1 Consider a variation of the bottle filling experiment from bottle problem Example (pictures attached) . Suppose that only two levels of ca
onation are used so that the experiment is a 23 factorial design with two replicates. The data are shown below.
Coded Factors
Fill Height Deviation
Run
A
B
C
Replicate 1
Replicate 2
1
–
–
–
-3
-1
2
+
–
–
0
1
3
–
+
–
-1
0
4
+
+
–
2
3
5
–
–
+
-1
0
6
+
–
+
2
1
7
–
+
+
1
1
8
+
+
+
6
5
Factor Levels
Low (–1)
High (+1)
A (%)
10
12
B (psi)
25
30
C (
m)
200
250
(a) Analyze the data from this experiment. Which factors significantly affect fill height deviation?
(b) Analyze the residuals from this experiment. Are there any indications of model inadequacy?
(c) Obtain a model for predicting fill height deviation in terms of the important process variables. Use this model to construct contour plots to assist in interpreting the results of the experiment.
(d) In part (a), you probably noticed that there was an interaction term that was borderline significant. If you did not include the interaction term in your model, include it now and repeat the analysis. What difference did this make? If you elected to include the interaction term in part (a), remove it and repeat the analysis. What difference does this make?
2 An experiment was conducted on a chemical process that produces a polymer. The four factors studied were temperature (A), catalyst concentration (B), time (C), and pressure (D). Two responses, molecular weight and viscosity, were observed. The design matrix and response data are shown below:
Actual
Run
Run
Molecula
Facto
Levels
Numbe
Orde
A
B
C
D
Weight
Viscosity
Low (–)
High (+)
1
18
–
–
–
–
2400
1400
A (°C)
100
120
2
9
+
–
–
–
2410
1500
B (%)
4
8
3
13
–
+
–
–
2315
1520
C (min)
20
30
4
8
+
+
–
–
2510
1630
D (psi)
60
75
5
3
–
–
+
–
2615
1380
6
11
+
–
+
–
2625
1525
7
14
–
+
+
–
2400
1500
8
17
+
+
+
–
2750
1620
9
6
–
–
–
+
2400
1400
10
7
+
–
–
+
2390
1525
11
2
–
+
–
+
2300
1500
12
10
+
+
–
+
2520
1500
13
4
–
–
+
+
2625
1420
14
19
+
–
+
+
2630
1490
15
15
–
+
+
+
2500
1500
16
20
+
+
+
+
2710
1600
17
1
0
0
0
0
2515
1500
18
5
0
0
0
0
2500
1460
19
16
0
0
0
0
2400
1525
20
12
0
0
0
0
2475
1500
(a) Consider only the molecular weight response. Plot the effect estimates on a normal probability scale. What effects appear important?
(b) Use an analysis of variance to confirm the results from part (a). Is there an indication of curvature?
(c) Write down a regression model to predict molecular weight as a function of the important variables.
(d) Analyze the residuals and comment on model adequacy.