Table 1 Parameter estimates \( \widehat{\alpha} \) and \( \widehat{\beta} \) associated standard errors (\( ste\left(\widehat{\alpha}\right), ste\Big(\widehat{\beta} \))) found by fitting the model of Eq. (1). Nonlinear regression estimates associate to the homoscedastic case of the model of Eqs. (5) and (6) (see Appendix 1). Values of \( \widehat{\rho} \) give an evaluation of reproducibility strength of the proxy of Eq. (1)
Analysis method Data | \( \widehat{\beta} \) | \( ste\left(\widehat{\beta}\right) \) | \( \widehat{\alpha} \) | \( ste\left(\widehat{\alpha}\right) \) | \( \widehat{\rho} \) |
|---|---|---|---|---|---|
Log-linear Transformation Raw | 1.3674x10−5 | 2.9355 × 10− 7 | 1.023 | 3.662 × 10− 3 | 0.8910 |
Nonlinear Regression Raw | 8.718x10−6 | 3.530 × 10−7 | 1.104 | 5.101 × 10−3 | 0.9307 |
Log-linear Transformation Processed | 1.142 x10−5 | 2.0831 × 10−7 | 1.046 | 3.035 × 10−3 | 0.9455 |
Nonlinear Regression Processed | 6.956 x10−6 | 2.200 × 10−7 | 1.132 | 3.954 × 10−3 | 0.9777 |