Table 5 External validation of MEP and GEP model.

\(s=\frac{\sum_{i=1}^{n}({e}_{i}\times {m}_{i})}{\sum_{i=1}^{n}({e}_{i}^{2})}\)

0.85 < s < 1.15

¹¹⁸

\({s}{\prime}=\frac{\sum_{i=1}^{n}({e}_{i}\times {m}_{i})}{\sum_{i=1}^{n}({m}_{i}^{2})}\)

0.85 < \({s}{\prime}\) < 1.15

¹¹⁸

\({R}_{m}= {R}^{2}\times (1-\sqrt{|{R}^{2}-{R}_{o}^{2}|})\)

where

\({R}_{m}>0.5\)

¹¹⁹

\({R}_{o}^{2}=1-\frac{\sum_{i=1}^{n}{\left({m}_{i}-{e}_{i}^{o}\right)}^{2}}{\sum_{i=1}^{n}{\left({m}_{i}-{m}_{i}^{o}\right)}^{2}}\),\({e}_{i}^{o}=s\times {m}_{i}\)

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

¹²⁰

\({R}_{o}^{{\prime}2}=1-\frac{\sum_{i=1}^{n}{({e}_{i}-{m}_{i}^{o})}^{2}}{\sum_{i=1}^{n}{({m}_{i}-{m}_{i}^{o})}^{2}}\),\({m}_{i}^{o}={s}{\prime}\times {e}_{i}\)

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

¹²¹