• Title/Summary/Keyword: Linear Multivariate Regression

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New Dispersion Function in the Rank Regression

  • Choi, Young-Hun
    • Communications for Statistical Applications and Methods
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    • v.9 no.1
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    • pp.101-113
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    • 2002
  • In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

Price Monitoring Automation with Marketing Forecasting Methods

  • Oksana Penkova;Oleksandr Zakharchuk;Ivan Blahun;Alina Berher;Veronika Nechytailo;Andrii Kharenko
    • International Journal of Computer Science & Network Security
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    • v.23 no.9
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    • pp.37-46
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    • 2023
  • The main aim of the article is to solve the problem of automating price monitoring using marketing forecasting methods and Excel functionality under martial law. The study used the method of algorithms, trend analysis, correlation and regression analysis, ANOVA, extrapolation, index method, etc. The importance of monitoring consumer price developments in market pricing at the macro and micro levels is proved. The introduction of a Dummy variable to account for the influence of martial law in market pricing is proposed, both in linear multiple regression modelling and in forecasting the components of the Consumer Price Index. Experimentally, the high reliability of forecasting based on a five-factor linear regression model with a Dummy variable was proved in comparison with a linear trend equation and a four-factor linear regression model. Pessimistic, realistic and optimistic scenarios were developed for forecasting the Consumer Price Index for the situation of the end of the Russian-Ukrainian war until the end of 2023 and separately until the end of 2024.

Evaluating Variable Selection Techniques for Multivariate Linear Regression (다중선형회귀모형에서의 변수선택기법 평가)

  • Ryu, Nahyeon;Kim, Hyungseok;Kang, Pilsung
    • Journal of Korean Institute of Industrial Engineers
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    • v.42 no.5
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    • pp.314-326
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    • 2016
  • The purpose of variable selection techniques is to select a subset of relevant variables for a particular learning algorithm in order to improve the accuracy of prediction model and improve the efficiency of the model. We conduct an empirical analysis to evaluate and compare seven well-known variable selection techniques for multiple linear regression model, which is one of the most commonly used regression model in practice. The variable selection techniques we apply are forward selection, backward elimination, stepwise selection, genetic algorithm (GA), ridge regression, lasso (Least Absolute Shrinkage and Selection Operator) and elastic net. Based on the experiment with 49 regression data sets, it is found that GA resulted in the lowest error rates while lasso most significantly reduces the number of variables. In terms of computational efficiency, forward/backward elimination and lasso requires less time than the other techniques.

MOISTURE CONTENT MEASUREMENT OF POWDERED FOOD USING RF IMPEDANCE SPECTROSCOPIC METHOD

  • Kim, K. B.;Lee, J. W.;S. H. Noh;Lee, S. S.
    • 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.

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A study on the multivariate sliced inverse regression (다변량 분할 역회귀모형에 관한 연구)

  • 이용구;이덕기
    • The Korean Journal of Applied Statistics
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    • v.10 no.2
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    • pp.293-308
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    • 1997
  • Sliced inverse regression is a method for reducing the dimension of the explanatory variable X without going through any parametric or nonparametric model fitting process. This method explores the simplicity of the inverse view of regression; that is, instead of regressing the univariate output varable y against the multivariate X, we regress X against y. In this article, we propose bivariate sliced inverse regression, whose method regress the multivariate X against the bivariate output variables $y_1, Y_2$. Bivariate sliced inverse regression estimates the e.d.r. directions of satisfying two generalized regression model simultaneously. For the application of bivariate sliced inverse regression, we decompose the output variable y into two variables, one variable y gained by projecting the output variable y onto the column space of X and the other variable r through projecting the output variable y onto the space orthogonal to the column space of X, respectively and then estimate the e.d.r. directions of the generalized regression model by utilize two variables simultaneously. As a result, bivariate sliced inverse regression of considering the variable y and r simultaneously estimates the e.d.r. directions efficiently and steadily when the regression model is linear, quadratic and nonlinear, respectively.

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Bayes Prediction Density in Linear Models

  • Kim, S.H.
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.797-803
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    • 2001
  • This paper obtained Bayes prediction density for the spatial linear model with non-informative prior. It showed the results that predictive inferences is completely unaffected by departures from the normality assumption in the direction of the elliptical family and the structure of prediction density is unchanged by more than one additional future observations.

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A study on log-density ratio in logistic regression model for binary data

  • Kahng, Myung-Wook
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.1
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    • pp.107-113
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    • 2011
  • We present methods for studying the log-density ratio, which allow us to select which predictors are needed, and how they should be included in the logistic regression model. Under multivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of many predictors. The linear, quadratic and crossproduct terms are required in general. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms.

EXPERIMENTAL ANALYSIS OF DRIVING PATTERNS AND FUEL ECONOMY FOR PASSENGER CARS IN SEOUL

  • Sa, J.-S.;Chung, N.-H.;Sunwoo, M.-H.
    • International Journal of Automotive Technology
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    • v.4 no.2
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    • pp.101-108
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    • 2003
  • There are a lot of factors that influence automotive fuel economy such as average trip time per kilometer, average trip speed, the number of times of vehicle stationary, and so forth. These factors depend on road conditions and traffic environment. In this study, various driving data were measured and recorded during road tests in Seoul. The accumulated road test mileage is around 1,300 kilometers. The objective of the study is to identify the driving patterns of the Seoul metropolitan area and to analyze the fuel economy based on these driving patterns. The driving data which was acquired through road tests was analysed statistically in order to obtain the driving characteristics via modal analysis, speed analysis, and speed-acceleration analysis. Moreover, the driving data was analyzed by multivariate statistical techniques including correlation analysis, principal component analysis, and multiple linear regression analysis in order to obtain the relationships between influencing factors on fuel economy. The analyzed results show that the average speed is around 29.2 km/h, and the average fuel economy is 10.23 km/L. The vehicle speed of the Seoul metropolitan area is slower, and the stop-and-go operation is more frequent than FTP-75 test mode which is used for emission and fuel economy tests. The average trip time per kilometer is one of the most important factors in fuel consumption, and the increase of the average speed is desirable for reducing emissions and fuel consumption.

EPB-TBM performance prediction using statistical and neural intelligence methods

  • Ghodrat Barzegari;Esmaeil Sedghi;Ata Allah Nadiri
    • Geomechanics and Engineering
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    • v.37 no.3
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    • pp.197-211
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    • 2024
  • This research studies the effect of geotechnical factors on EPB-TBM performance parameters. The modeling was performed using simple and multivariate linear regression methods, artificial neural networks (ANNs), and Sugeno fuzzy logic (SFL) algorithm. In ANN, 80% of the data were randomly allocated to training and 20% to network testing. Meanwhile, in the SFL algorithm, 75% of the data were used for training and 25% for testing. The coefficient of determination (R2) obtained between the observed and estimated values in this model for the thrust force and cutterhead torque was 0.19 and 0.52, respectively. The results showed that the SFL outperformed the other models in predicting the target parameters. In this method, the R2 obtained between observed and predicted values for thrust force and cutterhead torque is 0.73 and 0.63, respectively. The sensitivity analysis results show that the internal friction angle (φ) and standard penetration number (SPT) have the greatest impact on thrust force. Also, earth pressure and overburden thickness have the highest effect on cutterhead torque.

On a Bayesian Estimation of Multivariate Regression Models with Constrained Coefficient Matrix

  • Kim, Hea-Jung
    • Journal of Korean Society for Quality Management
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    • v.26 no.4
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    • pp.151-165
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    • 1998
  • Consider the linear multivariate regression model $Y=X_1B_1+X_2B_2+U$, where Vec(U)~N(0, $\sum \bigotimes I_N$). This paper is concerned with Bayes infreence of the model when it is suspected that the elements of $B_2$ are constrained in the form of intervals. The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior desnities of the parameters under a generalized conjugate prior is developed. It is shown that the a, pp.oach is straightforward to specify distributionally and to implement computationally, with output readily adopted for required inference summaries. The method developed is a, pp.ied to a real problem.

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