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, By subtracting ? i on both sides of Eq.1, only the residual term ? ij remains on the right-hand side of the equation: y ij ? ? i = µ(M w,i , ln R jb,ij , ln V s 30,j ; ?) + ? ij

, Therefore, the residuals are IID if x and y ? ? are used as the inputs and outputs of the ANN. Then, the algorithm described above is valid when the variance-covariance C is under the form of Eq.7. However

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