R-squared measurement in multifactor pricing model

Wang, Jianlong; Jaaman, Saiful Hafizah; Samsudin, Humaida Banu

doi:10.1063/1.4931328

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…The fitting accuracy provided by the R-squared (R 2 ) values indicates the curve's ability in fitting the real raw signal. R 2 values close to one imply that the estimations completely fit the data [81,82]. The adjusted R 2 is crucial in determining how well the model explains the response variable from the independent factors.…”

Section: Mathematical Modellingmentioning

confidence: 99%

Optimization of Laser Cutting Parameters for PMMA Using Metaheuristic Algorithms

Ürgün,

Yiğit,

Fidan

et al. 2024

Arab J Sci Eng

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This study fixates on determining the optimum laser input parameters that simultaneously meet the desired kerf width and depth during CO2 laser cutting of various polymethylmethacrylate (PMMA) sheets. It has three contributions. The first is to model the cutting process of PMMA by polynomial curve fitting as a function of laser power, laser speed, and standoff distance. R-squared (R2), adjusted R2 and root-mean-square error (RMSE) criteria were taken into account to measure the performance of the proposed model. The effect of laser parameters on the process is investigated by analysis of variance (ANOVA) and sensitivity analysis. The second is to optimize the derived nonlinear regression models using genetic algorithm (GA), particle swarm optimization (PSO), whale optimization algorithm (WOA) and ant lion optimization (ALO) metaheuristic methods and compare the performances of the algorithms. The third is to compare the adequacy of the optimization process with the artificial neural network (ANN). The investigations exhibited that the best-fitting polynomials are obtained with the R2 and adjusted R2 values of over 99% and 97%, respectively. ANOVA and sensitivity test revealed that the sensitivity of the laser power, which is the most effective parameter, was 150 at low powers and decreased to 0 as the power value increased. When the nozzle distance is 4.1, the proposed metaheuristics gave effective and sufficiently accurate results. PSO stood out in terms of both best cost value (3.49 × 10–8) and relative error value (0.19%). The relative error of the ANN was found as 3% in terms of kerf depth.

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Section: Mathematical Modellingmentioning

confidence: 99%

Optimization of Laser Cutting Parameters for PMMA Using Metaheuristic Algorithms

Ürgün,

Yiğit,

Fidan

et al. 2024

Arab J Sci Eng

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“…The fitted model was evaluated by considering the statistical criteria. The coefficient of determination (r 2 ) and adjusted R-square (R 2 adjusted ) were the evaluated by statistical criteria [10,21]. The r 2 and R 2 adjusted are calculated by Equations (6) and (9), respectively.…”

Section: Statistical Analysis For Kinetic Modeling Extractionsmentioning

confidence: 99%

“…The r 2 value is calculated to be between 0 and 1. The model with higher r 2 and R 2 adjusted for saponin extraction is considered the best choice for modeling the saponin extraction behavior during processing [21][22].…”

Section: Statistical Analysis For Kinetic Modeling Extractionsmentioning

confidence: 99%

Kinetic Study of Saponin Extraction from Sapindus rarak DC by Ultrasound-Assisted Extraction Methods

Nafiunisa

Aryanti

Wardhani

2019

Bull. Chem. React. Eng. Catal.

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Saponin is an important plant-derived compound that is commonly found in sapindaceae plants, such as Sapindus rarak DC. Saponin is extensively used in plenty of industries as a detergent or emulsifying agent in cleansers, shampoos, and cosmetics. The extraction of saponin was previously studied and shows that the extraction assisted by ultrasonic waves was found to be an effective method. However, the previous studies have rarely examined the extraction kinetic study of the ultrasound-assisted extraction (UAE). In the present study, the extraction of saponin from Sapindus rarak DC and its extraction kinetics is conducted. The results show that the highest saponin yield of 354.92 (mg of saponin per gram of dry feed) was obtained from the extraction using a solid-to-liquid (S/L) ratio of 1:50 (w/v) at 50 °C. The amount of extracted saponin increased with the increase of extraction temperature as well as the solute ratio in the solution. However, increasing the temperature to 60 °C decreased the saponin yield. The results of a simple kinetics study of saponin extraction also show that the second-order kinetics model can better describe the UAE process, with an R 2 value of 0.929 and a rate coefficient of 0.00495 L.g -1 .min -1 . The experimental results agree well with the practical calculations obtained using the second-order kinetics model based on an average error of 6.79%. glycoconjugate with a triterpenoidal or steroidal hydrophobic backbone and one or two hydrophilic glycoside moieties attached to the backbone [2]. A combination of the nonpolar sapogenin and the polar chain of saponin is very similar to the structure of most synthetic surfactants, having lipophilic and hydrophilic molecular parts [3]. Considering this characteristic, saponin has great potential to alternate synthetic surfactants. This kind of natural surfactant is easily degradable in nature, shows low

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