• Title/Summary/Keyword: Polynomial Linear Regression Analysis

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An Alternative Model for Determining the Optimal Fertilizer Level (수도(水稻) 적정시비량(適正施肥量) 결정(決定)에 대한 대체모형(代替模型))

  • Chang, Suk-Hwan
    • Korean Journal of Soil Science and Fertilizer
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    • v.13 no.1
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    • pp.21-32
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    • 1980
  • Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

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Performance Evaluation of Statistical Methods Applicable to Estimating Remaining Battery Runtime of Mobile Smart Devices (모바일 스마트 장치 배터리의 남은 시간 예측에 적용 가능한 통계 기법들의 평가)

  • Tak, Sungwoo
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.22 no.2
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    • pp.284-294
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    • 2018
  • Statistical methods have been widely used to estimate the remaining battery runtime of mobile smart devices, such as smart phones, smart gears, tablets, and etc. However, existing work available in the literature only considers a particular statistical method. Thus, it is difficult to determine whether statistical methods are applicable to estimating thr remaining battery runtime of mobile devices or not. In this paper, we evaluated the performance of statistical methods applicable to estimating the remaining battery runtime of mobile smart devices. The statistical estimation methods evaluated in this paper are as follows: simple and moving average, linear regression, multivariate adaptive regression splines, auto regressive, polynomial curve fitting, and double and triple exponential smoothing methods. Research results presented in this paper give valuable data of insight to IT engineers who are willing to deploy statistical methods on estimating the remaining battery runtime of mobile smart devices.

Long-term Trend Analysis of Extreme Temperatures in East Asia Using Quantile Regression (분위수 회귀분석을 이용한 동아시아 지역 극한기온의 장기 추세 분석)

  • Kim, Sang-Wook;Song, Kanghyun;Yoo, Young-Eun;Son, Seok-Woo;Jeong, Su-Jong
    • Journal of Climate Change Research
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    • v.9 no.2
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    • pp.157-169
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    • 2018
  • This study explores the long?term trends of extreme temperatures of 270 observation stations in East Asia (China, Japan, and Korea) for 1961?2013. The 5th percentile of daily minimum temperatures (TN05%) and 95th percentile of daily maximum temperatures (TX95%), derived from the quantile regression, are particularly examined in term of their linear and nonlinear trends. The warming trends of TN05% are typically stronger than those of TX95% with more significant trends in winter than in summer for most stations. In both seasons, warming trends of TN05% tend to amplify with latitudes. The nonlinear trends, quantified by the $2^{nd}$?order polynomial fitting, exhibit different structures with seasons. While summer TN05% and TX95% were accelerated in time, winter TN05% underwent weakening of warming since the 2000s. These results suggest that extreme temperature trends in East Asia are not homogeneous in time and space.

An Analysis of the Relationship between Rainfall and Recession Hydrograph for Base Flow Separation (기저유출 분리를 위한 강우와 감수곡선간의 상관해석)

  • 이원환;김재한
    • Water for future
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    • v.18 no.1
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    • pp.85-94
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    • 1985
  • A method is developed for the separation of the major base flow in a river hydrograph combining the numerical techniques and the empirical methods. The linearized Boussinesq equation and the storage function are used to obtain the base flow recession. The shape of base flow curve made by the recharge of the groundwater table aquifer resulting from rainfall in determined by the Singh and Stall's graphical method, and the continuous from for the curve is approximated by the multiple and polynomial regression. this procedure was successfully tested for the separation of base flow and the establishment of hydrograph in a natural watershed. It was found that the direct numerical method applied to the homogeneous linear second order ordinary differential equation system is not suited to obtain the recession curve, and the case that the loss is generated in the partially penetrating stream can not be solved by the method of this study.

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Development of a New Munk-type Breaker Height Formula Using Machine Learning (머신러닝을 이용한 새로운 Munk-type 쇄파파고 예측식의 제안)

  • Choi, Byung-Jong;Nam, Hyung-Sik;Lee, Kwang-Ho
    • Journal of Navigation and Port Research
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    • v.45 no.3
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    • pp.165-172
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    • 2021
  • Breaking wave is one of the important design factors in the design of coastal and port structures as they are directly related to various physical phenomena occurring on the coast, such as onshore currents, sediment transport, shock wave pressure, and energy dissipation. Due to the inherent complexity of the breaking wave, many empirical formulas have been proposed to predict breaker indices such as wave breaking height and breaking depth using hydraulic models. However, the existing empirical equations for breaker indices mainly were proposed via statistical analysis of experimental data under the assumption of a specific equation. In this study, a new Munk-type empirical equation was proposed to predict the height of breaking waves based on a representative linear supervised machine learning technique with high predictive performance in various research fields related to regression or classification challenges. Although the newly proposed breaker height formula was a simple polynomial equation, its predictive performance was comparable to that of the currently available empirical formula.

The Relationship Between Smoke-Yields and Tipping Materials of the Cigarette (담배 연기발생과 Tipping 재료와의 상관성 연구)

  • Kim, Young-Hoh;Lee, Young-Taek;Kim, Sung-Han;Kim, Chung-Ryul;Kim, Jong-Yeol;Shin, Chang-Ho;Lee, Keun-Hoi
    • Journal of the Korean Society of Tobacco Science
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    • v.20 no.1
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    • pp.131-138
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    • 1998
  • In order to minimize the trial frequency in the new filter cigarette design, we studied the relationship between smoke yield and tipping materials of cigarette. A three levels full factorial design involving filament denier (X1,2.5-3.3d), Porosity of the acetate filter plug wrap (X2, 3,500-16,000CU) and porosity of the tip paper (X3, 400-1,200CU) was used. Three independent factors (Xl, X2, X3) were chosen for their effects on the various responses and the function was expressed in terms of a quadratic polynomial equation, Y : $\beta$o + $\beta$1Xl + $\beta$2X2 + $\beta$3X3 + $\beta$11Xl2 + $\beta$22X22+ $\beta$33X32 + $\beta$12X1X2 + $\beta$13XIX3 $\beta$23X2X3 which measures the linear, quadratic, and interaction effects. Twenty-nine trial numbers were obtained as a results of using a three levels full factorial design and it was analyzed by the multiple regression analysis with backward stepwise in STATISTICA/pc under restricted conditions. Tar yields of the cigarette was affected by porosity of tip paper (0.66), filament denier (0.47) and porosity of plug wrap (0.28) in the decreasing order, and linear effect of tip paper porosity (B3) and filament denier (91) were significant at a level of 0.01($\alpha$). The filament denier and tipping paper porosity interaction F ratio among three factors had a P-value of 0,000041, indicating higher interaction between these factors. Based on the analysis of variance, the model fitted for Tar (Y1) was significant at 5% confidence level and the coefficient of determination (0.96) was the proportion of variability in the data fitted for by the model.

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A Study on Water Level Rising Travel Time due to Discharge of Paldang Dam and Tide of Yellow Sea in Downstream Part of Paldang Dam (팔당댐 방류량과 황해(서해) 조석영향에 따른 팔당댐 하류부 수위상승도달시간 예측)

  • Lee, Jong-Kyu;Lee, Jae-Hong
    • Journal of the Korean Society of Hazard Mitigation
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    • v.10 no.2
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    • pp.111-122
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    • 2010
  • As the Jamsu-bridge and the floodplains of the Han River can be flooded during the rainy season, the exact prediction of the peak flood time is very important for mitigation of flood hazard. This study analyzes the effect of outflow of Paldang Dam and tide of Yellow Sea on the Han River. A target area is from the Paldang dam to Jeonryu gauging station. Water level of Jeonryu as a downstream boundary condition was estimated through multi linear regression analysis with outflow of Paldang dam and tide level of Incheon, because it was influenced by both a tide of Yellow Sea and outflow of Paldang dam. In this study, Water Level Rising Travel Time of the Jamsu-bridge and some floodplains in the Han River are estimated. Also, The second order polynomial expressions for relationships of outflow of Paldang Dam and Water Level Rising Travel Time were developed considering the outflow of Paldang dam and tide of Yellow Sea.

A Study on the Crustal Structure of the Southern Korean Peninsula through Gravity Analysis (중력자료분석을 통한 한반도 지각구조에 관한 연구)

  • Kwon, Byung Doo;Yang, Su Yeong
    • Economic and Environmental Geology
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    • v.18 no.4
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    • pp.309-320
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    • 1985
  • The crustal structure of the southern part of the Korean peninsula has been investigated based on the results of processing and anlaysis of gravity data. The processing techniques involve i) seperation of regional and residual anomalies by polynomial fittings, ii) power spectral analyses to determine the mean depth to the crustal base, iii) a filtering operation called "high-cut filtering and resampling," and iv) downward continuation to determine the undulation of the crustal base. The Bouguer anomalies show a lineation in the NE-SW direction which is the same as that of most mountains and tectonic lines of this area. The mean crustal depth is found to be 34km. The depth of the crustal base is varying in the estimated range of 26km to 36km with a thinner crust below the east coast than that of the west coast. The relief of the crustal base is appeared to be correlated with the regional surface topography. The linear regression relations computed between elevations and gravity anomalies indicate that the crust of this area seems to be not in perfect isostatic equilibrium but a little undercompensated state.

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Estimation of GARCH Models and Performance Analysis of Volatility Trading System using Support Vector Regression (Support Vector Regression을 이용한 GARCH 모형의 추정과 투자전략의 성과분석)

  • Kim, Sun Woong;Choi, Heung Sik
    • Journal of Intelligence and Information Systems
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    • v.23 no.2
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    • pp.107-122
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    • 2017
  • Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.

Application of Predictive Microbiology for Microbiological Shelf Life Estimation of Fresh-cut Salad with Short-term Temperature Abuse (PMP 모델을 활용한 시판 Salad의 Short-term Temperature Abuse 시 미생물학적 유통기한 예측에의 적용성 검토)

  • Lim, Jeong-Ho;Park, Kee-Jea;Jeong, Jin-Woong;Kim, Hyun-Soo;Hwang, Tae-Young
    • Food Science and Preservation
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    • v.19 no.5
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    • pp.633-638
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    • 2012
  • The aim of this study was to investigate the growth of aerobic bacteria in fresh-cut salad during short-term temperature abuse ($4{\sim}30^{\circ}C$temperature for 1, 2, and 3 h) for 72 h and to develop predictive models for the growth of total viable cells (TVC) based on Predictive food microbiology (PFM). The tool that was used, Pathogen Modeling program (PMP 7.0), predicts the growth of Aeromonas hydrophila (broth Culture, aerobic) at pH 5.6, NaCl 2.5%, and sodium nitrite 150 ppm for 72 h. Linear models through linear regression analysis; DMFit program were created based on the results obtained at 5, 10, 20, and $30^{\circ}C$ for 72 h ($r^2$ >0.9). Secondary models for the growth rate and lag time, as a function of storage temperature, were developed using the polynomial model. The initial contamination level of fresh-cut salad was 5.6 log CFU/mL of TVC during 72 h storage, and the growth rate of TVC was shown to be 0.020~1.083 CFU/mL/h ($r^2$ >0.9). Also, the growth tendency of TVC was similar to that of PMP (grow rate: 0.017~0.235 CFU/mL/h; $r^2=0.994{\sim}1.000$). The predicted shelf life with PMP was 24.1~626.5 h, and the estimated shelf life of the fresh-cut salads with short-term temperature abuse was 15.6~31.1 h. The predicted shelf life was more than two times the observed one. This result indicates a 'fail safe' model. It can be taken to a ludicrous extreme by adopting a model that always predicts that a pathogenic microorganism will grow even under conditions so strict as to be actually impossible.