*3.5.3 Multiple regression analysis*

Following stepwise regression method, five models were generated in (Eqs. 1–5). The result indicated that between 25 and 33% of the variation in soil properties was explained by the combination of these predictors. In Eq. 5, 70% training dataset accounted for 33% variance with coefficient of determination (R2 = 0.33) and root mean square error of performance (RMSE = 7.8). Given the p-value <0.001 computed by analysis of variance (ANOVA), the significance level (5%) and the low bias (0.05), the prediction by the explanatory variables is significant.

$$\text{CBRs} = 0.008LL - 0.29PL - 0.5wPI - 0.10MC + 6.87MDD + 25.2 \tag{1}$$

$$\begin{aligned} \text{CBRs} &= 6.47 \text{MDD} - 0.014LL - 0.32PL - 0.59wPI - 0.12 \text{OMC} \\ &+ 0.12Fw + 26.7 \end{aligned} \tag{2}$$

8.51 0.1 0.2 0.56 0.1 0.11 38.1 0.13 0.2 0.88 14.02 = −−− − + + − −+ − *CBRs MDD LL PL wPI OMC Fsw Dr Wr LLr PIr* (3)

$$\text{CBRs} = 0.062LL - 0.51PL - 0.82wPI - 0.28Fsw - \text{38.06} \tag{4}$$

$$\begin{aligned} \text{CBRs} &= 0.31Fines + 1.88Ac + 0.41Fons - 0.298LL - 0.25PL - 0.73wPI \\ &- 0.50MC + 2.11MDD + 36.03 \end{aligned} \tag{5}$$
