위하여 복수의 중력모형을 구축하여 적용하는 방법을 개발하였다. 개발한 방법은 결정계수($R^2$)를 이용하여 목표수준을 결정하고, 중력모형을 구축한다. 구축된 중력모형의 결정계수가 목표수준을 만족하면 모형 구축을 종료하고, 장래 통행분포 예측을 행한다. 만약 결정계수가 목표수준을 만족하지 못하면 목표수준에 만족할 때까지 구축된 모형에서 표준화 잔차가 큰 순서로 죤 페어(Zone pair)를 제거한다. 제거된 죤 페어들은 구축된 모형을 기준으로 보면 +영역과 -영역으로 나누어지는데 각 영역에서 중력모형을 구축하고 목표수준에 도달할 수 있도록 한다. 제거해야 할 죤 페어가 존재하지 않으면 모형구축 작업이 중단되고, 장래 통행분포량 예측을 한다. 사례연구에서 개발된 방법을 42개 죤페어에 적용하여 보았는데, 기존방법, 즉 하나의 중력모형으로 구축하면 설명력($R^2$)이 51.3%였으나, 개발된 방법은 3개의 중력모형을 구축하고, 설명력($R^2$)이 90% 이상되었다. 또한, 장래 예측 정확도도 기존 방법보다 월등히 높은 것으로 검정 되었다.

• 응용통계연구
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• 제4권2호
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• pp.117-127
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• 1991

결정계수 $R^2$은 회귀분석에서 실제적으로는 매우 이용도가 높은 기술 측도라고 하겠으나, 회귀모형이 절편향을 포함하는 표준적인 선형회귀모형 이외인 경우에는 결정계수의 정의에 관하여 여러 논란이 있어 왔다. 절편항이 없는 선형회귀모형에서와 가중선형회귀모형, 로버스트 선형회귀모형에서의 결정계수의 적절한 정의와 용법이 대표적인 문제라고 하겠다. 기존의 여러 연구, 예를 들어 Kvalseth(1985) 나 Willet and Singer(1988)에서는 이러한 각 경우에 각기 적용될 수 있는 결정계수의 여러 변형들을 제안 $\cdot$ 이런 기존의 연구들이 일반적인 원칙이 없이 경우별로 단편적으로 대응하고 있을뿐더러 약간의 오류를 포함하고 있어 오히려 통계전문가가 아닌 통계 이용자들에게 혼란을 불러 일으킬 염려가 있다. 따라서 결정계수의 일반적 정의를 제안한 본 연구는 현재와 같은 결정계수의 여러변종의 범람으로 인한 혼란을 없애는 데 기여하리라고 생각된다. 이 통합결정계수는 尤度거리(likelihood distance)를 이용하여 정의되는데, 선형회귀모형 이외에도 비선형 회귀모형과 일반화 선형모형에 일관되게 적용 가능하다는 장점을 갖는다.

• 한국가축번식학회지
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• 제17권4호
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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.

• 치과방사선
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• 제29권1호
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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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• 제24권2호
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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.

• 대한원격탐사학회지
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• 제29권6호
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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.