Table 1.

Terminologies applied for model adequacy verification [33,38,44].

Variation source	Expression	Remarks
Coefficient of determination, R2	$R^2=\frac{S{S}_{\text{Re}g}}{S{S}_T}$	R2 must be close to 1.0
R2adjusted	$R_{adjusted}^2=1-\frac{S{S}_{\text{Re}s}/\left(n-p\right)}{S{S}_T/\left(n-1\right)}$	R2adjusted must be close to 1.0
R2predicted	$R_{predicted}^2=1-\frac{PRESS}{S{S}_T}$	R2predicted must not have a difference of more than 0.2 with R2adjusted
Prediction error sum of square (PRESS)	$PRESS=\sum _{i=1}^n{\left[y_i-{\hat{y}}_i\right]}^2$	PRESS must have a small value
Significance of regression	$F_0=\frac{Meansquareofmodel}{Meansquareofresidual}$	This ratio must be greater than the tabulated F value for a good model
Lack of fit (LOF) test	$F_{LOF}=\frac{S{S}_{LOF}/\left(f-p\right)}{S{S}_{PE}/\left(n-p\right)}$	This ratio must be lower than the tabulated F value for a good model

The deviation within a data set is assessed by examining its dispersion via ANOVA. A common metric for describing the overall efficacy of a predictive model is the coefficient of determination (R²), representing the ratio of the regression sum of squares (SSReg) to the total sum of squares (SST). This ratio indicates the extent of variation in the model's predicted values from the mean. An efficient predictive model should exhibit an R² value approaching 1.