Table 8 External validation of proposed models.

1

\(R\)

\(R>0.8\)

4

\({{R}_{o}}^{2}=1-\frac{{\sum }_{i=1}^{n}{\left({z}_{i}-{{e}_{ei}}^{o}\right)}^{2}}{{\sum }_{i=1}^{n}{\left({z}_{i}-{z}^{o}\right)}^{2}}\),\({{x}_{i}}^{o}=k\times {z}_{i}\)

\({{R}_{o}}^{2}\cong 1\)

5

\({{R{\prime}}_{o}}^{2}=1-\frac{{\sum }_{i=1}^{n}{\left({e}_{i}-{{z}_{i}}^{o}\right)}^{2}}{{\sum }_{i=1}^{n}{\left({e}_{i}-{e}^{o}\right)}^{2}}\),\({{z}_{i}}^{o}=k^{\prime}\times {x}_{i}\)

\({{R^{\prime}}_{o}}^{2}\cong 1\)

2

\(k={\sum }_{i=1}^{n}\frac{{(e}_{i}\times {z}_{i})}{{e}^{2}}\)

\(0.85<k<1.15\)

3

\({k}{\prime}={\sum }_{i=1}^{n}\frac{{(e}_{i}\times {z}_{i})}{{{z}_{i}}^{2}}\)

\(0.85<k^{\prime}<1.15\)