7/27/2019 Design of Experiments and Analysis HW#21

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Individual Homework #21

Design and Analysis of Experiments

8.11.

A B C D(ABC) E (AC) I=ACE I=BDE

tt

combination yield

-1 -1 -1 -1 1 1 1 e 23.2

1 -1 -1 1 -1 1 1 ad 16.9

-1 1 -1 1 1 1 1 bde 16.8

1 1 -1 -1 -1 1 1 ab 15.5

-1 -1 1 1 -1 1 1 cd 23.8

1 -1 1 -1 1 1 1 ace 23.4

-1 1 1 -1 -1 1 1 bc 16.2

1 1 1 1 1 1 1 abcde 18.1

b)See complete defining relation in table above. D=ABC E= ACAliases

A*ACE=CE A*BDE=ABDE

B*ACE = ABCE B*BDE=DE

C*ACE = AE C*BDE=BCDE

D*ACE = ACDE D*BDE=BE

E*ACE = AC E*BDE=BD

AB*ACE=BCE AB*BDE=ADE

AC*ACE=E AC*BDE=ABCDE

AD*ACE=DCE AD*BDE=ABE

AE*ACE=C AE*BDE=ABD

BC*ACE=ABE BC*BDE=CDE

BD*ACE=ABCDE BD*BDE=E

BE*ACE=ABC BE*BDE=D

CD*ACE=ADE CD*BDE=BCE

CE*ACE=A CE*BDE=CBD

DE*ACE=ACD DE*BDE=B

c)

d)

7/27/2019 Design of Experiments and Analysis HW#21

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e)Residuals meet assumptions. NID

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8.13

A B C D E F(ABC) G(BDC) I=ABCD I=ABDE

-1 -1 -1 -1 -1 -1 -1 1 1

1 -1 -1 -1 -1 1 -1 -1 -1

-1 1 -1 -1 -1 1 1 -1 -1

1 1 -1 -1 -1 -1 1 1 1

-1 -1 1 -1 -1 1 1 -1 1

1 -1 1 -1 -1 -1 1 1 -1

-1 1 1 -1 -1 -1 -1 1 -1

1 1 1 -1 -1 1 -1 -1 1

-1 -1 -1 1 -1 -1 1 -1 -1

1 -1 -1 1 -1 1 1 1 1

-1 1 -1 1 -1 1 -1 1 1

1 1 -1 1 -1 -1 -1 -1 -1

-1 -1 1 1 -1 1 -1 1 -1

1 -1 1 1 -1 -1 -1 -1 1-1 1 1 1 -1 -1 1 -1 1

1 1 1 1 -1 1 1 1 -1

-1 -1 -1 -1 1 -1 -1 1 -1

1 -1 -1 -1 1 1 -1 -1 1

-1 1 -1 -1 1 1 1 -1 1

1 1 -1 -1 1 -1 1 1 -1

-1 -1 1 -1 1 1 1 -1 -1

1 -1 1 -1 1 -1 1 1 1

-1 1 1 -1 1 -1 -1 1 1

1 1 1 -1 1 1 -1 -1 -1-1 -1 -1 1 1 -1 1 -1 1

1 -1 -1 1 1 1 1 1 -1

-1 1 -1 1 1 1 -1 1 -1

1 1 -1 1 1 -1 -1 -1 1

-1 -1 1 1 1 1 -1 1 1

1 -1 1 1 1 -1 -1 -1 -1

-1 1 1 1 1 -1 1 -1 -1

1 1 1 1 1 1 1 1 1

7/27/2019 Design of Experiments and Analysis HW#21

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A*ABCD = BCD A*ABDE= BDE

B*ABCD= ACD B*ABDE= ADE

C*ABCD= ABD C*ABDE= ABCDE

D*ABCD= ABC D*ABDE= ABE

E*ABCD= ABCDE E*ABDE= ABD

F*ABCD= ABCDF F*ABDE= ABDF

G*ABCD= ABCDG G*ABDE= ABDEG

AB*ABCD= CD AB*ABDE= DE

AC*ABCD= BD AC*ABDE= BCDE

AD*ABCD= BC AD*ABDE= BE

AE*ABCD= BCDE AE*ABDE= BD

AF*ABCD= BCDF AF*ABDE= BDEF

AG*ABCD= BCDG AG*ABDE= BDEG

BC*ABCD= AD BC*ABDE= ACDE

BD*ABCD= AC BD*ABDE= AEBE*ABCD= ACDE BF*ABDE= ADEF

BF*ABCD= ACDF BE*ABDE= AD

BG*ABCD= ACDG BG*ABDE= ADEG

CD*ABCD= AB CD*ABDE= ABCE

CE*ABCD= ABDE CE*ABDE= ABCD

CF*ABCD= ABDF CF*ABDE= ABCDEF

CG*ABCD= ABDG CG*ABDE= ABCDEG

DE*ABCD= ABCE DE*ABDE= AB

DF*ABCD= ABCF DF*ABDE= ABEF

DG*ABCD= ABDG DG*ABDE= ABEGEF*ABCD= ABCDEF EF*ABDE= ABDF

EG*ABCD= ABCDEG EG*ABDE= ABDG

ANOVA

Variable df

Intercept 1

Blocks 3A 1

B 1

C 1

D 1

E 1F 1

G 1

Error

Total 31