S/No	Model Type	Model Equation Form	Independent Variables	Model Parameter	Goodness of fit indices	Remark
1	Multiple Linear Regression	$\begin{matrix} y = a_{o} + a_{1} X_{1} + a_{2} X_{2} \\ + a_{3} X_{3} + a_{4} X_{4} \end{matrix}$	$X_{1}$ = Water Content $X_{2}$ = Dry Density $X_{3}$ = Liquid Limit $X_{4}$ = Plasticity Index	$a_{0}$ = −42.314 $a_{1}$ = −0.084 $a_{2}$ = 7.627 $a_{3}$ = 0.394 $a_{4}$ = −0.396	$R^{2}$ = 0.478 MSE = 178.62 RMSE = 13.37	Model unacceptable
2	Simple Linear Regression	$y = a_{o} + a_{1} X_{1}$	$X_{1}$ = Water Content	$a_{0}$ = 57.040 $a_{1}$ = −0.423	$R^{2}$ = 0.478 MSE = 178.62 RMSE = 13.37	Model unacceptable
3	Multiple Linear Regression	$y = a_{o} + a_{1} X_{1} + a_{2} X_{2}$	$X_{1}$ = Water Content $X_{2}$ = Effective stress	$a_{0}$ = 35.628 $a_{1}$ = −0.238 $a_{2}$ = 0.036	$R^{2}$ = 0.510 MSE = 133.91 RMSE = 11.57	Model unacceptable
4	Multiple Linear Regression (Outlier removed)	$y = a_{o} + a_{1} X_{1} + a_{2} X_{2}$	$X_{1}$ = Water Content $X_{2}$ = Effective stress	$a_{0}$ = 29.23 $a_{1}$ = −0.205 $a_{2}$ = 0.043	$R^{2}$ = 0.805 MSE = 40.612 RMSE = 6.37	Model acceptable
5	Multiple Quadratic Regression (Outlier removed)	$\begin{matrix} y = a_{o} + a_{1} X_{1} + a_{2} X_{2} \\ + a_{3} X_{3}^{2} + a_{4} X_{4}^{2} \end{matrix}$	$X_{1}$ = Water Content $X_{2}$ = Effective stress $X_{3}$ = Water Content $X_{4}$ = Effective stress	$a_{0}$ = 66.497 $a_{1}$ = −1.098 $a_{2}$ = 0.0696 $a_{3}$ = 0.0049 $a_{4}$ = −7E−5	$R^{2}$ = 0.828 MSE = 46.03 RMSE = 6.785	Model acceptable
6	Multiple Linear Regression (Outlier removed)	$\begin{matrix} y = a_{o} + a_{1} X_{1} + a_{2} X_{2} \\ + a_{3} X_{3} + a_{4} X_{4} \end{matrix}$	$X_{1}$ = Water Content $X_{2}$ = Liquid Limit $X_{3}$ = Plasticity Index $X_{4}$ = Effective stress	$a_{0}$ = 31.392 $a_{1}$ = −0.098 $a_{2}$ = −0.341 $a_{3}$ = 0.330 $a_{4}$ = −0.050	$R^{2}$ = 0.846 MSE = 41.232 RMSE = 6.421	Model acceptable
7	Multiple Power Regression (Outlier removed)	$y = a_{o} X_{1}^{a_{1}} X_{2}^{a_{2}} X_{2}^{a_{3}} X_{4}^{a_{4}}$	$X_{1}$ = Water Content $X_{2}$ = Liquid Limit $X_{3}$ = Plasticity Index $X_{4}$ = Effective stress	$a_{0}$ = 203.728 $a_{1}$ = −0.487 $a_{2}$ = −1.584 $a_{3}$ = 1.208 $a_{4}$ = 0.41	$R^{2}$ = 0.890 MSE = 29.37 RMSE = 5.419	Model acceptable
8	Multiple Power Regression No Outlier	$y = a_{o} X_{1}^{a_{1}} X_{2}^{a_{2}}$	$X_{1}$ = Water Content $X_{2}$ = Effective stress	$a_{0}$ = 175.797 $a_{1}$ = −0.833 $a_{2}$ = 0.286	$R^{2}$ = 0.861 MSE = 29.105 RMSE = 5.395	Model acceptable
9	Multiple Quadratic Regression (Outlier removed)	$\begin{matrix} y = a_{o} + a_{1} X_{1} + a_{2} X_{2} \\ + a_{3} X_{3} + a_{4} X_{4} \end{matrix}$	$X_{1}$ = Water Content $X_{2}$ = Effective stress $X_{3}$ = Water Content $X_{4}$ = Effective stress	$a_{0}$ = 66.497 $a_{1}$ = −1.098 $a_{2}$ = 0.0696 $a_{3}$ = 0.0049 $a_{4}$ = −7E−5	$R^{2}$ = 0.828 MSE = 46.03 RMSE = 6.785	Model acceptable