Equations

Code

Mathematical form

PSW

Outliers (%)

Leverage (%)

Volume

M1

$\ln \left(v\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d\right)+\epsilon$

0.8177

1.03

1.03

M2

$\ln \left(v\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d^{2}h\right)+\epsilon$

0.0184

2.58

1.03

M3

$\ln \left(v\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d^2\right)+{\beta }_2\ln \left(h\right)+\epsilon$

0.0750

2.58

1.55

M4

$v={\beta }_0\ast {\left(d\right)}^{{\beta }_1}\ast \epsilon$

<0.0001

5.15

M5

$v={\beta }_0\ast {\left(d^{2}h\right)}^{{\beta }_1}\ast \epsilon$

<0.0001

2.58

M6

$v={\beta }_0\ast {\left(d^2\right)}^{{\beta }_1}{\left(h\right)}^{{\beta }_2}\ast \epsilon$

<0.0001

2.58

Biomass

M7

$\ln \left(b\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d\right)+\text{ε}$

0.6697

1.55

1.03

M8

$\ln \left(b\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d^{2}h\right)+{\beta }_2\ln \left(\rho \right)+\text{ε}$

0.0917

4.12

18.04

M9

$\ln \left(b\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(d\right)+{\beta }_2\ln \left(h\right)+{\beta }_3\ln \left(\rho \right)+\text{ε}$

0.0194

3.61

13.92

M10

$\ln \left(b\right)=\ln \left({\beta }_0\right)+{\beta }_1\ln \left(\rho d^{2}h\right)+\text{ε}$

0.0690

2.58

1.03

M11

$b={\beta }_0\ast {\left(d\right)}^{{\beta }_1}$

<0.0001

4.64

M12

$b={\beta }_0\ast {\left(d^{2}h\right)}^{{\beta }_1}{\left(\rho \right)}^{{\beta }_2}$

<0.0001

2.06

M13

$b={\beta }_0\ast {\left(\rho d^{2}h\right)}^{{\beta }_1}$

<0.0001

2.06

M14

$b={\beta }_0\ast {\left(d\right)}^{{\beta }_1}{\left(h\right)}^{{\beta }_2}{\left(\rho \right)}^{{\beta }_3}$

<0.0001

5.15

Chave2005

NA

4.64

Chave2014

NA

3.61

Djomo2016

NA

1.55

Tetemke2018

NA

6.19