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The mean error percentage of the models were slightly different at − 0.21% and 0.53% for the ARIMA model and delta algorithm, respectively.
Although outcomes of all these methods, in the case of both Poisson's ratio and stiffness, were in a good agreement with the confirmation tests, however the result of grey relational analysis had the minimum mean error percentage.
After ANN training, correlation coefficients (R2) of both engine performance values for testing and training data were very close to 1. Similarly, root-mean-square error (RMSE) and mean error percentage (MEP) values for the testing and training data were less than 0.02% and 3.5% respectively.
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The rightmost two columns of Table 1 show the mean error percentages involved in the two-way interaction of repetition and N, F 1, 11) = 10.607, p =.008.
The prediction performance of the developed model was analyzed by root-mean square (RMS), mean absolute error percentage (MAEP) and coefficient of determination (R 2 ).
In order to show error levels, mean absolute error and mean absolute error percentage are used.
The obtained results show that the mean relative error percentage (MRE%) for training and testing data are less than 2.14% and 2.64%, respectively.
The correlation coefficient (R2) of 0.9908 and the mean absolute error percentage of less than 3.1% show a pretty good agreement between the modeling and experimental results.
Mean absolute error and mean absolute error percentages are very common and practical methods in literature.
The mean prediction error percentages for the reduced scattering coefficient are 9.73%, 2.57% and 0.79% for the PLS, LUT and LS-SVM models, respectively.
Similarly, the mean prediction error percentages for absorption coefficients are 29.03%, 7.94% and 3.77% for the PLS, LUT and LS-SVM models respectively.
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