Homework
1) Temperature, Pressure and yield on a chemical process is given below. Use the SPSS package to model this problem as a DOE problem and answer the questions below?
i. What factors are sensitive?
ii. Give the complete table of analysis of variance.
iii. What is the best combination of temperature and pressure to run this system?
|
|
Pressure lbs/sq. in.
|
|
Temperature in centigrade given below
|
250
|
300
|
350
|
|
100
|
44
|
74
|
85
|
|
100
|
43
|
72
|
81
|
|
100
|
49
|
73
|
72
|
|
100
|
56
|
60
|
84
|
|
100
|
50
|
78
|
78
|
|
100
|
49
|
76
|
71
|
|
100
|
54
|
67
|
86
|
|
100
|
55
|
74
|
89
|
|
100
|
47
|
72
|
83
|
|
100
|
59
|
80
|
72
|
|
150
|
49
|
60
|
78
|
|
150
|
54
|
77
|
86
|
|
150
|
47
|
64
|
79
|
|
150
|
59
|
73
|
72
|
|
150
|
53
|
71
|
80
|
|
150
|
50
|
62
|
74
|
|
150
|
42
|
61
|
72
|
|
150
|
42
|
78
|
89
|
|
150
|
53
|
66
|
85
|
|
150
|
48
|
64
|
76
|
|
200
|
59
|
60
|
73
|
|
200
|
52
|
71
|
80
|
|
200
|
42
|
72
|
72
|
|
200
|
55
|
79
|
87
|
|
200
|
44
|
78
|
82
|
|
200
|
49
|
76
|
84
|
|
200
|
53
|
70
|
72
|
|
200
|
42
|
78
|
80
|
|
200
|
50
|
69
|
83
|
|
200
|
58
|
69
|
77
|
(Figures inside the table are yield in pounds for the same starting batch size for a chemical reaction.)
2) Solve the following problem using logistic regression using SPSS. Data on admission to Top MBA programs and student profiles are given below. Answer the questions at the bottom of the page. (Science major =1 and non-science major =0, Admission is 1 and rejection is 0.)
|
GRE
|
GPA
|
Experience
|
Science_Major
|
Admission_top_MBA_Program
|
|
420
|
2.989713
|
4
|
1
|
0
|
|
410
|
3.062205
|
0
|
0
|
0
|
|
460
|
3.95905
|
2
|
0
|
1
|
|
740
|
3.969431
|
5
|
0
|
1
|
|
400
|
2.964876
|
3
|
1
|
0
|
|
740
|
3.016192
|
4
|
0
|
1
|
|
750
|
3.798612
|
1
|
0
|
1
|
|
610
|
3.779912
|
0
|
0
|
0
|
|
540
|
3.959263
|
4
|
0
|
1
|
|
460
|
2.873084
|
0
|
0
|
0
|
|
790
|
2.969328
|
2
|
0
|
1
|
|
420
|
2.952248
|
3
|
0
|
0
|
|
410
|
2.929681
|
3
|
0
|
0
|
|
670
|
2.853553
|
4
|
0
|
0
|
|
620
|
3.047547
|
5
|
1
|
0
|
|
550
|
3.660386
|
3
|
0
|
0
|
|
530
|
2.893152
|
5
|
0
|
0
|
|
790
|
3.193752
|
3
|
0
|
1
|
|
480
|
3.023745
|
2
|
0
|
0
|
|
580
|
3.902819
|
2
|
1
|
1
|
|
730
|
3.899274
|
1
|
0
|
0
|
|
480
|
3.869059
|
1
|
1
|
0
|
|
600
|
2.924105
|
2
|
0
|
0
|
|
700
|
2.960273
|
2
|
0
|
0
|
|
410
|
3.730714
|
0
|
0
|
0
|
|
720
|
3.934777
|
1
|
0
|
1
|
|
560
|
3.559107
|
3
|
1
|
0
|
|
620
|
3.088629
|
2
|
0
|
0
|
|
560
|
2.904412
|
3
|
0
|
0
|
|
610
|
3.897915
|
3
|
1
|
0
|
i. Run the logistic regression using SPSS and this data.
ii. Write down the logit function from your output.
iii. Using the logistic regression equation and input data, generate the probability of admission for each of the 30 students and compare it with SPSS produced probabilities.
3) Data on Yield % against two variables (temperature and catalyst level) is given below.
i. Do a spreadsheet based analysis of the data and report on which factors (temperature, catalyst level or interaction: temperature*Catalyst) is significant.
ii. If interaction is significant at 0.05 level, report on the best combination of the two factors that will maximize the yield percent.
|
|
Temperature (C )
|
|
|
600
|
650
|
700
|
|
Catalyst Level
|
Low
|
70
|
74
|
94
|
|
Low
|
61
|
73
|
74
|
|
Low
|
57
|
77
|
52
|
|
Morerate
|
95
|
60
|
93
|
|
Moderate
|
87
|
79
|
82
|
|
Moderate
|
97
|
54
|
84
|
|
High
|
53
|
69
|
58
|
|
High
|
73
|
66
|
65
|
|
Hjigh
|
71
|
74
|
76
|
|
|
Yield % in a chemical reactor
|
|
|
Data to be used in SPSS if you wanted to check your answer is given below.
|
Cat Level
|
Temp
|
yield
|
|
Low
|
600
|
70
|
|
Low
|
600
|
61
|
|
Low
|
600
|
57
|
|
Low
|
650
|
74
|
|
Low
|
650
|
73
|
|
Low
|
650
|
77
|
|
Low
|
700
|
94
|
|
Low
|
700
|
74
|
|
Low
|
700
|
52
|
|
Moderate
|
600
|
95
|
|
Moderate
|
600
|
87
|
|
Moderate
|
600
|
97
|
|
Moderate
|
650
|
60
|
|
Moderate
|
650
|
79
|
|
Moderate
|
650
|
54
|
|
Moderate
|
700
|
93
|
|
Moderate
|
700
|
82
|
|
Moderate
|
700
|
84
|
|
High
|
600
|
53
|
|
High
|
600
|
73
|
|
High
|
600
|
71
|
|
High
|
650
|
69
|
|
High
|
650
|
66
|
|
High
|
650
|
74
|
|
High
|
700
|
58
|
|
High
|
700
|
65
|
|
High
|
700
|
76
|
Format your assignment according to the give formatting requirements:
1. The answer must be double spaced, typed, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the course title, the student's name, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The references and Citations should follow APA format. The reference page is not included in the required page length.