6-20 General Linear Model: UEC versus Laser Power, Pulse Frequency, ... Factor Laser Power Pulse Frequency Cell Size Writing Speed
Type fixed fixed fixed fixed
Levels 2 2 2 2
Values -1, 1 -1, 1 -1, 1 -1, 1
Analysis of Variance for UEC, using Adjusted SS for Tests Source Laser Power Pulse Frequency Cell Size Writing Speed Laser Power*Pulse Frequency Laser Power*Cell Size Laser Power*Writing Speed Pulse Frequency*Cell Size Pulse Frequency*Writing Speed Cell Size*Writing Speed Laser Power*Pulse Frequency* Cell Size Laser Power*Pulse Frequency* Writing Speed Pulse Frequency*Cell Size* Writing Speed Laser Power*Cell Size*Writing Speed Error Total
DF 1 1 1 1 1 1 1 1 1 1 1
Seq SS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.002025
Adj SS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.002025
Adj MS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.002025
F 4096.00 64.00 2809.00 2025.00 49.00 484.00 16.00 100.00 16.00 225.00 81.00
1
0.001225
0.001225
0.001225
49.00
1
0.001600
0.001600
0.001600
64.00
1 1 15
0.001600 0.000025 0.253575
0.001600 0.000025
0.001600 0.000025
64.00
Source Laser Power Pulse Frequency Cell Size Writing Speed Laser Power*Pulse Frequency Laser Power*Cell Size Laser Power*Writing Speed Pulse Frequency*Cell Size Pulse Frequency*Writing Speed Cell Size*Writing Speed Laser Power*Pulse Frequency* Cell Size Laser Power*Pulse Frequency* Writing Speed Pulse Frequency*Cell Size* Writing Speed Laser Power*Cell Size*Writing Speed Error Total
P 0.010 0.079 0.012 0.014 0.090 0.029 0.156 0.063 0.156 0.042 0.070
S = 0.005
R-Sq = 99.99%
0.090 0.079 0.079
R-Sq(adj) = 99.85%
None of three ways are significant at the 5% level
Analysis of Variance for UEC, using Adjusted SS for Tests Source Laser Power Pulse Frequency Cell Size Writing Speed Laser Power*Pulse Frequency Laser Power*Cell Size Laser Power*Writing Speed Pulse Frequency*Cell Size Pulse Frequency*Writing Speed Cell Size*Writing Speed Error Total S = 0.0359861
R-Sq = 97.45%
DF 1 1 1 1 1 1 1 1 1 1 5 15
Seq SS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.006475 0.253575
Adj SS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.006475
Adj MS 0.102400 0.001600 0.070225 0.050625 0.001225 0.012100 0.000400 0.002500 0.000400 0.005625 0.001295
R-Sq(adj) = 92.34%
Unusual Observations for UEC Obs 11
UEC 0.630000
Fit 0.588750
SE Fit 0.029838
Residual 0.041250
St Resid 2.05 R
R denotes an observation with a large standardized residual. First Pass
Significant factors and interaction at 5% Laser power Cell Size Writing speed Laser power by cell size interaction Cell size by writing speed
F 79.07 1.24 54.23 39.09 0.95 9.34 0.31 1.93 0.31 4.34
P 0.000 0.317 0.001 0.002 0.375 0.028 0.602 0.223 0.602 0.092
Interaction Plot for UEC Fitted Means -1
1
-1
1
-1
1 0.90
Laser Power -1 1
0.75
Laser Power
0.60 0.90
Pulse Frequency -1 1
0.75
Pulse Frequency
0.60 0.90
C ell Size -1 1
0.75
Cell Size
0.60
Writing Speed
We would want cell size -1 and laser power 1. Main Effects Plot for UEC Fitted Means Laser Power
0.80
Pulse Frequency
0.75 0.70
Mean
0.65 -1
1
-1
Cell Size
0.80
1 W riting Speed
0.75 0.70 0.65 -1
We would want writing speed set at -1.
1
-1
1
Final Conclusion: Factor Laser Power Cell Size Writing speed
Coded Setting +1 -1 -1
Uncoded Setting 13 w 0.07 in 10 in/sec
The laser pulse frequency is not significant
Normal Probability Plot (response is UEC) 99
95 90
Percent
80 70 60 50 40 30 20 10 5
1
-0.050
-0.025
0.000 Residual
0.025
Residual plot looks a little clumpy. Possibly a measurement problem.
0.050
6-29
Normal Plot of the Standardized Effects (response is Molecular Weight, Alpha = 0.05) 99 C
95
Percent
Effect Ty pe Not Significant Significant
90
A
80
AB
F actor A B C D
70 60 50 40 30
Name Temperature C ataly st C oncentration Time P ressure
20 10 5
1
-2
0
2 4 Standardized Effect
6
8
Estimated Effects and Coefficients for Molecular Weight (coded units) Term Constant Temperature Catalyst Concentration Time Pressure Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure Temperature*Catalyst Concentration* Time Temperature*Catalyst Concentration* Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure Temperature*Catalyst Concentration* Time*Pressure S = 53.5490 R-Sq = 96.22%
PRESS = 4677501 R-Sq(pred) = 0.00%
Effect 123.75 -11.25 201.25 6.25 120.00 20.00 -17.50 -22.50 7.50 12.50 16.25
Coef 2499.50 61.87 -5.62 100.62 3.12 60.00 10.00 -8.75 -11.25 3.75 6.25 8.13
SE Coef 11.97 13.39 13.39 13.39 13.39 13.39 13.39 13.39 13.39 13.39 13.39 13.39
T 208.75 4.62 -0.42 7.52 0.23 4.48 0.75 -0.65 -0.84 0.28 0.47 0.61
P 0.000 0.010 0.696 0.002 0.827 0.011 0.497 0.549 0.448 0.793 0.665 0.577
-11.25
-5.63
13.39
-0.42
0.696
-18.75 3.75 -22.50
-9.38 1.88 -11.25
13.39 13.39 13.39
-0.70 0.14 -0.84
0.522 0.895 0.448
R-Sq(adj) = 82.06%
Analysis of Variance for Molecular Weight (coded units) Source Main Effects Temperature Catalyst Concentration Time Pressure 2-Way Interactions Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure 3-Way Interactions Temperature*Catalyst Concentration*Time Temperature*Catalyst Concentration*Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure 4-Way Interactions Temperature*Catalyst Concentration*Time*Pressure Residual Error Lack of Fit Pure Error Total
DF 4 1 1 1 1 6 1 1 1 1 1 1 4 1 1 1 1 1 1 4 1 3 19
Seq SS 223925 61256 506 162006 156 63300 57600 1600 1225 2025 225 625 3025 1056 506 1406 56 2025 2025 11470 3645 7825 303745
Source Main Effects Temperature Catalyst Concentration Time Pressure 2-Way Interactions Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure 3-Way Interactions Temperature*Catalyst Concentration*Time Temperature*Catalyst Concentration*Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure 4-Way Interactions Temperature*Catalyst Concentration*Time*Pressure Residual Error Lack of Fit Pure Error Total
F 19.52 21.36 0.18 56.50 0.05 3.68 20.09 0.56 0.43 0.71 0.08 0.22 0.26 0.37 0.18 0.49 0.02 0.71 0.71
P 0.007 0.010 0.696 0.002 0.827 0.114 0.011 0.497 0.549 0.448 0.793 0.665 0.888 0.577 0.696 0.522 0.895 0.448 0.448
1.40
0.322
Adj SS 223925 61256 506 162006 156 63300 57600 1600 1225 2025 225 625 3025 1056 506 1406 56 2025 2025 11470 3645 7825
Estimated Coefficients for Molecular Weight using data in uncoded units Term Constant Temperature Catalyst Concentration Time Pressure Temperature*Catalyst Concentration Temperature*Time
Coef -8806.7 97.750 2450.00 540.000 165.333 -21.8125 -4.67500
Adj MS 55981 61256 506 162006 156 10550 57600 1600 1225 2025 225 625 756 1056 506 1406 56 2025 2025 2868 3645 2608
Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure Temperature*Catalyst Concentration* Time Temperature*Catalyst Concentration* Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure Temperature*Catalyst Concentration* Time*Pressure
-1.51667 -123.125 -37.5000 -7.1333 1.09375 0.337500 0.065000 1.67500 -0.0150000
Interaction Plot for Molecular Weight Data Means 4
6
8
60.0
67.5
75.0 2600 2500
Temperature
2400
2600 2500
Catalyst Concentration
2400
2600 2500
Time
2400
2600 2500
Pressure
2400 100
110
120
20
25
30
c) y = 2499.5+61.87temp-5.62catalyst concentration+100.62time+10temp*time
Temperature 100 110 120 C ataly st C oncentration 4 6 8 Time 20 25 30 Pressure 60.0 67.5 75.0
Residual Plots for Molecular Weight Normal Probabilit y Plot
Versus Fit s
99
100 50 Residual
Percent
90 50 10
0 -50 -100
1
-100
0 Residual
100
2300
2400
Hist ogram
2600
2700
Versus Order 100
4.8
50
3.6
Residual
Frequency
2500 Fitted Value
2.4 1.2
0 -50 -100
0.0
-100
-50
0 Residual
50
100
2
4
6
8 10 12 14 Obser vation Order
16
18
20
d)
Normal Plot of the Standardized Effects (response is Viscosity, Alpha = 0.05) 99 A
95 90
B
Percent
80 70 60 50 40
Effect Ty pe Not Significant Significant F actor A B C D
Name Temperature C ataly st C oncentration Time P ressure
30 20 10 5
1
-2
0
2 4 Standardized Effect
6
8
Estimated Effects and Coefficients for Viscosity (coded units) Term Constant Temperature Catalyst Concentration
Effect 96.25 91.25
Coef 1499.75 48.12 45.62
SE Coef 5.280 5.903 5.903
T 284.06 8.15 7.73
P 0.000 0.001 0.002
Time Pressure Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure Temperature*Catalyst Concentration* Time Temperature*Catalyst Concentration* Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure Temperature*Catalyst Concentration* Time*Pressure S = 23.6114 R-Sq = 97.41%
PRESS = 80857.3 R-Sq(pred) = 6.06%
7.50 -17.50 -13.75 12.50 -22.50 10.00 -25.00 13.75 15.00
3.75 -8.75 -6.88 6.25 -11.25 5.00 -12.50 6.88 7.50
5.903 5.903 5.903 5.903 5.903 5.903 5.903 5.903 5.903
0.64 -1.48 -1.16 1.06 -1.91 0.85 -2.12 1.16 1.27
0.560 0.212 0.309 0.349 0.129 0.445 0.102 0.309 0.273
-10.00
-5.00
5.903
-0.85
0.445
-1.25 18.75 23.75
-0.63 9.38 11.88
5.903 5.903 5.903
-0.11 1.59 2.01
0.921 0.187 0.115
R-Sq(adj) = 87.69%
Analysis of Variance for Viscosity (coded units) Source Main Effects Temperature Catalyst Concentration Time Pressure 2-Way Interactions Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure 3-Way Interactions Temperature*Catalyst Concentration*Time Temperature*Catalyst Concentration*Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure 4-Way Interactions Temperature*Catalyst Concentration*Time*Pressure Residual Error Lack of Fit Pure Error Total
DF 4 1 1 1 1 6 1 1 1 1 1 1 4 1 1 1 1 1 1 4 1 3 19
Seq SS 71812.5 37056.2 33306.2 225.0 1225.0 7062.5 756.3 625.0 2025.0 400.0 2500.0 756.3 2712.5 900.0 400.0 6.3 1406.2 2256.3 2256.3 2230.0 61.3 2168.8 86073.7
Source Main Effects Temperature Catalyst Concentration Time Pressure 2-Way Interactions Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure 3-Way Interactions
Adj MS 17953.1 37056.2 33306.2 225.0 1225.0 1177.1 756.3 625.0 2025.0 400.0 2500.0 756.3 678.1
Adj SS 71812.5 37056.2 33306.2 225.0 1225.0 7062.5 756.3 625.0 2025.0 400.0 2500.0 756.3 2712.5 900.0 400.0 6.3 1406.2 2256.3 2256.3 2230.0 61.3 2168.8
F 32.20 66.47 59.74 0.40 2.20 2.11 1.36 1.12 3.63 0.72 4.48 1.36 1.22
P 0.003 0.001 0.002 0.560 0.212 0.245 0.309 0.349 0.129 0.445 0.102 0.309 0.427
Temperature*Catalyst Concentration*Time Temperature*Catalyst Concentration*Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure 4-Way Interactions Temperature*Catalyst Concentration*Time*Pressure Residual Error Lack of Fit Pure Error Total
900.0 400.0 6.3 1406.2 2256.3 2256.3 557.5 61.3 722.9
1.61 0.72 0.01 2.52 4.05 4.05
0.273 0.445 0.921 0.187 0.115 0.115
0.08
0.790
Estimated Coefficients for Viscosity using data in uncoded units Term Constant Temperature Catalyst Concentration Time Pressure Temperature*Catalyst Concentration Temperature*Time Temperature*Pressure Catalyst Concentration*Time Catalyst Concentration*Pressure Time*Pressure Temperature*Catalyst Concentration* Time Temperature*Catalyst Concentration* Pressure Temperature*Time*Pressure Catalyst Concentration*Time*Pressure Temperature*Catalyst Concentration* Time*Pressure
Coef 16869.1 -151.500 -2665.00 -646.000 -253.333 26.7500 6.20000 2.46667 101.375 43.2500 10.0667 -0.993750 -0.429167 -0.0966667 -1.61667 0.0158333
Interaction Plot for Viscosity Data Means 4
6
8
20
25
30
60.0
67.5
75.0 1600
1500
Temperature
1400 1600
1500
Catalyst Concentration
1400 1600
1500
Time
1400
Pressure
Y=1499.75+48.12temp+45.62catalyst concentration
Temperature 100 110 120 C ataly st C oncentration 4 6 8 Time 20 25 30
Residual Plots for Viscosity Normal Probabilit y Plot
Versus Fit s
99
50
Residual
Percent
90 50 10 1 -100
-50
0 Residual
0
-50
50
1400
1450
Hist ogram
1600
Versus Order
6
Residual
Frequency
1550
50
8
4 2 0
1500 Fitted Value
-80
-60
-40
-20 0 Residual
20
40
0
-50
2
4
6
8 10 12 14 Observation Order
16
18
20