718 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
were 0.9984, 0.9979, and 0.9996, while the adjusted R2
(R2 (adj)) values were 0.9951, 0.9935, and 0.9988 for ISR,
water recovery, and water turbidity responses, respectively.
These results indicate that the variability of the data in the
model could be explained.
Usually, a high value of the correlation coefficient
(R2), close to 1, is desirable and a reasonable agreement
with adjusted R2 (R2adj) is necessary (Wu et al., 2020).
Moreover, the R2(adj) values closely align with the R2 val-
ues, indicating a satisfactory adjustment of the models to
the experimental results. This alignment is confirmed by
Figure 4, where the plots depicting predicted Initial Settling
Rate (ISR), water recovery, and water turbidity against their
measured counterparts are presented.
The coefficient of variation C.V of three models
were 1.2%, 0.3544% and 3.41% for ISR, water recovery,
and water turbidity responses, respectively that are less
than 10%, indicating high dependability and adequacy.
Adequate Precision assesses the signal-to-noise ratio, with
a ratio exceeding 4 considered desirable. In this context,
signal-to-noise ratios of 57.3448, 57.5392, and 114.5365
for ISR, water recovery, and water turbidity responses,
respectively, signify sufficient signal strength in the three
models obtained. This robust signal-to-noise ratio supports
effective navigation within the design space. The Lack of
Fit F-values for ISR, water recovery, and water turbidity
responses are 0.954, 0.0341, and 5.46, respectively. These
values suggest that the Lack of Fit is not statistically signifi-
cant when compared to the pure error. The corresponding
probabilities of obtaining a Lack of Fit F-value of this mag-
nitude purely by chance are 37.36%, 86.08%, and 6.66%
for ISR, water recovery, and water turbidity responses,
respectively.
Based on the experimental results of the 20 experiment
conducted, the cubic polynomial regression models for ISR
(Y1), WR (Y2), and water turbidity (Y3) in terms of coded
factors were obtained, as shown in Eq. (3), (4), and (5),
respectively.
..47 .
..0763 .6987x
..4x .2936x
..4488x12x
..2438x
Y ISR x x
x x x x x
x x2 x
x x x
13 21 1 2 1 0.9x
0 5063 0 0
0 0186x 2 0
0 4312 0
0 4912 0
1 1 2 3
1 2 1 3 2 3
1
2
2
2
3
2
1 3 2
1
2
3 1 2
2
==++-
++-
+-+
+-
+-
(3)
.
..9938x
..8786x .86x
.
.
Y WR x
x x x x x
x
x x2 x
x x x
83.4 1.83x 1 09 3.2x
1 47 0.1663 0
0 4886 0 2
1 32 1.89x12x
2 13 0.2613x –
2 1 2 3
1 2 1 3 2 3
1
2
2
2
3
2
1 3 2
1
2
3 1 2
2
==+++
-++
---
++
-
(4)
.8829 ..55x
..26x
..39x32
..9013x
..5837x1x22
Y WT x
x x x x x
x
x x x x
x x3
0 0 33 1.81x 0
2 51 0.3212 1
1 07 3.86x22 1
0 3588 0
0 0888 0
3 1 2 3
1 2 1 3 2 3
1
2
1 2 3 1
2
2
1
2
==--+
+++
++++
-
--
(5)
From the experimental design models, it is evident that all
the linear, quadratic, cubic, and interaction terms in Eq. (3,
4, and 5) are statistically significant at a 95% confidence
level (p 0.05). This underscores the importance of floc-
culant dose, slurry pH, and mixing velocity as key factors
influencing the initial settling rate, water recovery, and the
turbidity of the supernatant responses.
Upon analysing the coefficient estimate values, it is
evident that the terms exerting the most substantial main
Table 6. Summarized ANOVA for ISR, WR and turbidity responses
Response Source F-Value
p-Value
Prob F R2 R2
adj
C.V
(%)
Adequate
Precision Mean Std. Dev. Remarks
ISR
(cm/min)
Model 297.14 0.0001 0.9984 0.9951 1.2 57.3448 12.17 0.1457 Significant
Residual
(lack of fit)
0.954 0.3736 Not significant
Water
recovery
(%)
Model 223.25 0.0001 0.9979 0.9935 0.3544 57.5392 81.29 0.2881 Significant
Residual
(lack of fit)
0.0341 0.8608 Not significant
Water
turbidity
(NTU)
Model 1194.64 0.0001 0.9996 0.9988 3.41 114.5365 4.04 0.1379 Significant
Residual
(lack of fit)
5.46 0.0666 Not significant
were 0.9984, 0.9979, and 0.9996, while the adjusted R2
(R2 (adj)) values were 0.9951, 0.9935, and 0.9988 for ISR,
water recovery, and water turbidity responses, respectively.
These results indicate that the variability of the data in the
model could be explained.
Usually, a high value of the correlation coefficient
(R2), close to 1, is desirable and a reasonable agreement
with adjusted R2 (R2adj) is necessary (Wu et al., 2020).
Moreover, the R2(adj) values closely align with the R2 val-
ues, indicating a satisfactory adjustment of the models to
the experimental results. This alignment is confirmed by
Figure 4, where the plots depicting predicted Initial Settling
Rate (ISR), water recovery, and water turbidity against their
measured counterparts are presented.
The coefficient of variation C.V of three models
were 1.2%, 0.3544% and 3.41% for ISR, water recovery,
and water turbidity responses, respectively that are less
than 10%, indicating high dependability and adequacy.
Adequate Precision assesses the signal-to-noise ratio, with
a ratio exceeding 4 considered desirable. In this context,
signal-to-noise ratios of 57.3448, 57.5392, and 114.5365
for ISR, water recovery, and water turbidity responses,
respectively, signify sufficient signal strength in the three
models obtained. This robust signal-to-noise ratio supports
effective navigation within the design space. The Lack of
Fit F-values for ISR, water recovery, and water turbidity
responses are 0.954, 0.0341, and 5.46, respectively. These
values suggest that the Lack of Fit is not statistically signifi-
cant when compared to the pure error. The corresponding
probabilities of obtaining a Lack of Fit F-value of this mag-
nitude purely by chance are 37.36%, 86.08%, and 6.66%
for ISR, water recovery, and water turbidity responses,
respectively.
Based on the experimental results of the 20 experiment
conducted, the cubic polynomial regression models for ISR
(Y1), WR (Y2), and water turbidity (Y3) in terms of coded
factors were obtained, as shown in Eq. (3), (4), and (5),
respectively.
..47 .
..0763 .6987x
..4x .2936x
..4488x12x
..2438x
Y ISR x x
x x x x x
x x2 x
x x x
13 21 1 2 1 0.9x
0 5063 0 0
0 0186x 2 0
0 4312 0
0 4912 0
1 1 2 3
1 2 1 3 2 3
1
2
2
2
3
2
1 3 2
1
2
3 1 2
2
==++-
++-
+-+
+-
+-
(3)
.
..9938x
..8786x .86x
.
.
Y WR x
x x x x x
x
x x2 x
x x x
83.4 1.83x 1 09 3.2x
1 47 0.1663 0
0 4886 0 2
1 32 1.89x12x
2 13 0.2613x –
2 1 2 3
1 2 1 3 2 3
1
2
2
2
3
2
1 3 2
1
2
3 1 2
2
==+++
-++
---
++
-
(4)
.8829 ..55x
..26x
..39x32
..9013x
..5837x1x22
Y WT x
x x x x x
x
x x x x
x x3
0 0 33 1.81x 0
2 51 0.3212 1
1 07 3.86x22 1
0 3588 0
0 0888 0
3 1 2 3
1 2 1 3 2 3
1
2
1 2 3 1
2
2
1
2
==--+
+++
++++
-
--
(5)
From the experimental design models, it is evident that all
the linear, quadratic, cubic, and interaction terms in Eq. (3,
4, and 5) are statistically significant at a 95% confidence
level (p 0.05). This underscores the importance of floc-
culant dose, slurry pH, and mixing velocity as key factors
influencing the initial settling rate, water recovery, and the
turbidity of the supernatant responses.
Upon analysing the coefficient estimate values, it is
evident that the terms exerting the most substantial main
Table 6. Summarized ANOVA for ISR, WR and turbidity responses
Response Source F-Value
p-Value
Prob F R2 R2
adj
C.V
(%)
Adequate
Precision Mean Std. Dev. Remarks
ISR
(cm/min)
Model 297.14 0.0001 0.9984 0.9951 1.2 57.3448 12.17 0.1457 Significant
Residual
(lack of fit)
0.954 0.3736 Not significant
Water
recovery
(%)
Model 223.25 0.0001 0.9979 0.9935 0.3544 57.5392 81.29 0.2881 Significant
Residual
(lack of fit)
0.0341 0.8608 Not significant
Water
turbidity
(NTU)
Model 1194.64 0.0001 0.9996 0.9988 3.41 114.5365 4.04 0.1379 Significant
Residual
(lack of fit)
5.46 0.0666 Not significant