This chapter deals with the multiple linear regression. That is we investigate the situation where the mean of a variable depends linearly on a set of covariables. The noise is supposed to be gaussian. We develop the ...
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(纸本)9782759817290
This chapter deals with the multiple linear regression. That is we investigate the situation where the mean of a variable depends linearly on a set of covariables. The noise is supposed to be gaussian. We develop the least squared method to get the parameter estimators and estimates of their precisions. This leads to design confidence intervals, prediction intervals, global tests, individual tests and more generally tests of submodels defined by linear constraints. Methods for model's choice and variables selection, measures of the quality of the fit, residuals study, diagnostic methods are presented. Finally identification of departures from the model's assumptions and the way to deal with these problems are addressed. A real data set is used to illustrate the methodology with software R. Note that this chapter is intended to serve as a guide for other regression methods, like logistic regression or AFT models and Cox regression.
Understanding student academic performance is a cornerstone for developing sustainable educational practices that benefit students, teachers, policymakers, and society. This analysis directly impacts students' abi...
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Understanding student academic performance is a cornerstone for developing sustainable educational practices that benefit students, teachers, policymakers, and society. This analysis directly impacts students' ability to engage in and promote sustainable practices, thereby shaping their future academic success. While many studies focus on predicting student performance based on a set of features, our study takes an approach by reducing these features into factors and analyzing their impact. We aim to identify the factors influencing student performance within the middle school education system using a combined approach of Factor Analysis for Mixed Data (FAMD) and multiple linear regression (MLR). Our analysis is based on a robust and reliable large dataset of 1,073,450 observations, encompassing qualitative and quantitative features. FAMD analysis identified four underlying factors: prior academic performance, academic delay, socioeconomic status, and class environment;all these factors have good to excellent reliability, with Cronbach's Alpha values ranging from 0.809 to 0.930. Feeding these factors into the MLR produces a robust model that explains 88.53% of the variance in the CGPA, indicating a strong fit. Prior Academic Performance factor emerges as the most powerful predictor, accounting for 76.6% of the explained variance. Academic Delay follows, explaining 14.34% of the variance. Socioeconomic Status contributes 6.02%, and Class Environment adds 3.03%, reflecting smaller but meaningful impacts. All predictors are statistically significant (p <0.001), confirming their critical roles in influencing student performance (CGPA). The insights gained from this study are critically important in the field of education. They enable teachers and educational leaders to identify at-risk students early and develop targeted interventions that address the factors influencing their performance. This approach aims to enhance learning outcomes, improve educational practices, a
In industrial plants noise is a major threat to the mental and physical health of employees. The risk increases more due to the presence of high noise sources and the presence of too many employees in textile industry...
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In industrial plants noise is a major threat to the mental and physical health of employees. The risk increases more due to the presence of high noise sources and the presence of too many employees in textile industry plants. This paper aims to predict the consequences of variables that may arise in the plants for acoustic improvement in textile industry plants. For this purpose, scenario plants have been created according to architectural properties and source-transmission path-receiver characteristics. The acoustic analyses of the scenario plants were performed in the ODEON Auditorium, and A-weighted sound pressure level (LA), noise reduction (NR), and reverberation time (RT) were determined. From the data, prediction equations were created with a multiple linear regression (MLR) model. To test the prediction equations, acoustic measurements were made, and acoustics improvements were carried out at a textile industry plant located in Turkiye. When the obtained results, the success, validity, and reliability of the prediction method are provided. In conclusion, the effect of architectural properties and the surface absorption on acoustic improvements in the textile industry was revealed. It was emphasized that prediction methods can be used to determine the effectiveness of interventions that can be applied in different facilities and can be improved in future studies.
The French Moss Survey employs forest mosses as indicators to monitor the deposition of atmospheric substances, notably focusing on cadmium (Cd), a known carcinogenic and contributor to respiratory illnesses. This com...
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There are some problems in the cost benefit estimation of enterprise environmental management, such as poor precision of estimation results, low correlation of estimation indexes and long estimation time. Therefore, a...
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Gait analysis plays a vital role in clinical assessments by providing clear, objective insights into how diseases progress, how impairments in walking are manifested, and the effectiveness of various treatments. Our s...
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The concept of annular wing has been reintroduced and applied as a result of the fast development of UAVs. The manufacturing problems of annular wings can be solved by 3D printing technology to realize rapid response ...
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The concept of annular wing has been reintroduced and applied as a result of the fast development of UAVs. The manufacturing problems of annular wings can be solved by 3D printing technology to realize rapid response improvement of design. To achieve the changing design targets immediately, a theoretical aerodynamic estimation method of annular wings is proposed in this paper to provide input for the rapid response process. In the method, annular wings with high L/D construction are decomposed into lateral and orthography configurations in corresponding projection directions. A small number of CFD simulation samples are adopted in the multiple linear regressions to realize the combination of configurations. Leading-edge suction analogy and drag polar equation are adopted for fast calculation. Then, the rapid estimation model is established exhaustively. The model is proven to be able to provide aerodynamic characteristics of annular wings accurately in the applicable ranges. The model has the potential to cover more configuration characteristics and larger ranges of applications. The method and model in this paper can provide input for 3D printing rapid response manufacturing of annular wing UAVs to short design and improvement cycles.
This study develops a signal-based trading strategy for the SPDR S&P 500 ETF Trust(SPY)using a multiple linear regression framework to analyze interrelationships between SPY and global equity indices across U.S.,E...
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This study develops a signal-based trading strategy for the SPDR S&P 500 ETF Trust(SPY)using a multiple linear regression framework to analyze interrelationships between SPY and global equity indices across U.S.,European,Asian,and Australian *** synthesizing historical pricing data from these major benchmarks,the model generates systematic trading signals through predicted price *** controlled training scenarios,the strategy achieved superior risk-adjusted returns compared to passive buy-and-hold approaches,demonstrating the value of cross-market signal *** the framework shows promise for algorithmic trading systems,the study acknowledges limitations in generalizing historical patterns to evolving market *** findings highlight opportunities to enhance predictive accuracy through machine learning architectures capable of processing nonlinear market *** insights advance quantitative trading research by establishing methodologies for cross-market signal synthesis and proposing pathways to develop adaptive models for volatile capital markets.
This research focused on developing and implementing a fault detection model for photovoltaic (PV) systems in remote areas, utilizing a Fuzzy-Based multiple linear regression (FMLR) approach. The study aimed to addres...
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Solar cells play a crucial role in generating clean, renewable energy. Accurate modeling of photovoltaic (PV) systems is essential for their development, and simulating their behaviors requires precise estimation of t...
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Solar cells play a crucial role in generating clean, renewable energy. Accurate modeling of photovoltaic (PV) systems is essential for their development, and simulating their behaviors requires precise estimation of their parameters. However, many optimization methods exhibit high or unstable root mean square error (RMSE) due to local optima entrapment and parameter interdependence. To address these challenges, we propose MLR-DE, a novel hybrid approach that integrates adaptive differential evolution (DE) with multiple linear regression (MLR). The main innovation is to decompose the PV model into linear coefficients and non-linear functions, the latter being iteratively estimated using DE. By treating nonlinear function outputs as independent variables and known measured currents as dependent variables, linear coefficients are analytically solved through MLR. Additionally, we introduce a data-fusion-based parameter generation scheme to improve DE's reliability by integrating historical crossover rates with estimated crossover rates. We validate MLR-DE through experiments across 11 PV configurations: 3 standard diode models and 8 environmental variants. The results demonstrate MLR-DE's superiority in all tests. It achieves the lowest average RMSE compared to other algorithms, with standard deviations at or below 2e-16. In the Friedman test, MLR-DE ranked first with a score of 1.94, outperforming the second-place (3.72) and last-place (7.58) competitors. The convergence curve shows that MLR-DE achieves convergence in less than 3,000 function evaluations over standard models, with an average convergence time of less than 0.6 s.
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