Parameter Estimates from Fit to Full-Factorial Model
Term
|
Estimate
|
Std Error
|
t Ratio
|
Prob>|t|
|
|
Intercept
|
7.5838154
|
0.228814
|
33.14
|
<.0001*
|
|
Glutamine
|
-0.572075
|
0.209098
|
-2.74
|
0.0170*
|
|
EAA
|
0.0998006
|
0.27464
|
0.36
|
0.7222
|
|
NEAA
|
1.2100318
|
0.331635
|
3.65
|
0.0029*
|
|
ITS
|
0.5629417
|
0.202966
|
2.77
|
0.0158*
|
|
Lipids
|
-0.727668
|
0.368208
|
-1.98
|
0.0697
|
|
Glutamine*EAA
|
-1.04495
|
0.268457
|
-3.89
|
0.0019*
|
|
EAA*NEAA
|
0.8313522
|
0.344822
|
2.41
|
0.0314*
|
|
EAA*Lipids
|
1.2371315
|
0.334539
|
3.70
|
0.0027*
|
|
NEAA*ITS
|
-1.070604
|
0.260279
|
-4.11
|
0.0012*
|
|
NEAA*Lipids
|
0.840536
|
0.276571
|
3.04
|
0.0095*
|
The ANOVA results indicate the model is significantly better at fitting the data than normal process variations.
ANOVA Results of Fit to Full-Factorial Model
Source
|
DF
|
Sum of Squares
|
Mean Square
|
F Ratio
|
Model
|
10
|
237.42417
|
23.7424
|
26.6759
|
Error
|
13
|
11.57041
|
0.8900
|
Prob > F
|
C. Total
|
23
|
248.99458
|
<.0001*
|
The resulting prediction profiler shows linear responses (no square terms used at this point), and at the coded point 0, the middle of the ranges explored, the expected viable cell density is 7.58x10^6. Note that the exponents were omitted from the plot to improve visualization.
Prediction Profiler for Fit to Full-Factorial Model
Stepping back for a minute, let's recall the purpose of this exercise: I wanted to find the minimum number of experiments needed to explain how the different media components affected the viable cell density. I reasoned that this could be achieved in fewer than the 54 experiments that were used in the cited paper. At the moment, I'm 24 experiments into the analysis and most of the effects that were observed in the results from the CCD analysis are present. My current problem is that when the center point data is included, the full factorial model is unable to predict the measured values (red triangles).
Actual by Predicted with Center Points Shown but Excluded from Fit to Model
Despite the 24 experiments, the process space has yet to be fully explored from a full-factorial perspective - as a result, trying to include square terms to the model would be useless because they continue to be aliased against each other. The only path forward is to augment the data further to see if the results allow model refinement.
Augmenting the experiment to a total of 32 now and selecting only the statistically significant terms from a fit to the full-factorial model gives the same results as obtained from the previous analysis. The key differences are the reduction in the F ratio and the loss of the pairwise interaction of NEAA and EAA.
ANOVA Results from Fit of Augmented Data to Full Factorial Model
Source
|
DF
|
Sum of Squares
|
Mean Square
|
F Ratio
|
Model
|
9
|
228.02583
|
25.3362
|
15.8153
|
Error
|
22
|
35.24409
|
1.6020
|
Prob > F
|
C. Total
|
31
|
263.26992
|
<.0001*
|
Parameter Estimates from Fit of Augmented Data to Full Factorial Model
Term
|
Estimate
|
Std Error
|
t Ratio
|
Prob>|t|
|
|
Intercept
|
7.5813733
|
0.228694
|
33.15
|
<.0001*
|
|
Glutamine
|
-0.560817
|
0.22865
|
-2.45
|
0.0226*
|
|
EAA
|
0.170159
|
0.241575
|
0.70
|
0.4886
|
|
NEAA
|
1.3289597
|
0.23971
|
5.54
|
<.0001*
|
|
ITS
|
0.4425618
|
0.226401
|
1.95
|
0.0634
|
|
Lipids
|
-0.191069
|
0.228817
|
-0.84
|
0.4127
|
|
Glutamine*EAA
|
-1.2019
|
0.238782
|
-5.03
|
<.0001*
|
|
EAA*Lipids
|
0.9275438
|
0.24142
|
3.84
|
0.0009*
|
|
NEAA*ITS
|
-0.775146
|
0.240365
|
-3.22
|
0.0039*
|
|
NEAA*Lipids
|
0.7488445
|
0.239475
|
3.13
|
0.0049*
|
The model is still unable to predict the VCD at the midpoint of the range explored (solid red triangles). In spite of completing enough runs for a full factorial (32), the square terms of each of the main effects remain indistinguishable from each other! What to do next? Stay tuned!
Actual versus Predicted of Augmented Design
Singularity Details
Glutamine*Glutamine = EAA*EAA = NEAA*NEAA = ITS*ITS = Lipids*Lipids
