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Table 5 Internal and external validation parameters for each model

From: Computational modeling and ligand-based design of some novel hypothetical compound as prominent inhibitors against Mycobacterium tuberculosis

S/NO

Validation parameters

Formula

Threshold

Model 1

Model 2

Internal validation

1

Friedman’s lack of fit (LOF)

\( \frac{SEE}{{\left(1-\frac{w+q\times j}{N}\right)}^2} \)

 

0.0274

0.0301

2

R-squared

\( 1-\left[\frac{\sum {\left({Y}_{obs\kern0.5em -{Y}_{pred}}\right)}^2}{\sum {\left({Y}_{obs\kern0.5em -{\overline{Y}}_{training}}\right)}^2}\right] \)

R2 > 0.6

0.9183

0.8429

3

Adjusted R-squared

\( \frac{R^2-P\ \left(N-1\right)}{N-p+1} \)

\( {R}_{\mathrm{adj}}^2>0.6 \)

0.8854

0.8189

4

Cross validated R-squared (\( {Q}_{cv}^2\Big) \)

\( 1-\left[\frac{\sum {\left({Y}_{pred\kern0.5em -{Y}_{obs}}\right)}^2}{\sum {\left({Y}_{obs\kern0.5em -{\overline{Y}}_{training}}\right)}^2}\right] \)

Q2 > 0.6

0.8202

0.7400

5

Significant regression

  

Yes

Yes

6

Critical SOR F value (95%)

\( \frac{\sum {\left({Y}_{pred\kern0.5em -{Y}_{obs}}\right)}^2}{p}/\frac{\sum {\left({Y}_{pred\kern0.5em -{Y}_{obs}}\right)}^2}{N-p-1} \)

F(test) > 2.09

4.3892

4.3892

7

Replicate points

  

0

0

8

Computed observed error

  

0

0

9

Min expt. error for non-significant LOF (95%)

  

0.0278

0.0278

Model randomization

10

Average of the correlation coefficient for randomized data (\( {\overline{R}}_r \))

 

\( \overline{R}<0.5 \)

0.3371

0.3983

11

Average of determination coefficient for randomized data (\( {\overline{R}}_r^2\Big) \)

 

\( {\overline{\mathrm{R}}}_r^2<0.5 \)

0.1521

0.1763

12

Average of leave-one-out cross-validated determination coefficient for randomized data (\( {\overline{Q}}_r^2 \))

 

\( {\overline{Q}}_r^2<0.5 \)

− 1.3198

− 1.3719

13

Y-randomization coefficient (c\( {R}_p^2\Big) \)

\( {R}^2\times \left(1-\sqrt{\left|{R}^2-{\overline{R}}_{\mathrm{r}}^2\right|}\ \right) \)

c\( {R}_{\mathrm{p}}^2>0.6 \)

0.7362

0.7058

External validation

14

Slope of the plot of observed activity against predicted activity values at zero intercept (K)

\( \frac{\boldsymbol{\Delta }{\boldsymbol{Y}}_{\boldsymbol{Obs}}}{{\boldsymbol{\Delta Y}}_{\boldsymbol{pred}}} \)

0.85 < k < 1.15

1.0013

1.0582

15

Slope of the plot of predicted against observed activity at zero intercept (k′)

\( \frac{\boldsymbol{\Delta }{\boldsymbol{Y}}_{\boldsymbol{pred}}}{\boldsymbol{\Delta }{\boldsymbol{Y}}_{\boldsymbol{Obs}}} \)

0.85 < k < 1.15

0.9290

0.9016

16

\( /{\boldsymbol{r}}_{\mathbf{0}}^{\mathbf{2}}-{{\boldsymbol{r}}^{\prime}}_{\mathbf{0}}^{\mathbf{2}}/ \)

 

< 0.3

0.0834

0.0610

17

\( \frac{{\boldsymbol{r}}^{\mathbf{2}}-{\boldsymbol{r}}_{\mathbf{0}}^{\mathbf{2}}}{{\boldsymbol{r}}^{\mathbf{2}}} \)

 

< 0.1

0.0028

0.0042

18

\( \frac{{\boldsymbol{r}}^{\mathbf{2}}-{{\boldsymbol{r}}^{\prime}}_{\mathbf{0}}^{\mathbf{2}}}{{\boldsymbol{r}}^{\mathbf{2}}} \)

 

< 0.1

0.0610

0.0582

19

\( {\boldsymbol{R}}_{\mathbf{test}}^{\mathbf{2}} \)

\( {R}_{test}^2=1-\frac{\sum {\left(Y{pred}_{test}-{Y}_{obs_{test}}\right)}^2}{\sum {\left(Y{pred}_{test}-{\overline{Y}}_{training}\ \right)}^2} \)

>0.6

0.8052

0.7281