• Title/Summary/Keyword: multi-variable linear regression

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Multi-objective Genetic Algorithm for Variable Selection in Linear Regression Model and Application (선형회귀모델의 변수선택을 위한 다중목적 유전 알고리즘과 응용)

  • Kim, Dong-Il;Park, Cheong-Sool;Baek, Jun-Geol;Kim, Sung-Shick
    • Journal of the Korea Society for Simulation
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    • v.18 no.4
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    • pp.137-148
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    • 2009
  • The purpose of this study is to implement variable selection algorithm which helps construct a reliable linear regression model. If we use all candidate variables to construct a linear regression model, the significance of the model will be decreased and it will cause 'Curse of Dimensionality'. And if the number of data is less than the number of variables (dimension), we cannot construct the regression model. Due to these problems, we consider the variable selection problem as a combinatorial optimization problem, and apply GA (Genetic Algorithm) to the problem. Typical measures of estimating statistical significance are $R^2$, F-value of regression model, t-value of regression coefficients, and standard error of estimates. We design GA to solve multi-objective functions, because statistical significance of model is not to be estimated by a single measure. We perform experiments using simulation data, designed to consider various kinds of situations. As a result, it shows better performance than LARS (Least Angle Regression) which is an algorithm to solve variable selection problems. We modify algorithm to solve portfolio selection problem which construct portfolio by selecting stocks. We conclude that the algorithm is able to solve real problems.

Estimating Demand Functions of Tractor, Combine and Rice Transplanter (트랙터, 콤바인, 이앙기의 수요 함수 추정)

  • Kim K.;Park C.K.;Kim K.U.;Kim B.G.
    • Journal of Biosystems Engineering
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    • v.31 no.3 s.116
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    • pp.194-202
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    • 2006
  • Using a multi-variable linear regression technique and SUR(seemingly unrelated regression) model, the demand functions of tractor, combine and rice transplanter were estimated. The demand was regarded as an annual supply of each machine and modeled as a function of 11 independent variables which reflect the actual farmer's income, actual prices of farm machines, previous supply, previous stock, actual amount of available subsidy, actual amount of available loan, arable land, import of farm machines and rice price. The actual amount of available loan affects most significantly the demand functions. The actual farmer's income, actual farmer's asset, loan coverage, and rice price affect the demand positively while prices of farm machines and import negatively. The annual demands of tractor, combine and rice transplanter estimated using the demand functions were also presented over the next 4 years.

Subset selection in multiple linear regression: An improved Tabu search

  • Bae, Jaegug;Kim, Jung-Tae;Kim, Jae-Hwan
    • Journal of Advanced Marine Engineering and Technology
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    • v.40 no.2
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    • pp.138-145
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    • 2016
  • This paper proposes an improved tabu search method for subset selection in multiple linear regression models. Variable selection is a vital combinatorial optimization problem in multivariate statistics. The selection of the optimal subset of variables is necessary in order to reliably construct a multiple linear regression model. Its applications widely range from machine learning, timeseries prediction, and multi-class classification to noise detection. Since this problem has NP-complete nature, it becomes more difficult to find the optimal solution as the number of variables increases. Two typical metaheuristic methods have been developed to tackle the problem: the tabu search algorithm and hybrid genetic and simulated annealing algorithm. However, these two methods have shortcomings. The tabu search method requires a large amount of computing time, and the hybrid algorithm produces a less accurate solution. To overcome the shortcomings of these methods, we propose an improved tabu search algorithm to reduce moves of the neighborhood and to adopt an effective move search strategy. To evaluate the performance of the proposed method, comparative studies are performed on small literature data sets and on large simulation data sets. Computational results show that the proposed method outperforms two metaheuristic methods in terms of the computing time and solution quality.

Multivariate Analysis for Clinicians (임상의를 위한 다변량 분석의 실제)

  • Oh, Joo Han;Chung, Seok Won
    • Clinics in Shoulder and Elbow
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    • v.16 no.1
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    • pp.63-72
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    • 2013
  • In medical research, multivariate analysis, especially multiple regression analysis, is used to analyze the influence of multiple variables on the result. Multiple regression analysis should include variables in the model and the problem of multi-collinearity as there are many variables as well as the basic assumption of regression analysis. The multiple regression model is expressed as the coefficient of determination, $R^2$ and the influence of independent variables on result as a regression coefficient, ${\beta}$. Multiple regression analysis can be divided into multiple linear regression analysis, multiple logistic regression analysis, and Cox regression analysis according to the type of dependent variables (continuous variable, categorical variable (binary logit), and state variable, respectively), and the influence of variables on the result is evaluated by regression coefficient${\beta}$, odds ratio, and hazard ratio, respectively. The knowledge of multivariate analysis enables clinicians to analyze the result accurately and to design the further research efficiently.

Optimal Process Condition for Products with Multi-Categorical Ordinal Quality Characteristic (다범주 순서형 품질특성을 갖는 제품의 최적 공정조건 결정에 관한 연구)

  • Kim Sang-Cheol;Yun Won-Young;Chun Young-Rok
    • Journal of Korean Society for Quality Management
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    • v.32 no.3
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    • pp.109-125
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    • 2004
  • This paper deals with an optimal process control problem in production of hull structural steel plate with high defective rate. The main quality characteristic(dependent variable) is the internal quality(defect) of plates and is dependent on process parameters(independent variables). The dependent variable(quality characteristics) has three categorical ordinal data and there are 35 independent variables(29 continuous variables and 6 categorical variables). In this paper, we determine the main factors and to develop the mathematical model between internal quality predicted probabilities and the main factors. Secondly, we find out the optimal process condition of main factors through analysis of variance(ANOVA) using simulation. We consider three models to obtain the main factors and the optimal process condition: linear, quadratic, error models.

Customer Experience and Repurchase Intention in Multi-Channel: Customer Satisfaction as Mediating Variable

  • MUSTIKASARI, Anita;KRISNAWATI, Maria;SUTRISNO, Endro
    • The Journal of Industrial Distribution & Business
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    • v.12 no.3
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    • pp.7-19
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    • 2021
  • Purpose: This study aims to examine customer experience toward repurchase intention in offline and online stores and discuss customer satisfaction as a mediator variable. Research design, data, and methodology: This study investigates customer experience that consists of product, customer service, staff service, shopping environment and shopping procedure toward customer satisfaction using Regression Linear. This study also measures customer satisfaction as a mediated variable in the relationship between customer experience and repurchase intention using Sobel Test. Results: Almost all of the customer experience hypothesis is significant toward customer satisfaction, shopping process experience in the context of the online channel to customer satisfaction is not significant. We also found that customer satisfaction can be mediated variable in customer experience toward repurchase intention. Conclusions: Retails who want to make customers feel satisfied to have to make sure that have good resources in improving the product, the customer service is easy to contact to find the solution over customer problem in purchasing product, also develop the staff member skill in functional product knowledge, presentations, and communicating with customers online or offline, the retailer has to create enjoyment and pleasurable customer emotion through the shopping environment and also give seamless shopping experience to their customer in two-channel.

Comparison of CT numbers between cone-beam CT and multi-detector CT (Cone-beam CT와 multi-detector CT영상에서 측정된 CT number에 대한 비교연구)

  • Kim, Dong-Soo;Han, Won-Jeong;Kim, Eun-Kyung
    • Imaging Science in Dentistry
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    • v.40 no.2
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    • pp.63-68
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    • 2010
  • Purpose : To compare the CT numbers on 3 cone-beam CT (CBCT) images with those on multi-detector CT (MDCT) image using CT phantom and to develop linear regressive equations using CT numbers to material density for all the CT scanner each. Materials and Methods : Mini CT phantom comprised of five 1 inch thick cylindrical models with 1.125 inches diameter of materials with different densities (polyethylene, polystyrene, plastic water, nylon and acrylic) was used. It was scanned in 3 CBCTs (i-CAT, Alphard VEGA, Implagraphy SC) and 1 MDCT (Somatom Emotion). The images were saved as DICOM format and CT numbers were measured using OnDemand 3D. CT numbers obtained from CBCTs and MDCT images were compared and linear regression analysis was performed for the density, $\rho$ ($g/cm^3$), as the dependent variable in terms of the CT numbers obtained from CBCTs and MDCT images. Results : CT numbers on i-CAT and Implagraphy CBCT images were smaller than those on Somatom Emotion MDCT image (p<0.05). Linear relationship on a range of materials used for this study were $\rho$=0.001H+1.07 with $R^2$ value of 0.999 for Somatom Emotion, $\rho$=0.002H+1.09 with $R^2$ value of 0.991 for Alphard VEGA, $\rho$=0.001H+1.43 with $R^2$ value of 0.980 for i-CAT and $\rho$=0.001H+1.30 with $R^2$ value of 0.975 for Implagraphy. Conclusion: CT numbers on i-CAT and Implagraphy CBCT images were not same as those on Somatom Emotion MDCT image. The linear regressive equations to determine the density from the CT numbers with very high correlation coefficient were obtained on three CBCT and MDCT scan.

Development of Neural Network Model for Pridiction of Daily Maximum Ozone Concentration in Summer (하계의 일 최고 오존농도 예측을 위한 신경망모델의 개발)

  • 김용국;이종범
    • Journal of Korean Society for Atmospheric Environment
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    • v.10 no.4
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    • pp.224-232
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    • 1994
  • A new neural network model has been developed to predict short-term air pollution concentration. In addition, a multiple regression model widely used in statistical analysis was tested. These models were applied for prediction of daily maximum ozone concentration in Seoul during the summer season of 1991. The time periods between May and September 1989 and 1990 were utilized to train set of learning patterns in neural network model, and to estimate multiple regression model. To evaluate the results of the different models, several Performance indices were used. The results indicated that the multiple regression model tended to underpredict the daily maximum ozone concentration with small r$^{2}$(0.38). Also, large errors were found in this model; 21.1 ppb for RMSE, 0.324 for NMSE, and -0.164 for MRE. On the other hand, the results obtained from the neural network model were very promising. Thus, we can know that this model has a prominent efficiency in the adaptive control for the non-linear multi- variable systems such as photochemical oxidants. Also, when the recent new information was added in the neural network model, prediction accuracy was increased. From the new model, the values of RMSE, NMSE and r$^{2}$ were 13.2ppb, 0.089, 0.003 and 0.55 respectively.

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Estimation of drift force by real ship using multiple regression analysis (다중회귀분석에 의한 실선의 표류력 추정)

  • AHN, Jang-Young;KIM, Kwang-il;KIM, Min-Son;LEE, Chang-Heon
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.57 no.3
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    • pp.236-245
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    • 2021
  • In this study, a drifting test using a experimental vessel (2,966 tons) in the northern waters of Jeju was carried out for the first time in order to obtain the fundamental data for drift. During the test, it was shown that the average leeway speed and direction by GPS position were 0.362 m/s and 155.54° respectively and the leeway rate for wind speed was 8.80%. The analysis of linear regression modes about leeway speed and direction of the experimental vessel indicated that wind or current (i.e. explanatory variable) had a greater influence upon response variable (e.g. leeway speed or direction) with the speed of the wind and current rather than their directions. On the other hand, the result of multiple regression model analysis was able to predict that the direction was negative, and it was demonstrated that predicted values of leeway speed and direction using an experimental vessel is to be more influential by current than wind while the leeway speed through variance and covariance was positive. In terms of the leeway direction of the experimental vessel, the same result of the leeway speed appeared except for a possibility of the existence of multi-collinearity. Then, it can be interpreted that the explanatory variables were less descriptive in the predicted values of the leeway direction. As a result, the prediction of leeway speed and direction can be demonstrated as following equations. Ŷ1= 0.4031-0.0032X1+0.0631X2-0.0010X3+0.4110X4 Ŷ2= 0.4031-0.6662X1+27.1955X2-0.6787X3-420.4833X4 However, many drift tests using actual vessels and various drifting objects will provide reasonable estimations, so that they can help search and rescue fishing gears as well.

Development of Ship Valuation Model by Neural Network (신경망기법을 활용한 선박 가치평가 모델 개발)

  • Kim, Donggyun;Choi, Jung-Suk
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.27 no.1
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    • pp.13-21
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    • 2021
  • The purpose of this study is to develop the ship valuation model by utilizing the neural network model. The target of the valuation was secondhand VLCC. The variables were set as major factors inducing changes in the value of ship through prior research, and the corresponding data were collected on a monthly basis from January 2000 to August 2020. To determine the stability of subsequent variables, a multi-collinearity test was carried out and finally the research structure was designed by selecting six independent variables and one dependent variable. Based on this structure, a total of nine simulation models were designed using linear regression, neural network regression, and random forest algorithm. In addition, the accuracy of the evaluation results are improved through comparative verification between each model. As a result of the evaluation, it was found that the most accurate when the neural network regression model, which consist of a hidden layer composed of two layers, was simulated through comparison with actual VLCC values. The possible implications of this study first, creative research in terms of applying neural network model to ship valuation; this deviates from the existing formalized evaluation techniques. Second, the objectivity of research results was enhanced from a dynamic perspective by analyzing and predicting the factors of changes in the shipping. market.