Fit Summary

Response 3: Reinforcement

Source Sequential p-value Lack of Fit p-value Adjusted R² Predicted R²

Linear 0.0183 0.0058 0.2839 -0.1856
2FI 0.0716 0.0103 0.4283 -1.0379
Quadratic 0.0161 0.0386 0.6480 -1.3770 Suggested
Cubic 0.0274 0.2923 0.8635 Aliased

Sequential Model Sum of Squares [Type I]

Response 3: Reinforcement

Source Sum of Squares df Mean Square F-value p-value

Mean vs Total 14.74 1 14.74
Block vs Mean 0.0000 1 0.0000
Linear vs Block 0.0008 3 0.0003 4.17 0.0183
2FI vs Linear 0.0004 3 0.0001 2.77 0.0716
Quadratic vs 2FI 0.0005 3 0.0002 4.75 0.0161 Suggested
Cubic vs Quadratic 0.0004 7 0.0001 4.38 0.0274 Aliased
Residual 0.0001 8 0.0000
Total 14.74 26 0.5670

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

Model Summary Statistics

Source Std. Dev. R² Adjusted R² Predicted R² PRESS

Linear 0.0081 0.3734 0.2839 -0.1856 0.0026
2FI 0.0072 0.5712 0.4283 -1.0379 0.0045
Quadratic 0.0057 0.7800 0.6480 -1.3770 0.0052 Suggested
Cubic 0.0035 0.9545 0.8635 * Aliased

 Case(s) with leverage of 1.0000: PRESS statistic not defined.

Focus on the model maximizing the Adjusted R² and the Predicted R².
Lack of Fit Tests

Source Sum of Squares df Mean Square F-value p-value

Linear 0.0013 14 0.0001 7.66 0.0058
2FI 0.0009 11 0.0001 6.47 0.0103
Quadratic 0.0004 8 0.0000 4.14 0.0386 Suggested
Cubic 0.0000 1 0.0000 1.30 0.2923 Aliased
Pure Error 0.0001 7 0.0000

The selected model should have insignificant lack-of-fit.

ANOVA for Quadratic model

Response 3: Reinforcement

Source Sum of Squares df Mean Square F-value p-value

Block 0.0000 1 0.0000
Model 0.0017 9 0.0002 5.91 0.0013 significant
A-Current 0.0008 1 0.0008 24.32 0.0002
B-Volatage 1.612E-07 1 1.612E-07 0.0050 0.9444
C-Gas flow 0.0003 1 0.0003 7.83 0.0135
AB 0.0002 1 0.0002 5.05 0.0402
AC 0.0001 1 0.0001 3.34 0.0876
BC 0.0005 1 0.0005 15.65 0.0013
A² 0.0004 1 0.0004 10.93 0.0048
B² 0.0000 1 0.0000 1.54 0.2338
C² 0.0000 1 0.0000 0.5694 0.4622
Residual 0.0005 15 0.0000
Lack of Fit 0.0004 8 0.0000 4.14 0.0386 significant
Pure Error 0.0001 7 0.0000
Cor Total 0.0022 25

Factor coding is Coded.

Sum of squares is Type III - Partial

The Model F-value of 5.91 implies the model is significant. There is only a 0.13% chance
that an F-value this large could occur due to noise.

P-values less than 0.0500 indicate model terms are significant. In this case A, C, AB, BC, A²
are significant model terms. Values greater than 0.1000 indicate the model terms are not
significant. If there are many insignificant model terms (not counting those required to
support hierarchy), model reduction may improve your model.
The Lack of Fit F-value of 4.14 implies the Lack of Fit is significant. There is only a 3.86%
chance that a Lack of Fit F-value this large could occur due to noise. Significant lack of fit is
bad -- we want the model to fit.

Fit Statistics

Std. Dev. 0.0057 R² 0.7800

Mean 0.7530 Adjusted R² 0.6480
C.V. % 0.7516 Predicted R² -1.3770
Adeq Precision 10.7292

A negative Predicted R² implies that the overall mean may be a better predictor of your
response than the current model. In some cases, a higher order model may also predict better.

Adeq Precision measures the signal to noise ratio. A ratio greater than 4 is desirable. Your
ratio of 10.729 indicates an adequate signal. This model can be used to navigate the design
space.

Model Comparison Statistics

PRESS 0.0052
-2 Log Likelihood -209.59
BIC -173.75
AICc -168.73

Coefficients in Terms of Coded Factors

Factor Coefficient Estimate df Standard Error 95% CI Low 95% CI High VIF
Intercept 0.7478 1 0.0021 0.7434 0.7522
Block 1 0.0033 1
Block 2 -0.0033
A-Current -0.0108 1 0.0022 -0.0155 -0.0062 4.42
B-Volatage 0.0002 1 0.0024 -0.0049 0.0052 1.56
C-Gas flow -0.0061 1 0.0022 -0.0107 -0.0015 1.80
AB -0.0059 1 0.0026 -0.0116 -0.0003 1.65
AC -0.0046 1 0.0025 -0.0099 0.0008 1.89
BC -0.0082 1 0.0021 -0.0126 -0.0038 1.11
A² 0.0039 1 0.0012 0.0014 0.0063 3.04
B² 0.0042 1 0.0034 -0.0030 0.0114 2.09
C² -0.0026 1 0.0034 -0.0098 0.0047 2.22
The coefficient estimate represents the expected change in response per unit change in factor
value when all remaining factors are held constant. The intercept in an orthogonal design is
the overall average response of all the runs. The coefficients are adjustments around that
average based on the factor settings. When the factors are orthogonal the VIFs are 1; VIFs
greater than 1 indicate multi-colinearity, the higher the VIF the more severe the correlation of
factors. As a rough rule, VIFs less than 10 are tolerable.

Final Equation in Terms of Coded Factors

Reinforcement =
+0.7478
-0.0108 A
+0.0002 B
-0.0061 C
-0.0059 AB
-0.0046 AC
-0.0082 BC
+0.0039 A²
+0.0042 B²
-0.0026 C²

The equation in terms of coded factors can be used to make predictions about the response for
given levels of each factor. By default, the high levels of the factors are coded as +1 and the
low levels are coded as -1. The coded equation is useful for identifying the relative impact of
the factors by comparing the factor coefficients.

Final Equation in Terms of Actual Factors

Reinforcement =
-0.496516
+0.000337 Current
+0.031732 Volatage
+0.096043 Gas flow
-0.000198 Current * Volatage
-0.000152 Current * Gas flow
-0.002053 Volatage * Gas flow
+0.000017 Current²
+0.001047 Volatage²
-0.000643 Gas flow²

The equation in terms of actual factors can be used to make predictions about the response for
given levels of each factor. Here, the levels should be specified in the original units for each
factor. This equation should not be used to determine the relative impact of each factor
because the coefficients are scaled to accommodate the units of each factor and the intercept
is not at the center of the design space.
Report

Run Actual Predicted Residual Leverage Internally Externally Cook's Influence Standard
 on Fitted
Studentized Studentized
Order Value Value⁽¹⁾ Distance Value Order
Residuals Residuals
DFFITS
1 0.7570 0.7544 0.0026 0.443 0.611 0.598 0.027 0.533 14
2 0.7490 0.7511 -0.0021 0.140 -0.401 -0.389 0.002 -0.157 11
3 0.7540 0.7588 -0.0048 0.821 -2.023 -2.292 1.703⁽²⁾ -4.903⁽²⁾ 4
4 0.7500 0.7468 0.0032 0.305 0.673 0.660 0.018 0.437 16
5 0.7500 0.7461 0.0039 0.623 1.117 1.127 0.187 1.447 8
6 0.7900 0.7833 0.0067 0.810 2.736 3.736 2.909⁽²⁾ 7.722⁽²⁾ 3
7 0.7500 0.7511 -0.0011 0.140 -0.210 -0.204 0.001 -0.082 20
8 0.7420 0.7535 -0.0115 0.144 -2.198 -2.580 0.074 -1.059 19
9 0.7450 0.7438 0.0012 0.137 0.236 0.228 0.001 0.091 10
10 0.7450 0.7491 -0.0041 0.908⁽³⁾ -2.364 -2.882 5.012⁽²⁾ -9.055⁽²⁾ 6
11 0.7510 0.7479 0.0031 0.142 0.587 0.574 0.005 0.233 15
12 0.7540 0.7546 -0.0006 0.383 -0.141 -0.136 0.001 -0.108 13
13 0.7540 0.7534 0.0006 0.753 0.215 0.208 0.013 0.363 2
14 0.7560 0.7479 0.0081 0.142 1.541 1.623 0.036 0.659 17
15 0.7450 0.7468 -0.0018 0.305 -0.386 -0.375 0.006 -0.248 12
16 0.7540 0.7546 -0.0006 0.540 -0.160 -0.155 0.003 -0.168 1
17 0.7450 0.7468 -0.0018 0.305 -0.386 -0.375 0.006 -0.248 9
18 0.7700 0.7680 0.0020 0.818 0.833 0.824 0.284 1.750 5
19 0.7540 0.7511 0.0029 0.140 0.552 0.539 0.005 0.218 18
20 0.7580 0.7638 -0.0058 0.642 -1.707 -1.837 0.475 -2.461⁽²⁾ 7
21 0.7450 0.7508 -0.0058 0.255 -1.190 -1.208 0.044 -0.707 25
22 0.7540 0.7581 -0.0041 0.412 -0.939 -0.935 0.056 -0.782 21
23 0.7500 0.7508 -0.0008 0.255 -0.166 -0.161 0.001 -0.094 26
24 0.7510 0.7455 0.0055 0.652 1.633 1.740 0.455 2.382⁽²⁾ 22
25 0.7540 0.7508 0.0032 0.255 0.653 0.640 0.013 0.374 24
26 0.7500 0.7479 0.0021 0.531 0.531 0.518 0.029 0.551 23

⁽¹⁾ Predicted values include block corrections.

⁽²⁾ Exceeds limits.

⁽³⁾ Observation with leverage > 2.00 × (average leverage).