T-Mobile 9:34 PM Done 4 of 4 2 of 2 Question 2) Anlyis o 25 43 3332 32 -544 52 4
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T-Mobile 9:34 PM Done 4 of 4 2 of 2 Question 2) Anlyis o 25 43 3332 32 -544 52 47 40 453 2 419 " 49.6236 -sq *$, 361 " @fad), . Question 3) "An experiment descnbed by M.G.Natrella in the National Bureau of Standards Handhook of Eyrrimrnsal Si-isti 1963, No 91 , involves arno-srsting fabrics aner applying ferretadant trament, The four factors considered are type of fabrK (A3. type of fire-retardant treatmest (B)·laundering condition €C--the low level i. no laundering, the high level is afler one laundering), and method of conducting the flame sest D. All factors are run at two levels and the response variable is the inches of fabric burned on a standard size lest samplesingle replicate). The da 39 cd= 40 46 ahr 32 a Construet the design matrix b. Estimate the main and interaction effects manually using contrasts. Show all of your woek. (assume single replication d. Calculee the deces of freedoms for cach Icm fr ANOVA table what did you find as error degrees of Eroodoes Explain how this value will create a peoblem whon you ry to creatc ANOVA table and perform F test Now Censtruct ANOVA table censidering only main ffects and two-factor interactions Since you will ec ludk higher order inicractions calculate arror degrees of freedom again. Does it diffo from what you Sound in part d (Use SS total-sum (each observation 2)-(sum of all ebservations 2)/16) E Which factors and or interactions are significan? (alpha-005)Explanation / Answer
Que 3]
Full Factorial Design
Factors: 4 Base Design: 4, 16
Runs: 16 Replicates: 1
Blocks: 1 Center pts (total): 0
All terms are free from aliasing.
Design Table
Run A B C D
1 - - - -
2 + - - -
3 - + - -
4 + + - -
5 - - + -
6 + - + -
7 - + + -
8 + + + -
9 - - - +
10 + - - +
11 - + - +
12 + + - +
13 - - + +
14 + - + +
15 - + + +
16 + + + +
Factorial Regression: response versus A, B, C, D
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 15 1250.94 83.40 * *
Linear 4 1089.25 272.31 * *
A 1 1040.06 1040.06 * *
B 1 39.06 39.06 * *
C 1 5.06 5.06 * *
D 1 5.06 5.06 * *
2-Way Interactions 6 129.38 21.56 * *
A*B 1 76.56 76.56 * *
A*C 1 1.56 1.56 * *
A*D 1 39.06 39.06 * *
B*C 1 10.56 10.56 * *
B*D 1 0.06 0.06 * *
C*D 1 1.56 1.56 * *
3-Way Interactions 4 32.25 8.06 * *
A*B*C 1 1.56 1.56 * *
A*B*D 1 22.56 22.56 * *
A*C*D 1 5.06 5.06 * *
B*C*D 1 3.06 3.06 * *
4-Way Interactions 1 0.06 0.06 * *
A*B*C*D 1 0.06 0.06 * *
Error 0 * *
Total 15 1250.94
In above ANOVA Table there is no values of f test and pvalue. so recompute the ANOVA TABLE excluding 3 way interaction and 4 way interaction.
Regression Equation in Uncoded Units
response = 35.94 - 8.062 A + 1.563 B - 0.5625 C - 0.5625 D - 2.188 A*B - 0.3125 A*C
- 1.563 A*D + 0.8125 B*C + 0.06250 B*D - 0.3125 C*D + 0.3125 A*B*C - 1.188 A*B*D
- 0.5625 A*C*D - 0.4375 B*C*D + 0.06250 A*B*C*D
ANOVA table
Factorial Regression: response versus A, B, C, D
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 8 1217.00 152.12 31.38 0.000
Linear 4 1089.25 272.31 56.17 0.000
A 1 1040.06 1040.06 214.52 0.000
B 1 39.06 39.06 8.06 0.025
C 1 5.06 5.06 1.04 0.341
D 1 5.06 5.06 1.04 0.341
2-Way Interactions 4 127.75 31.94 6.59 0.016
A*B 1 76.56 76.56 15.79 0.005
A*D 1 39.06 39.06 8.06 0.025
B*C 1 10.56 10.56 2.18 0.183
C*D 1 1.56 1.56 0.32 0.588
Error 7 33.94 4.85
Total 15 1250.94
The PVALUE of factor A ,B < Alpha = 0.05
they are significant.
pvalue of 2 way interaction AB ,AD < 0.05 so they are significant .
Regression Equation in Uncoded Units
response = 35.938 - 8.062 A + 1.563 B - 0.563 C - 0.563 D - 2.188 A*B - 1.563 A*D + 0.813 B*C
- 0.312 C*D
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