• Title/Summary/Keyword: Polynomial Linear Regression Analysis

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FUZZY POLYNOMIAL REGRESSION ANALYSIS USING SHAPE PRESERVING IOERATION

  • Hong, Dug-Hun;Do, Hae-Young
    • Journal of applied mathematics & informatics
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    • v.8 no.3
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    • pp.869-880
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    • 2001
  • In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input-output data using shape preserving operations based on Tanaka’s approach. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using general linear program.

Improving Polynomial Regression Using Principal Components Regression With the Example of the Numerical Inversion of Probability Generating Function (주성분회귀분석을 활용한 다항회귀분석 성능개선: PGF 수치역변환 사례를 중심으로)

  • Yang, Won Seok;Park, Hyun-Min
    • The Journal of the Korea Contents Association
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    • v.15 no.1
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    • pp.475-481
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    • 2015
  • We use polynomial regression instead of linear regression if there is a nonlinear relation between a dependent variable and independent variables in a regression analysis. The performance of polynomial regression, however, may deteriorate because of the correlation caused by the power terms of independent variables. We present a polynomial regression model for the numerical inversion of PGF and show that polynomial regression results in the deterioration of the estimation of the coefficients. We apply principal components regression to the polynomial regression model and show that principal components regression dramatically improves the performance of the parameter estimation.

Optimized Neural Network Weights and Biases Using Particle Swarm Optimization Algorithm for Prediction Applications

  • Ahmadzadeh, Ezat;Lee, Jieun;Moon, Inkyu
    • Journal of Korea Multimedia Society
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    • v.20 no.8
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    • pp.1406-1420
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    • 2017
  • Artificial neural networks (ANNs) play an important role in the fields of function approximation, prediction, and classification. ANN performance is critically dependent on the input parameters, including the number of neurons in each layer, and the optimal values of weights and biases assigned to each neuron. In this study, we apply the particle swarm optimization method, a popular optimization algorithm for determining the optimal values of weights and biases for every neuron in different layers of the ANN. Several regression models, including general linear regression, Fourier regression, smoothing spline, and polynomial regression, are conducted to evaluate the proposed method's prediction power compared to multiple linear regression (MLR) methods. In addition, residual analysis is conducted to evaluate the optimized ANN accuracy for both training and test datasets. The experimental results demonstrate that the proposed method can effectively determine optimal values for neuron weights and biases, and high accuracy results are obtained for prediction applications. Evaluations of the proposed method reveal that it can be used for prediction and estimation purposes, with a high accuracy ratio, and the designed model provides a reliable technique for optimization. The simulation results show that the optimized ANN exhibits superior performance to MLR for prediction purposes.

A Study of the Nonlinear Characteristics Improvement for a Electronic Scale using Multiple Regression Analysis (다항식 회귀분석을 이용한 전자저울의 비선형 특성 개선 연구)

  • Chae, Gyoo-Soo
    • Journal of Convergence for Information Technology
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    • v.9 no.6
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    • pp.1-6
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    • 2019
  • In this study, the development of a weight estimation model of electronic scale with nonlinear characteristics is presented using polynomial regression analysis. The output voltage of the load cell was measured directly using the reference mass. And a polynomial regression model was obtained using the matrix and curve fitting function of MS Office Excel. The weight was measured in 100g units using a load cell electronic scale measuring up to 5kg and the polynomial regression model was obtained. The error was calculated for simple($1^{st}$), $2^{nd}$ and $3^{rd}$ order polynomial regression. To analyze the suitability of the regression function for each model, the coefficient of determination was presented to indicate the correlation between the estimated mass and the measured data. Using the third order polynomial model proposed here, a very accurate model was obtained with a standard deviation of 10g and the determinant coefficient of 1.0. Based on the theory of multi regression model presented here, it can be used in various statistical researches such as weather forecast, new drug development and economic indicators analysis using logistic regression analysis, which has been widely used in artificial intelligence fields.

Optimum Performance Analysis of KSR-III LRE (KSR-III 로켓엔진 최적성능 분석)

  • Ha, Seong-Up;Moon, Yoon-Wan;Ryu, Chul-Sung;Han, Sang-Yeop
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.4
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    • pp.80-87
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    • 2004
  • To understand the each performance parameter correlation of flight type liquid-propellant rocket engine for KSR-III(Korea Sounding Rocket-III), the analysis of engine stand-alone combustion test results was carried out. Considering the variation of ablative material combustion chamber caused by erosion, linear regression analysis that ignores oxidizer/fuel ratio effect and two-variable 2nd-order polynomial regression analysis that considers oxidizer/fuel ratio change were performed. It can be described that linear regression analysis is simple and very practical method, and can predict the performance within 1% error inside analyzed region. And two-variable 2nd-order polynomial regression analysis can predict with very high accuracy inside region and shows that KSR-III engine's optimum oxidizer/fuel ratio for thrust(or specific impulse) is 2.22 and that for combustion chamber pressure(or characteristic velocity) is 2.17.

Longitudinal Analysis of Body Weight and Feed Intake in Selection Lines for Residual Feed Intake in Pigs

  • Cai, W.;Wu, H.;Dekkers, J.C.M.
    • Asian-Australasian Journal of Animal Sciences
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    • v.24 no.1
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    • pp.17-27
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    • 2011
  • A selection experiment for reduced residual feed intake (RFI) in Yorkshire pigs consisted of a line selected for lower RFI (LRFI) and a random control line (CTRL). Longitudinal measurements of daily feed intake (DFI) and body weight (BW) from generation 5 of this experiment were used. The objectives of this study were to evaluate the use of random regression (RR) and nonlinear mixed models to predict DFI and BW for individual pigs, accounting for the substantial missing information that characterizes these data, and to evaluate the effect of selection for RFI on BW and DFI curves. Forty RR models with different-order polynomials of age as fixed and random effects, and with homogeneous or heterogeneous residual variance by month of age, were fitted for both DFI and BW. Based on predicted residual sum of squares (PRESS) and residual diagnostics, the quadratic polynomial RR model was identified to be best, but with heterogeneous residual variance for DFI and homogeneous residual variance for BW. Compared to the simple quadratic and linear regression models for individual pigs, these RR models decreased PRESS by 1% and 2% for DFI and by 42% and 36% for BW on boars and gilts, respectively. Given the same number of random effects as the polynomial RR models, i.e., two for BW and one for DFI, the non-linear Gompertz model predicted better than the polynomial RR models but not as good as higher order polynomial RR models. After five generations of selection for reduced RFI, the LRFI line had a lower population curve for DFI and BW than the CTRL line, especially towards the end of the growth period.

Analysis of the relationship between interest rate spreads and stock returns by industry (금리 스프레드와 산업별 주식 수익률 관계 분석)

  • Kim, Kyuhyeong;Park, Jinsoo;Suh, Jihae
    • Journal of Intelligence and Information Systems
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    • v.28 no.3
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    • pp.105-117
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    • 2022
  • This study analyzes the effects between stock returns and interest rate spread, difference between long-term and short-term interest rate through the polynomial linear regression analysis. The existing research concentrated on the business forecast through the interest rate spread focusing on the US market. The previous studies verified the interest rate spread based on the leading indicators of business forecast by moderating the period of long-term/short-term interest rates and analyzing the degree of leading. After the 7th reform of composite indices of business indicators in Korea of 2006, the interest rate spread was included in the items of composing the business leading indicators, which is utilized till today. Nevertheless, there are a few research on stock returns of each industry and interest rate spread in domestic stock market. Therefore, this study analyzed the stock returns of each industry and interest rate spread targeting Korean stock market. This study selected the long-term/short-term interest rates with high causality through the regression analysis, and then understood the correlations with each leading period and industry. To overcome the limitation of the simple linear regression analysis, polynomial linear regression analysis is used, which raised explanatory power. As a result, the high causality was verified when using differences between returns of corporate bond(AA-) without guarantee for three years by leading six months and call rate returns as interest rate spread. In addition, analyzing the stock returns of each industry, the relation between the relevant interest rate spread and returns of the automobile industry was the closest. This study is significant in the aspect of verifying the causality of interest rate spread, business forecast, and stock returns in Korea. Even though it could be limited to forecast the stock price by using only the interest rate spread, it would be working as a strong factor when it is properly utilized with other various factors.

Beverage Sales Data Analysis and Prediction using Polynomial Models (다항식 모델을 이용한 음료 판매 데이터 분석 및 예측)

  • Lee, Min Goo;Park, Yong Kuk;Jung, Kyung Kwon
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2014.10a
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    • pp.701-704
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    • 2014
  • This Paper proposed the analysis and prediction method of beverage sales. We assumed weather had a relationship with beverage sales. We got the output as sales amount from a temperature and humidity of weather as input by using polynomial equation. We had modelling as quadric function with input and output data. In order to verify the effectiveness of proposed method, the sales data were collected over a 4 months during February 2014. The results showed that the proposed method can estimate sales data.

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Axial load prediction in double-skinned profiled steel composite walls using machine learning

  • G., Muthumari G;P. Vincent
    • Computers and Concrete
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    • v.33 no.6
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    • pp.739-754
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    • 2024
  • This study presents an innovative AI-driven approach to assess the ultimate axial load in Double-Skinned Profiled Steel sheet Composite Walls (DPSCWs). Utilizing a dataset of 80 entries, seven input parameters were employed, and various AI techniques, including Linear Regression, Polynomial Regression, Support Vector Regression, Decision Tree Regression, Decision Tree with AdaBoost Regression, Random Forest Regression, Gradient Boost Regression Tree, Elastic Net Regression, Ridge Regression, and LASSO Regression, were evaluated. Decision Tree Regression and Random Forest Regression emerged as the most accurate models. The top three performing models were integrated into a hybrid approach, excelling in accurately estimating DPSCWs' ultimate axial load. This adaptable hybrid model outperforms traditional methods, reducing errors in complex scenarios. The validated Artificial Neural Network (ANN) model showcases less than 1% error, enhancing reliability. Correlation analysis highlights robust predictions, emphasizing the importance of steel sheet thickness. The study contributes insights for predicting DPSCW strength in civil engineering, suggesting optimization and database expansion. The research advances precise load capacity estimation, empowering engineers to enhance construction safety and explore further machine learning applications in structural engineering.

A New Modeling Approach to Fuzzy-Neural Networks Architecture (퍼지 뉴럴 네트워크 구조로의 새로운 모델링 연구)

  • Park, Ho-Sung;Oh, Sung-Kwun;Yoon, Yang-Woung
    • Journal of Institute of Control, Robotics and Systems
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    • v.7 no.8
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    • pp.664-674
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    • 2001
  • In this paper, as a new category of fuzzy-neural networks architecture, we propose Fuzzy Polynomial Neural Networks (FPNN) and discuss a comprehensive design methodology related to its architecture. FPNN dwells on the ideas of fuzzy rule-based computing and neural networks. The FPNN architecture consists of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as Fuzzy Polynomial Neuron(FPN). The conclusion part of the rules, especially the regression polynomial, uses several types of high-order polynomials such as linear, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. It is worth stressing that the number of the layers and the nods in each layer of the FPNN are not predetermined, unlike in the case of the popular multilayer perceptron structure, but these are generated in a dynamic manner. With the aid of two representative time series process data, a detailed design procedure is discussed, and the stability is introduced as a measure of stability of the model for the comparative analysis of various architectures.

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