Environmental Engineering Reference
In-Depth Information
9. As shown in this table,
Sequential Model Sum of Squares
select the highest
order polynomial, where the additional terms are significant. In this table, each
row tests whether the coefficients of certain model terms are equal to zero. For
example, the row with source ―Linear‖ tests whether the coefficients of the
linear terms are equal to zero. A low value (say, less than 0.05) of ―Prob > F‖ ,
also called the p-value, supports the conclusion that the coefficients differ
from zero and should be included in the model. The row with source
―Quadratic‖ tests whether any quadratic coefficients differ from zero. Since
the ―Prob >F‖ of 0.001 is less than 0.05, the quadratic terms should also be
included in the model. Similarly, the special cubic coefficients are required in
the model. However, cubic coefficients are not required as ―Prob > F‖ of 0.77
exceeds the value 0.05. ANOVA results for water absorption, shrinkage, brick
density, leaching of cadmium and lead are given in Tables 10 to Table 14
respectively.
Table 9. Sequential model sum of squares
for response compressive strength
Source
Sum of
Squares
DF
Mean
Square
F Value
Proc>F
Mean
38263.73
1
38263.73
---
---
Linear
14374.12
2
7187.06
31.77
< 0.0001
Quadratic
2132.60
3
710.87
15.98
0.0010
Special Cubic
341.54
1
341.54
167.07
< 0.0001
Cubic
3.21
3
1.07
0.38
0.7706
Residual
11.10
4
2.78
---
--
Total
55126.30
14
3937.59
---
--
Table 10. Sequential model sum of squares for response water absorption
Source
Sum of
Squares
DF
Mean
Square
F Value
Proc>F
Mean
3689.08
1
3689.08
Linear
74.63
2
37.32
40.95
< 0.0001
Quadratic
7.68
3
2.56
8.75
0.0066
Special Cubic
0.66
1
0.66
2.76
0.1404
Cubic
0.33
3
0.11
0.32
0.8104
Residual
1.35
4
0.34
---
--
Total
3773.73
14
269.55
---
--
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