**3. Statistical results analysis and the model properties**

Regression model and test for coefficients significance on individual model achieved using ANOVA method. **Table 2** show summary statistics of the model, values of "Adjusted and Predicted R<sup>2</sup> " are higher for quadratic model which is suggested for the present analysis; experimental data analysis was performed to identify statistical significance of the aim's parameters. The dry unit weight, degree of saturation, water content, plasticity index, preconsolidation pressure and the swelling index on the measured response swelling pressure Ps. The model was developed for 95% confidence level with R2 = 0.9155, and the results are summarized in **Table 2**.

In **Table 2** the value of 0.2 between **Predicted and Adjusted R<sup>2</sup>** indicate the reasonable agreement.

**Adeq Precision** is the SNR, greater than 4 is desirable, so the obtained model can be used to delineate a design space.


#### **Table 2.**

*Model summary fit statistics.*


#### **Table 3.**

*Sequential model sum of squares [type I].*


*Factor coding is Coded.*

*Sum of squares is Type III - Partial.*

*F-value of 37.74 indicates a significant model. Only a 0.01% chance that F-value could occur due to noise. P-values < 0.0500 implies significant terms model. A, E, F, AE, EF are the chosen terms. Values >0.1000 implies a not significant model term. The other terms may be used to reduce the improved model require to support hierarchy Table 4.*

#### **Table 4.**

*ANOVA response surface quadratic model, analysis of variance table [Partial sum of squares - Type III].*

*Swelling Clay Parameters Investigation Using Design of Experiments (A Case Study) DOI: http://dx.doi.org/10.5772/intechopen.95443*

Select the highest order polynomial where the additional terms are significant and the model is not aliased.

The F-Value of 90.65−5.80 indicates a significant model with P- value <0.0001 that provide the suggested one 2FI vs. linear with 5.80 F-value, out of the cited condition the models are aliased (**Table 3)**. In this case A, B, C, BC are significant model terms where P- Values >0.10 as mentioned in **Table 4**.

Normal plot of residuals, shown in **Figures 3**–**8**, should be in a straight line, in the residuals the errors distribution is normal regards the strait line form. Whereas the nonlinear patterns such as S-curve form implies a non-normality of the error term and can be corrected by a transformation. Residuals versus predicted response should be randomly scattered without pattern as shown in **Figure 8**. Other analysis can be provided in other cases.

#### **Figure 3.**

*Residual plots for the swelling pressure of the study soil case***.**

#### **Figure 4.**

*All factors contribution and effects on the response output for the swelling pressure of the study soil case.*

**Figure 5.** *Normal probability plot of residuals for swelling pressure.*

**Figure 6.** *Residuals versus predicted response for swelling pressure.*

**Figure 7.** *Residuals versus run for swelling pressure.*

*Swelling Clay Parameters Investigation Using Design of Experiments (A Case Study) DOI: http://dx.doi.org/10.5772/intechopen.95443*

**Figure 8.** *Predicted response versus actual for swelling pressure.*
