Table 7 External validation suggested by Golbraikh and Tropsha (2002)⁷³.

\(\:R=\frac{n\sum\:\left({d}_{i}{y}_{i}\right)-\left(\sum\:{d}_{i})\right(\sum\:{y}_{i})}{\sqrt{[n\sum\:{d}_{i}^{2}-{\left({\sum\:d}_{i}\right)}^{2}\left]\:\right[n\sum\:{y}_{i}^{2}-{\left(\sum\:{y}_{i}\right)}^{2}]}}\)

\(\:R\:>\:0.8\)

0.9790

✔

0.9463

✔

0.9706

✔

0.9674

✔

\(\:k=\frac{\sum\:_{i=0}^{n}({d}_{i}\times\:{y}_{i})}{\sum\:_{i=0}^{n}{y}_{i}^{2}}\)

\(\:0.85<k<1.15\)

1.0547

✔

1.0792

✔

1.0415

✔

1.0399

✔

\(\:k{\prime\:}=\frac{\sum\:_{i=0}^{n}({d}_{i}\times\:{y}_{i})}{\sum\:_{i=0}^{n}{d}_{i}^{2}}\)

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

0.9359

✔

0.8945

✔

0.9415

✔

0.9408

✔

\(\:{R}_{o}^{{\prime\:}2}=1-\left(\frac{\sum\:_{i=1}^{n}{y}_{i}^{2}{\left(1-k\right)}^{2}}{\sum\:_{i=1}^{n}({y}_{i}-\stackrel{-}{y})}\right)\)

Should be close to 1

0.9903

✔

0.9811

✔

0.9949

✔

0.9953

✔

\(\:{R{\prime\:}{\prime\:}}_{o}^{2}=1-\left(\frac{\sum\:_{i=1}^{n}{d}_{i}^{2}{\left(1-{k}^{{\prime\:}}\right)}^{2}}{\sum\:_{i=1}^{n}({d}_{i}-\stackrel{-}{d})}\right)\)

Should be close to 1

0.9867

✔

0.9639

✔

0.9889

✔

0.9886

✔

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

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

0.7874

✔

0.6335

✔

0.7259

✔

0.7079

✔

\(\:m=\frac{{R}^{2}-{R}_{o}^{2}}{{R}^{2}}\)

\(\:\left|m\right|<0.1\)

−0.0332

−0.0956

−0.0559

−0.0634

\(\:n=\frac{{R}^{2}-{R{\prime\:}}_{o}^{2}}{{R}^{2}}\)

\(\:\left|n\right|<0.1\)

−0.0295

✔

−0.0765

✔

−0.0496

✔

−0.0563

✔

Number of conditions met

8

8

8

8