• Journal of Microbiology and Biotechnology
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• v.10 no.4
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• pp.476-481
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• 2000

A linear correlation, by the stepwise multiple regression analysis, was found between the sensory test of Sigumjang aroma and the gas chromatographic data which were transformed with logarithm. GC data is the most objective method to evaluate Sigumjang aroma. A multiple correlation coefficient and a determination coefficient of more than 0.9 were obtained at the 9th and 13th steps, respectively. At step 31, the coefficient of determination level of 0.95 was attained. The accuracy of its estimation became higher as the number of the variables entered into the regression model increased. Over 90% of the Sigumjang aroma was explained by 13 compounds indentified on GC. The contributing proportion of the peak 26 was the highest followed by peaks 57 (9.27%), 29 (7.51%), 54 (6.01%), 8 (5.99%), 49 (4.97%), and 13 (4.11%).

• Imaging Science in Dentistry
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• v.30 no.2
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• pp.101-108
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• 2000

Purpose : The effects of step numbers of copper wedge and exposure on the coefficient of determination (r²) of the conversion equation to Cu-equivalent image and on the Cu-equivalent value (mmCu) and it's coefficient of variation measured at each copper step and the mandibular premolar area were evaluated. Method: Digital image analyzing system consisted of scanner, personal computer, and a stepwedge with 10 steps of 0.03 mm copper in thickness as reference material was prepared for quantitative assessment of the bone mineral density. NIH image program was used for analyzing images. Results : The film having moderately high film density showed the discrepancy between the real thickness and the measured Cu-equivalent value of each copper step. The Cu-equivalent image was dependent on the determinational coefficient of the conversion equation than the coefficient of variance of the measured value. Conclusion : Obtaining conversion equation with high coefficient of determination and proper film exposure are supposed to be neccessary for quantitative assessment of bone density. Multiple steps in the range of the corresponding copper thickness to the bone density of the area to be measured should be prepared.

• Journal of the Korean Statistical Society
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• v.5 no.1
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• pp.19-28
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• 1976

In empirical study for fitting a multiple linear regression model for successive cross-sections data observed on the same set of independent variables over several time periods, one often faces the problem of poor $R^2$, the multiple coefficient of determination, which provides a standard measure of how good a specified regression line fits the sample 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.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.1
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• pp.29-43
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• 2012

We design a DEA-AR model using multiple regression analysis with new methods which limit weights. When there are multiple input and single output variables, our model can be used, and the weights of input variables use the regression coefficient and coefficient of determination. To verify the effectiveness of the new model, we evaluate the efficiency of the Regional Corporations in Korea. Accordance with statistical analysis, it proved that there is no difference between the efficiency value of the DEA-AR using AHP and our DEA-AR model. Our model can be applied to a lot of research by substituting DEA-AR model relying on AHP in the future.

• Magazine of the Korean Society of Agricultural Engineers
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• v.22 no.3
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• pp.75-87
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• 1980

Most hydro]ogic phenomena are the complex and organic products of multiple causations like climatic and hydro-geological factors. A certain significant correlation on the run-off in river basin would be expected and foreseen in advance, and the effect of each these causual and associated factors (independant variables; present-month rainfall, previous-month run-off, evapotranspiration and relative humidity etc.) upon present-month run-off(dependent variable) may be determined by multiple regression analysis. Functions between independant and dependant variables should be treated repeatedly until satisfactory and optimal combination of independant variables can be obtained. Reliability of the estimated function should be tested according to the result of statistical criterion such as analysis of variance, coefficient of determination and significance-test of regression coefficients before first estimated multiple regression model in historical sequence is determined. But some error between observed and estimated run-off is still there. The error arises because the model used is an inadequate description of the system and because the data constituting the record represent only a sample from a population of monthly discharge observation, so that estimates of model parameter will be subject to sampling errors. Since this error which is a deviation from multiple regression plane cannot be explained by first estimated multiple regression equation, it can be considered as a random error governed by law of chance in nature. This unexplained variance by multiple regression equation can be solved by stochastic approach, that is, random error can be stochastically simulated by multiplying random normal variate to standard error of estimate. Finally hybrid model on estimation of monthly run-off in nonhistorical sequence can be determined by combining the determistic component of multiple regression equation and the stochastic component of random errors. Monthly run-off in Naju station in Yong-San river basin is estimated by multiple regression model and hybrid model. And some comparisons between observed and estimated run-off and between multiple regression model and already-existing estimation methods such as Gajiyama formula, tank model and Thomas-Fiering model are done. The results are as follows. (1) The optimal function to estimate monthly run-off in historical sequence is multiple linear regression equation in overall-month unit, that is; Qn=0.788Pn+0.130Qn-1-0.273En-0.1 About 85% of total variance of monthly runoff can be explained by multiple linear regression equation and its coefficient of determination (R2) is 0.843. This means we can estimate monthly runoff in historical sequence highly significantly with short data of observation by above mentioned equation. (2) The optimal function to estimate monthly runoff in nonhistorical sequence is hybrid model combined with multiple linear regression equation in overall-month unit and stochastic component, that is; Qn=0. 788Pn+0. l30Qn-1-0. 273En-0. 10+Sy.t The rest 15% of unexplained variance of monthly runoff can be explained by addition of stochastic process and a bit more reliable results of statistical characteristics of monthly runoff in non-historical sequence are derived. This estimated monthly runoff in non-historical sequence shows up the extraordinary value (maximum, minimum value) which is not appeared in the observed runoff as a random component. (3) "Frequency best fit coefficient" (R2f) of multiple linear regression equation is 0.847 which is the same value as Gaijyama's one. This implies that multiple linear regression equation and Gajiyama formula are theoretically rather reasonable functions.

• Journal of the Korean Society for Nondestructive Testing
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• v.11 no.2
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• pp.22-31
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• 1991

Various types of ultrasonic techniques have been used for the estimation of compressive strength of concrete structures. However, conventional ultrasonic velocity method using only longitudial wave cannot be determined the compressive strength of concrete structures with accuracy. In this paper, by using the introduction of multiple parameter, e. g. velocity of shear wave, velocity of longitudinal wave, attenuation coefficient of shear wave, attenuation coefficient of longitudinal wave, combination condition, age and preservation method, multiple regression analysis method was applied to the determination of compressive strength of concrete structures. The experimental results show that velocity of shear wave can be estimated compressive strength of concrete with more accuracy compared with the velocity of longitudinal wave, accuracy of estimated error range of compressive strength of concrete structures can be enhanced within the range of ${\pm}$10% approximately.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.1
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• pp.25-31
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• 2003

There are a lot of factors influencing on the automobile fuel economy such as average speed, average acceleration, acceleration sum per kilometer, and so on. In this study, various driving data were recorded during road tests. The accumulated road test mileage in Seoul metropolitan area is around 1,300 kilometers. The data were analyzed by multivariate statistical techniques including correlation analysis, principal component analysis, and multiple linear regression analysis. The analyzed results show that the average trip time per kilometer is one of the most important factors to fuel consumption and the increase of the average speed is desirable for reducing emissions and fuel consumption.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.4104-4104
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• 2001

Milk somatic cell count (SCC) is a recognized indicator of cow health and milk quality. The potential of near infrared (NIR) spectroscopy in the region from 1100 to 2500nm to measure SCC content of cow milk was investigated. A total of 196 milk samples from 7 Holstein cows were collected for 28 days, consecutively, and analyzed for fat, protein, lactose and SCC. Three of the cows were healthy, and the rest had mastitis periods during the experiment. NIR transflectance milk spectra were obtained by the InfraAlyzer 500 spectrophotometer in a wavelength range from 1100 to 2500 nm. The calibration for logSCC was performed using partial least square (PLS) regression and different spectral data pretreatment. The best accuracy of determination was found for equation, obtained using smoothed absorbance data and 10 PLS factors. The standard error of calibration was 0.361, calibration coefficient of multiple correlation 0.868, standard error of prediction for independent validation set of samples 0.382, correlation coefficient 0.854 and the variation coefficient 7.63%. The accuracy of logSCC determination by NIR spectroscopy would allow health screening of cows, and differentiation between healthy and mastitic milk samples. When the spectral information was studied it has been found that SCC determination by NIR milk spectra was indirect and based on the related changes in milk composition. In the case of mastitis, when the disease occurred, the most significant factors that simultaneously influenced milk spectra were alteration of milk proteins and changes in ionic concentration of milk.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2000.11b
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• pp.188-195
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• 2000

This study was conducted to measure the moisture content of powdered food using RF impedance spectroscopic method. In frequency range of 1.0 to 30㎒, the impedance such as reactance and resistance of parallel plate type sample holder filled with wheat flour and red-pepper powder of which moisture content range were 5.93∼-17.07%w.b. and 10.87 ∼ 27.36%w.b., respectively, was characterized using by Q-meter (HP4342). The reactance was a better parameter than the resistance in estimating the moisture density defined as product of moisture content and bulk density which was used to eliminate the effect of bulk density on RF spectral data in this study. Multivariate data analyses such as principal component regression, partial least square regression and multiple linear regression were performed to develop one calibration model having moisture density and reactance spectral data as parameters for determination of moisture content of both wheat flour and red-pepper powder. The best regression model was one by the multiple linear regression model. Its performance for unknown data of powdered food was showed that the bias, standard error of prediction and determination coefficient are 0.179% moisture content, 1.679% moisture content and 0.8849, respectively.