Using Power Transformations in Response Surface Methodology

Al-Saffar, Avan; Ali, Haithem Taha Mohammed

doi:10.1109/csase51777.2022.9759781

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…The residual vs. predicted plot and the residual vs. experimental run plot of the COF for the MoS 2 nanolubricants are shown in Figures 5 and 6, respectively, which is the significant diagnosis for the model. According to Draper and Smith [28,29], linear relationships are normal in error terms. Our results have shown no defects, suggesting that errors obey the normal distribution and endorse the experimental model.…”

Section: Coefficient Of Frictionmentioning

confidence: 99%

Microwave Synthesis of Molybdenum Disulfide Nanoparticles Using Response Surface Methodology for Tribological Application

et al. 2022

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We used response surface methodology (RSM) based on the central composite design (CCD) model to optimize the synthesis time and temperature of the molybdenum disulfide (MoS2) nanoparticles using the flexiWAVE microwave. Furthermore, the synthesized MoS2 nanoparticles were used in SAE 20W50 diesel engine oil to study the tribological properties according to ASTM standards using a four-ball tribotester. The optimization result shows that the synthesis temperature and time for the MoS2 nanoparticles in the microwave were ~200 °C and ~15 min, respectively, with a coefficient of friction (COF) and average wear scar diameter (WSD) of 0.0849 and 320 μm. Furthermore, the difference between the experimental and predicted values was minimal (1.88% (COF) and 0.625% (WSD)), which was similar to the optimization model.

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Section: Coefficient Of Frictionmentioning

confidence: 99%

Microwave Synthesis of Molybdenum Disulfide Nanoparticles Using Response Surface Methodology for Tribological Application

et al. 2022

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“…"For example, see [6][7][8][9][10][11]". While the second direction, which will be focused on in this chapter was concerned with the selecting methods of optimal power parameters in different PT families and datasets, "For example, see [8,[12][13][14][15][16][17][18]". There are many methods used to estimate the power parameters in Multiple Linear Regression (MLR).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, in addition to the traditional estimation methods, there are some other proposed methods based on the indicators of statistical modeling efficiency. These indicators were used as decision rules to choose the optimal value of the PT parameter [14,15]. In general, multiplicity of criteria used for a particular dataset does not lead to a single value or at least a closed feasible region for a power parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Anscombe, 1961 and Anscombe and Tukey 1963 indicated how a certain function of the residuals can be providing us with a certain insight into the PT model [19]. While some other authors went on to propose algorithms for power parameter selection using the goodness of fit tests of the normality transformed data [12,20] and coefficient of determination of the estimated linear regression of transformed response [15,21,22].…”

Section: Introductionmentioning

confidence: 99%

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On the Selection of Power Transformation Parameters in Regression Analysis

Taha Mohammed Ali,

Adil Shareef

2024

Artificial Intelligence

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In multiple linear regression, there are several classical methods used to estimate the parameters of power transformation models that are used to transform the response variable. Traditionally, these parameters can be estimated using either Maximum Likelihood Estimation or Bayesian methods in conjunction with the other model parameters. In this chapter, attention has been paid to four indicators of the efficiency and reliability of the regressive modeling, and study the possibility of considering them as decision rules through which the optimal power parameter can be chosen. The indicators are the coefficient of determination and p-value of the general linear F-test statistic. Also, the p-value of Shapiro-Wilk test (SWT) statistic for the residual’s normality of the estimated linear regression of the transformed response vector and the estimated nonlinear regression of the original response vector resulting from the back transform of the power Transformation model. Real data were used and a computational algorithm was proposed to estimate the optimal power parameter. The authors concluded that the multiplicity of indicators does not lead to obtaining an optimal single value for the power parameter, but this multiplicity may be useful in fortifying the decision-making ability.

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“…This approach aimed to improve the accuracy and reliability of these models. [13]. The article emphasizes the widespread utility of the BCT, a versatile transformation function applicable to various regression models, including ER.…”

Section: Introductionmentioning

confidence: 99%

Transforming to Normality in Regression Analysis with Exponentially Residuals

Mohammed Ali,

Adil Shareef

2023

ACAD J NAWROZ UNIV

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In this article, a simulated study is introduced, focusing on the use of power transformation to estimate a nonlinear regression model in the presence of residuals following an exponential distribution. Four criteria were employed to estimate the power parameter: the p-value of Shapiro-Wilk test statistics for both the transformed and back-transformed data's normality, maximum likelihood estimation, and coefficient of determination. The findings of the study indicate that while it is possible to identify a range of viable solutions to select the optimal power parameter, finding a single optimal value that satisfies all estimation and decision methods is not feasible.

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Using Power Transformations in Response Surface Methodology

Cited by 3 publications

References 13 publications

Microwave Synthesis of Molybdenum Disulfide Nanoparticles Using Response Surface Methodology for Tribological Application

Microwave Synthesis of Molybdenum Disulfide Nanoparticles Using Response Surface Methodology for Tribological Application

On the Selection of Power Transformation Parameters in Regression Analysis

Transforming to Normality in Regression Analysis with Exponentially Residuals

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