Assignment 4 In this assignment you are provided information on an experiment and you are required to investigate and interpret the output which is provided below Problem Consider the three variable central composite design shown in the table RunOrder PtType Blocks Temperature Time Catalyst Conversion ( ) y1 Viscosity y2 1 1 1 1 1 1 74 53 2 2 1 1 1 1 1 51 62 9 3 1 1 1 1 1 88 53 4 4 1 1 1 1 1 70 62 6 5 1 1 1 1 1 71 57 3 6 1 1 1 1 1 90 67 9 7 1 1 1 1 1 66 59 8 8 1 1 1 1 1 97 67 8 9 1 1 1 68179 0 0 76 59 1 10 1 1 1 681793 0 0 79 65 9 11 1 1 0 1 68179 0 85 60 12 1 1 0 1 681793 0 97 60 7 13 1 1 0 0 1 68179 55 57 4 14 1 1 0 0 1 681793 81 63 2 15 0 1 0 0 0 81 59 2 16 0 1 0 0 0 75 60 4 17 0 1 0 0 0 76 59 1 18 0 1 0 0 0 83 60 6 19 0 1 0 0 0 80 60 8 20 0 1 0 0 0 91 58 9 Modified fromDesign and Analysis of Experiments (9th Edition) Texidium version (2017) Retrieved fromhttp texidium com Part 1 Conversion percent A partial Minitab output for the full model is shown below Model Summary S R sq R sq(adj) R sq(pred) 4 71669 91 99 84 79 75 66 Fits and Diagnostics for Unusual Observations Obs Conversion (y1) Fit Resid Std Resid 20 91 00 81 09 9 91 2 30 R R Large residual Analysis of Variance Source DF Adj SS Adj MS F Value P Value Model 9 2555 73 283 97 12 76 0 000 Linear 3 763 05 254 35 11 43 0 001 Temperature 1 14 44 14 44 0 65 0 439 Time 1 222 96 222 96 10 02 0 010 Catalyst 1 525 64 525 64 23 63 0 001 Square 3 601 30 200 43 9 01 0 003 Temperature Temperature 1 48 47 48 47 2 18 0 171 Time Time 1 124 48 124 48 5 60 0 040 Catalyst Catalyst 1 388 59 388 59 17 47 0 002 2 Way Interaction 3 1191 37 397 12 17 85 0 000 Temperature Time 1 36 12 36 12 1 62 0 231 Temperature Catalyst 1 1035 12 1035 12 46 53 0 000 Time Catalyst 1 120 13 120 13 5 40 0 043 Error 10 222 47 22 25 Lack of Fit 5 56 47 11 29 0 34 0 869 Pure Error 5 166 00 33 20 Total 19 2778 20 Interpret the above output As well as discussing factor significance you are expected to discuss the unusual residual and how it may (or may not) affect the overall analysis Is there a specific recommendation that you would make The partial output for the reduced model is provided Model Summary S R sq R sq(adj) R sq(pred) 5 05856 88 95 82 50 69 18 Coded Coefficients Term Coef SE Coef T Value P Value VIF Constant 79 59 1 75 45 45 0 000 Temperature 1 03 1 37 0 75 0 467 1 00 Time 4 04 1 37 2 95 0 012 1 00 Catalyst 6 20 1 37 4 53 0 001 1 00 Time Time 3 12 1 33 2 35 0 036 1 01 Catalyst Catalyst 5 01 1 33 3 78 0 003 1 01 Temperature Catalyst 11 37 1 79 6 36 0 000 1 00 Time Catalyst 3 88 1 79 2 17 0 051 1 00 Analysis of Variance Source DF Adj SS Adj MS F Value P Value Model 7 2471 13 353 02 13 80 0 000 Linear 3 763 05 254 35 9 94 0 001 Temperature 1 14 44 14 44 0 56 0 467 Time 1 222 96 222 96 8 71 0 012 Catalyst 1 525 64 525 64 20 54 0 001 Square 2 552 83 276 42 10 80 0 002 Time Time 1 141 78 141 78 5 54 0 036 Catalyst Catalyst 1 365 42 365 42 14 28 0 003 2 Way Interaction 2 1155 25 577 62 22 57 0 000 Temperature Catalyst 1 1035 12 1035 12 40 45 0 000 Time Catalyst 1 120 13 120 13 4 69 0 051 Error 12 307 07 25 59 Lack of Fit 7 141 07 20 15 0 61 0 736 Pure Error 5 166 00 33 20 Total 19 2778 20 Image transcription text Residual Plots for Conversion ( ) y1 Normal Probability Plot Versus Fits 10 90 Percent 50 Residual 10 10 50 70 90 Residual Fitted Value Histogram Versus Order 10 4 5 Frequency 3 0 Residual 1 5 S 5 0 2 5 0 0 2 5 5 0 7 5 10 0 12 5 2 4 6 10 12 14 16 18 20 Residual Observation Order State (with justification) your proposed model equation for Conversion percent Part 2 A reduced model for viscosity was developed in Minitab Coded Coefficients Term Coef SE Coef T Value P Value VIF Constant 59 948 0 417 143 65 0 000 Temperature 3 583 0 395 9 07 0 000 1 00 Catalyst 2 230 0 395 5 65 0 000 1 00 Temperature Temperature 0 823 0 381 2 16 0 046 1 00 Model Summary S R sq R sq(adj) R sq(pred) 1 45933 88 14 85 91 63 02 Analysis of Variance Source DF Adj SS Adj MS F Value P Value Model 3 253 204 84 401 39 63 0 000 Linear 2 243 264 121 632 57 11 0 000 Temperature 1 175 352 175 352 82 34 0 000 Catalyst 1 67 912 67 912 31 89 0 000 Square 1 9 939 9 939 4 67 0 046 Temperature Temperature 1 9 939 9 939 4 67 0 046 Error 16 34 074 2 130 Lack of Fit 11 30 421 2 766 3 78 0 077 Pure Error 5 3 653 0 731 Total 19 287 278 Fits and Diagnostics for Unusual Observations Obs Viscosity (y2) Fit Resid Std Resid 9 59 100 56 250 2 850 2 98 R 10 65 900 68 302 2 402 2 51 R R Large residual Image transcription text Residual Plots for Viscosity (y2) Normal Probability Plot Versus Fits 3 0 1 5 Percent 50 Residual 10 1 5 3 0 4 SE 70 Residual Fitted Value Histogram Versus Order 3 0 1 5 Frequency Residual A 1 5 3 0 2 1 2 2 4 10 12 14 16 18 20 Residual Observation Order Comment on this model What further action might you take based on the residuals Part 3 We are required to optimize the two responses Contour plots are as shown Image transcription text Contour Plots of Conversion ( ) y1 Time Temperature Catalyst Temperature Hold Values Temperature 0 Time 0 Catalyst 61 0 1 $7 47 1 0 1 Catalyst Time 1 1 Image transcription text Contour Plot of Viscosity y2 vs Catalyst, Temperature 1 5 62 5 65 9 69 3 59 1 1 0 0 5 67 6 Catalyst 0 0 $5 7 0 5 1 0 04 2 1 5 54 0 57 4 60 8 1 5 1 0 0 5 0 0 0 5 1 0 1 5 Temperature On the assumption that we want to maximize conversion percent while maintaining viscosity between 55 and 60 where would you propose that the inputs be set Clearly justify your response on the basis of the contour plots Your manager has decided to change the viscosity requirement to be a target of 65 Interpret the response optimizer output below Image transcription text Optimal Temperat Time Catalyst D 1 000 High 1 6818 1 6818 1 6318 Cur 1 0984 1 6818 0 0552 Low 1 6818 1 6818 1 6818 Composite Desirability D 1 000 Viscosit Targ 65 0 y 65 0 d 1 0000 Conversi Maximum y 97 0 d 1 0000

The Answer is in the image, click to view ...

Question: Assignment 4 In this assignment you are provided information on an experiment and you are required to investigate and interpret the output which is provided

Assignment 4

In this assignment you are provided information on an experiment and you are required to investigate and interpret the output which is provided below.

Problem: Consider the three?variable central composite design shown in the table.

RunOrder	PtType	Blocks	Temperature	Time	Catalyst	Conversion (%) y1	Viscosity y2
1	1	1	-1	-1	-1	74	53.2
2	1	1	1	-1	-1	51	62.9
3	1	1	-1	1	-1	88	53.4
4	1	1	1	1	-1	70	62.6
5	1	1	-1	-1	1	71	57.3
6	1	1	1	-1	1	90	67.9
7	1	1	-1	1	1	66	59.8
8	1	1	1	1	1	97	67.8
9	-1	1	-1.68179	0	0	76	59.1
10	-1	1	1.681793	0	0	79	65.9
11	-1	1	0	-1.68179	0	85	60
12	-1	1	0	1.681793	0	97	60.7
13	-1	1	0	0	-1.68179	55	57.4
14	-1	1	0	0	1.681793	81	63.2
15	0	1	0	0	0	81	59.2
16	0	1	0	0	0	75	60.4
17	0	1	0	0	0	76	59.1
18	0	1	0	0	0	83	60.6
19	0	1	0	0	0	80	60.8
20	0	1	0	0	0	91	58.9

Modified fromDesign and Analysis of Experiments (9th Edition) [Texidium version]. (2017). Retrieved from http://texidium.com

Part 1- Conversion percent

A partial Minitab output for the full model is shown below.

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
4.71669	91.99%	84.79%	75.66%

Fits and Diagnostics for Unusual Observations

Obs	Conversion % (y1)	Fit	Resid	Std Resid
20	91.00	81.09	9.91	2.30	R

R Large residual

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	9	2555.73	283.97	12.76	0.000
Linear	3	763.05	254.35	11.43	0.001
Temperature	1	14.44	14.44	0.65	0.439
Time	1	222.96	222.96	10.02	0.010
Catalyst	1	525.64	525.64	23.63	0.001
Square	3	601.30	200.43	9.01	0.003
Temperature*Temperature	1	48.47	48.47	2.18	0.171
Time*Time	1	124.48	124.48	5.60	0.040
Catalyst*Catalyst	1	388.59	388.59	17.47	0.002
2-Way Interaction	3	1191.37	397.12	17.85	0.000
Temperature*Time	1	36.12	36.12	1.62	0.231
Temperature*Catalyst	1	1035.12	1035.12	46.53	0.000
Time*Catalyst	1	120.13	120.13	5.40	0.043
Error	10	222.47	22.25
Lack-of-Fit	5	56.47	11.29	0.34	0.869
Pure Error	5	166.00	33.20
Total	19	2778.20

Interpret the above output. As well as discussing factor significance you are expected to discuss the unusual residual and how it may (or may not) affect the overall analysis. Is there a specific recommendation that you would make?

The partial output for the reduced model is provided.

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
5.05856	88.95%	82.50%	69.18%

Coded Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	79.59	1.75	45.45	0.000
Temperature	1.03	1.37	0.75	0.467	1.00
Time	4.04	1.37	2.95	0.012	1.00
Catalyst	6.20	1.37	4.53	0.001	1.00
Time*Time	3.12	1.33	2.35	0.036	1.01
Catalyst*Catalyst	-5.01	1.33	-3.78	0.003	1.01
Temperature*Catalyst	11.37	1.79	6.36	0.000	1.00
Time*Catalyst	-3.88	1.79	-2.17	0.051	1.00

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	7	2471.13	353.02	13.80	0.000
Linear	3	763.05	254.35	9.94	0.001
Temperature	1	14.44	14.44	0.56	0.467
Time	1	222.96	222.96	8.71	0.012
Catalyst	1	525.64	525.64	20.54	0.001
Square	2	552.83	276.42	10.80	0.002
Time*Time	1	141.78	141.78	5.54	0.036
Catalyst*Catalyst	1	365.42	365.42	14.28	0.003
2-Way Interaction	2	1155.25	577.62	22.57	0.000
Temperature*Catalyst	1	1035.12	1035.12	40.45	0.000
Time*Catalyst	1	120.13	120.13	4.69	0.051
Error	12	307.07	25.59
Lack-of-Fit	7	141.07	20.15	0.61	0.736
Pure Error	5	166.00	33.20
Total	19	2778.20

Image transcription text

Residual Plots for Conversion (%) y1 Normal Probability Plot Versus Fits 10 90 Percent 50 Residual 10
10 50 70 90 Residual Fitted Value Histogram Versus Order 10 4.5 Frequency 3.0 Residual 1.5 -S -5.0
-2.5 0.0 2.5 5.0 7.5 10.0 12.5 2 4 6 10 12 14 16 18 20 Residual Observation Order

State (with justification) your proposed model equation for Conversion percent.

Part 2

A reduced model for viscosity was developed in Minitab

Coded Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	59.948	0.417	143.65	0.000
Temperature	3.583	0.395	9.07	0.000	1.00
Catalyst	2.230	0.395	5.65	0.000	1.00
Temperature*Temperature	0.823	0.381	2.16	0.046	1.00

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
1.45933	88.14%	85.91%	63.02%

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	3	253.204	84.401	39.63	0.000
Linear	2	243.264	121.632	57.11	0.000
Temperature	1	175.352	175.352	82.34	0.000
Catalyst	1	67.912	67.912	31.89	0.000
Square	1	9.939	9.939	4.67	0.046
Temperature*Temperature	1	9.939	9.939	4.67	0.046
Error	16	34.074	2.130
Lack-of-Fit	11	30.421	2.766	3.78	0.077
Pure Error	5	3.653	0.731
Total	19	287.278

Fits and Diagnostics for Unusual Observations

Obs	Viscosity (y2)	Fit	Resid	Std Resid
9	59.100	56.250	2.850	2.98	R
10	65.900	68.302	-2.402	-2.51	R

R Large residual

Image transcription text

Residual Plots for Viscosity (y2) Normal Probability Plot Versus Fits 3.0 1.5 Percent 50 Residual 10 -1.5
-3.0 4 SE 70 Residual Fitted Value Histogram Versus Order 3.0 1.5 Frequency Residual A -1.5 -3.0 -2 -1 2
2 4 10 12 14 16 18 20 Residual Observation Order

Comment on this model. What further action might you take based on the residuals?

Part 3

We are required to optimize the two responses.

Contour plots are as shown

Image transcription text

Contour Plots of Conversion (%) y1 Time*Temperature Catalyst*Temperature Hold Values Temperature
0 Time 0 Catalyst 61 0 -1- $7 . 47 -1 0 1 Catalyst* Time -1 1

Image transcription text

Contour Plot of Viscosity y2 vs Catalyst, Temperature 1.5 62.5 65.9 69.3 59.1 1.0 0.5 67.6 Catalyst 0.0
$5.7 -0.5 -1.0 04 2 -1.5 54.0 57.4 60.8 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Temperature

On the assumption that we want to maximize conversion percent while maintaining viscosity between 55 and 60 where would you propose that the inputs be set? Clearly justify your response on the basis of the contour plots.

Your manager has decided to change the viscosity requirement to be a target of 65. Interpret the response optimizer output below

Image transcription text

Optimal Temperat Time Catalyst D: 1.000 High 1.6818 1.6818 1.6318 Cur [1.0984] [1.6818] [0.0552] Low
-1.6818 -1.6818 -1.6818 Composite Desirability D: 1.000 Viscosit Targ: 65.0 y = 65.0 d = 1.0000 Conversi
Maximum y = 97.0 d = 1.0000

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Engineering Questions!

Question: Old MathJax webview Old MathJax webview i need ans of these question but the source is alot Old MathJax webviewOld MathJax webview i need ans of these question but the source is alot these...

My question is how to write the code in WareHouse.java This is WareHouse.java package warehouse; /* * * This class implements a warehouse on a Hash Table like structure, * where each entry of the...

Using an organisation of your choice, discuss how macro environmental forces impacted on the operations of the organisation from 2020 to 2021

Knoko Systems is considering a capital budgeting project with a life of five years that requires an outlay of $90,000. It has free cash flows each period as shown in the following distribution:...

In each of the following situations, discuss whether free markets are likely to provide Pareto-optimal levels of the goods, or whether a market failure distorts the markets. (a) Although a restaurant...

Create a fictitious emergency situation with a classmate or colleague. Challenge each other on how each of you would handle the situation. Share your experience with others.

What do Barber and Odean (2001) theorize is a key factor in explaining the difference in investor behavior across gender? What evidence do they provide to support their argument?

Naoko Ohno, a Japanese citizen, obtained a $1.2 million tort judgment against the Saints of Glory Church, a California corporation, and its pastor Yuko Yasuma, a California resident, in Tokyo...

\ table [ [ Range of Adjusted Gross Income,Marginal Tax Rate ] , [ $ 0 - $ 1 9 , 0 5 0 , 1 0 %

CableTech Bell Corporation (CTB) operates in the telecommunications industry. CTB has two divisions: the Phone Division and the Cable Service Division. The Phone Division manufactures telephones in...

Which of the following safeguards data within the patient portal? Using the same password for all medical assistants Using a cryptographic key Using encryption Linking other accounts to it

Thoroughly respond to the prompts below. Enter your responses on a new line. 1. Analyze the project risk: What could cause the problem to occur? How can each problem be prevented? If the problem...

4. From the conservation of momentum equation below, write out the 2 scalar equilibrium equations for a 2-dimensional isotropic elasticity problem. ft pf = (2+) Fix +N+fXx + pl. fu fx, fx, fx, fx,...

Draw a circle representing one platter surface of a hard disk. On your drawing show an example of a track, of a sector, and of a block. 10.5 Draw a sector representing one platter surface of a hard...

Construct and submit the Future State VSM using seconds for TT , PT , and CT calculations. Make the map fit on one page by turning the page landscape. The map must be legible and professional. Based...

1) If you were worth $1 Million at the end of World War II, calculate how much you would need today to maintain the same purchasing power as in 1945? 2) How much would Rockefellar's fortune be worth...

A stock has annual returns of 21.0 percent, 24.8 percent, 7.3 percent, 9.4 percent, and 18.4 percent for the past five years. What is the geometric average return for the period is percent. Show your...

A fuel pump sends gasoline from a car's fuel tank to the engine at a rate of 5.88 10-2 kg/s. The density of the gasoline is 735 kg/m3, and the radius of the fuel line is 3.18 10-3 m. What is the...

An experiment was conducted to compare the effects of four different drugs (A, B, C, and D) in delaying atrophy of denervated muscles. A certain leg muscle in each of 48 rats was deprived of its...

The average generation times for four different strains of influenza virus were determined using six cultures for each strain. The data are summarized in the following table. a. Test whether the true...

The data shown in the following table were obtained from the 1990 Census. Included is information on 26 randomly selected Metropolitan Statistical Areas (MSAs). Of interest are factors that...

A response can fall into one of k =4 categories with hypothesized cell probabilities given. If 250 responses are recorded, what are the four expected cell counts for the chi-square test? 14. P P2 P3...

Use the information given and Table 5 in Appendix I to bound the p-value for a chi-square test 13. X2 9.56, df =2

A response can fall into one of k =4 categories with hypothesized cell probabilities given. If 250 responses are recorded, what are the four expected cell counts for the chi-square test? 15. p.25,...