Operation Management HW, SPSS program

1. (25 points) 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?

a. What factors are sensitive?

b. Give the complete table of analysis of variance.

c. What is the best combination of temperature and pressure to run this system?

(Figures inside the table are yield in pounds for the same starting batch size for a chemical reaction.)

	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

2. (20 points) 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

a. Run the logistic regression using SPSS and this data.

b. Write down the logit function from your output.

c. 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. (15 points) Data on Yield % against two variables (temperature and catalyst level) is given below.

a. Do a spreadsheet based analysis of the data and report on which factors (temperature, catalyst level or interaction: temperature*Catalyst) is significant.

b. 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