Light bias between the estimated mean and its assigned target. Because of this, the EQL is chosen as an identification and comparison tool to evaluate optimal solutions obtained from each model. MATLAB is applied in this study to perform the estimated regression functions of mean and regular deviation applying the proposed dual-response approach and conventional LSMbased RSM, respectively. The correlation coefficients of your estimated response functions based on Vining and Myers’ [8] dual-response method are listed in Table 1.Table 1. Coefficients on the estimated response functions working with LSM. Coefficients Therapy Combinations Continuous x1 x2 x3 two x1 two x2 2 x3 x1 x2 x1 x3 x2 x3 Mean SM 327.630 177.000 109.430 131.460 32.000 -22.389 -29.056 66.028 75.472 43.^Standard Deviation LSM 34.883 11.527 15.323 29.190 four.204 -1.316 16.778 7.720 5.109 14.^Table two lists the proposed NN-functional-link-based dual-response RD estimation model soon after the training process.Appl. Sci. 2021, 11,eight ofTable 2. Parameters of NN-based estimation process.Objective Imply Std Response Function mse mse Training Algorithm Trainlm Trainlm Structure 3-21-1 3-2-1 No. of Epoch 13The weights and biases of the NN for the estimated imply and standard deviationmean functions are listed in Tables three and four, respectively. In these tables, Win_hid , wmean hid_out T,and represent the weight connection from the input to the Ampicillin (trihydrate) Epigenetics hidden layers, the weight connection from the hidden layers to the output, the method bias in the hidden layers, as well as the course of action bias in the output layer with the observed mean formula, respectively.std std Similarly, Win_hid , wstd , bstd , and bout represent the weight connection in the hid hid_out input to the hidden layers, the weight connection in the hidden layers towards the output, the process bias in the hidden layers, as well as the Vialinin A Technical Information procedure bias within the output layer of your observed standard deviation formula, respectively. Tbmean , hidmean boutTable 3. Weight and bias terms in the NN for the estimated method imply.Weightmean Win_hidBias wmean hid_out 1.54028 0.73934 -0.80124 1.11264 -0.26521 0.21240 0.56006 -0.02559 -0.37276 1.96605 -1.17218 -0.58818 -0.67588 0.01320 0.17376 -0.27889 0.34659 0.76126 0.10545 -0.09037 -0.Tbmean hid three.63174 0.77913 3.88614 1.68918 -0.70557 -0.84332 -0.39605 -0.44870 -0.43415 5.36510 -1.47882 0.05234 -0.02238 -0.58988 -0.88337 0.04470 -0.31859 0.80572 0.51167 0.67887 -0.mean bout0.96075 0.75123 -0.28537 1.17461 0.27560 -0.72625 -0.45138 -0.40578 0.75884 2.86524 -1.13144 -0.06226 0.32760 -0.01851 0.11633 -0.68532 -0.27500 0.91857 0.29861 0.56297 0.0.11736 0.38223 -0.34012 0.63199 0.60510 0.41018 -0.37180 -0.11631 -0.59636 1.95064 -0.73588 -0.41228 -0.75682 -0.81573 0.16928 0.37096 -0.52907 0.59698 -0.39570 -0.03477 -0.two.10096 1.62200 two.30133 1.73056 -0.48992 -0.11370 -1.03860 -0.09612 -0.29991 four.72650 0.84079 0.40969 -0.11504 -0.27318 -0.45037 -0.27210 -0.85252 0.59614 0.28709 0.43088 -0.1.Table 4. Weight and bias terms of the NN for the estimated process standard deviation.Weightstd Win_hidBias wstd hid_outTbstd hidstd bout-2.04505 -0.-3.02946 -1.-4.90330 -0.0.86246 -2.-4.32652 -2.-0.According to the estimated regression formulas of your course of action mean and normal deviation, the response functions of your dual-response models involving parameters x1 and x2 for two estimation techniques (i.e., LSM and NN) are illustrated in Figures 4 and 5, like statistical indexes including coefficients of determination ( R2 ) and root-meansquare error (.