Week 13 - Homework
Mary Adepoju
11/27/2021
8.2
## A B C D results
## 1 -1 -1 -1 -1 7.037
## 2 1 -1 -1 1 14.707
## 3 -1 1 -1 1 11.635
## 4 1 1 -1 -1 17.273
## 5 -1 -1 1 1 10.403
## 6 1 -1 1 -1 4.368
## 7 -1 1 1 -1 9.360
## 8 1 1 1 1 13.440
## class=design, type= FrF2There are no significan factors
8.24 \(2^{5-1}\) Block Design
## Warning in FrF2(nruns = 16, nfactors = 5, randomize = FALSE, resolution = 5, :
## resolution is ignored, if nruns is given.## run.no run.no.std.rp Blocks A B C D E
## 1 1 1.1.1 1 -1 -1 -1 -1 -1
## 2 2 3.1.2 1 -1 -1 1 -1 1
## 3 3 6.1.3 1 -1 1 -1 1 1
## 4 4 8.1.4 1 -1 1 1 1 -1
## 5 5 10.1.5 1 1 -1 -1 1 1
## 6 6 12.1.6 1 1 -1 1 1 -1
## 7 7 13.1.7 1 1 1 -1 -1 -1
## 8 8 15.1.8 1 1 1 1 -1 1
## run.no run.no.std.rp Blocks A B C D E
## 9 9 2.2.1 2 -1 -1 -1 1 -1
## 10 10 4.2.2 2 -1 -1 1 1 1
## 11 11 5.2.3 2 -1 1 -1 -1 1
## 12 12 7.2.4 2 -1 1 1 -1 -1
## 13 13 9.2.5 2 1 -1 -1 -1 1
## 14 14 11.2.6 2 1 -1 1 -1 -1
## 15 15 14.2.7 2 1 1 -1 1 -1
## 16 16 16.2.8 2 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frame## Call:
## FrF2(nruns = 16, nfactors = 5, randomize = FALSE, resolution = 5,
## blocks = 2)
##
## Experimental design of type FrF2.blocked
## 16 runs
## blocked design with 2 blocks of size 8
##
## Factor settings (scale ends):
## A B C D E
## 1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E
##
## $`generators for design itself`
## [1] E=ABC
##
## $`block generators`
## [1] ABD
##
##
## Alias structure:
## $fi2
## [1] AB=CE AC=BE AE=BC
##
## Aliased with block main effects:
## [1] none
##
## The design itself:
## run.no run.no.std.rp Blocks A B C D E
## 1 1 1.1.1 1 -1 -1 -1 -1 -1
## 2 2 3.1.2 1 -1 -1 1 -1 1
## 3 3 6.1.3 1 -1 1 -1 1 1
## 4 4 8.1.4 1 -1 1 1 1 -1
## 5 5 10.1.5 1 1 -1 -1 1 1
## 6 6 12.1.6 1 1 -1 1 1 -1
## 7 7 13.1.7 1 1 1 -1 -1 -1
## 8 8 15.1.8 1 1 1 1 -1 1
## run.no run.no.std.rp Blocks A B C D E
## 9 9 2.2.1 2 -1 -1 -1 1 -1
## 10 10 4.2.2 2 -1 -1 1 1 1
## 11 11 5.2.3 2 -1 1 -1 -1 1
## 12 12 7.2.4 2 -1 1 1 -1 -1
## 13 13 9.2.5 2 1 -1 -1 -1 1
## 14 14 11.2.6 2 1 -1 1 -1 -1
## 15 15 14.2.7 2 1 1 -1 1 -1
## 16 16 16.2.8 2 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frameThe blocks are confounded by AB and CDE
8.25 \(2^{7-1}\) Block Design
## run.no run.no.std.rp Blocks A B C D E F G
## 1 1 1.1.1 1 -1 -1 -1 -1 -1 -1 -1
## 2 2 7.1.2 1 -1 -1 1 1 -1 1 1
## 3 3 10.1.3 1 -1 1 -1 -1 1 1 1
## 4 4 16.1.4 1 -1 1 1 1 1 -1 -1
## 5 5 20.1.5 1 1 -1 -1 1 1 1 -1
## 6 6 22.1.6 1 1 -1 1 -1 1 -1 1
## 7 7 27.1.7 1 1 1 -1 1 -1 -1 1
## 8 8 29.1.8 1 1 1 1 -1 -1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 9 9 2.2.1 2 -1 -1 -1 -1 1 -1 -1
## 10 10 8.2.2 2 -1 -1 1 1 1 1 1
## 11 11 9.2.3 2 -1 1 -1 -1 -1 1 1
## 12 12 15.2.4 2 -1 1 1 1 -1 -1 -1
## 13 13 19.2.5 2 1 -1 -1 1 -1 1 -1
## 14 14 21.2.6 2 1 -1 1 -1 -1 -1 1
## 15 15 28.2.7 2 1 1 -1 1 1 -1 1
## 16 16 30.2.8 2 1 1 1 -1 1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 17 17 3.3.1 3 -1 -1 -1 1 -1 -1 1
## 18 18 5.3.2 3 -1 -1 1 -1 -1 1 -1
## 19 19 12.3.3 3 -1 1 -1 1 1 1 -1
## 20 20 14.3.4 3 -1 1 1 -1 1 -1 1
## 21 21 18.3.5 3 1 -1 -1 -1 1 1 1
## 22 22 24.3.6 3 1 -1 1 1 1 -1 -1
## 23 23 25.3.7 3 1 1 -1 -1 -1 -1 -1
## 24 24 31.3.8 3 1 1 1 1 -1 1 1
## run.no run.no.std.rp Blocks A B C D E F G
## 25 25 4.4.1 4 -1 -1 -1 1 1 -1 1
## 26 26 6.4.2 4 -1 -1 1 -1 1 1 -1
## 27 27 11.4.3 4 -1 1 -1 1 -1 1 -1
## 28 28 13.4.4 4 -1 1 1 -1 -1 -1 1
## 29 29 17.4.5 4 1 -1 -1 -1 -1 1 1
## 30 30 23.4.6 4 1 -1 1 1 -1 -1 -1
## 31 31 26.4.7 4 1 1 -1 -1 1 -1 -1
## 32 32 32.4.8 4 1 1 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frame## Call:
## FrF2(nruns = 32, nfactors = 7, randomize = FALSE, blocks = 4)
##
## Experimental design of type FrF2.blocked
## 32 runs
## blocked design with 4 blocks of size 8
##
## Factor settings (scale ends):
## A B C D E F G
## 1 -1 -1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1 1 1
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E F=F G=G
##
## $`generators for design itself`
## [1] F=ABC G=ABD
##
## $`block generators`
## [1] ACD ABE
##
##
## Alias structure:
## $fi2
## [1] AB=CF=DG AC=BF AD=BG AF=BC AG=BD CD=FG CG=DF
##
## Aliased with block main effects:
## [1] none
##
## The design itself:
## run.no run.no.std.rp Blocks A B C D E F G
## 1 1 1.1.1 1 -1 -1 -1 -1 -1 -1 -1
## 2 2 7.1.2 1 -1 -1 1 1 -1 1 1
## 3 3 10.1.3 1 -1 1 -1 -1 1 1 1
## 4 4 16.1.4 1 -1 1 1 1 1 -1 -1
## 5 5 20.1.5 1 1 -1 -1 1 1 1 -1
## 6 6 22.1.6 1 1 -1 1 -1 1 -1 1
## 7 7 27.1.7 1 1 1 -1 1 -1 -1 1
## 8 8 29.1.8 1 1 1 1 -1 -1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 9 9 2.2.1 2 -1 -1 -1 -1 1 -1 -1
## 10 10 8.2.2 2 -1 -1 1 1 1 1 1
## 11 11 9.2.3 2 -1 1 -1 -1 -1 1 1
## 12 12 15.2.4 2 -1 1 1 1 -1 -1 -1
## 13 13 19.2.5 2 1 -1 -1 1 -1 1 -1
## 14 14 21.2.6 2 1 -1 1 -1 -1 -1 1
## 15 15 28.2.7 2 1 1 -1 1 1 -1 1
## 16 16 30.2.8 2 1 1 1 -1 1 1 -1
## run.no run.no.std.rp Blocks A B C D E F G
## 17 17 3.3.1 3 -1 -1 -1 1 -1 -1 1
## 18 18 5.3.2 3 -1 -1 1 -1 -1 1 -1
## 19 19 12.3.3 3 -1 1 -1 1 1 1 -1
## 20 20 14.3.4 3 -1 1 1 -1 1 -1 1
## 21 21 18.3.5 3 1 -1 -1 -1 1 1 1
## 22 22 24.3.6 3 1 -1 1 1 1 -1 -1
## 23 23 25.3.7 3 1 1 -1 -1 -1 -1 -1
## 24 24 31.3.8 3 1 1 1 1 -1 1 1
## run.no run.no.std.rp Blocks A B C D E F G
## 25 25 4.4.1 4 -1 -1 -1 1 1 -1 1
## 26 26 6.4.2 4 -1 -1 1 -1 1 1 -1
## 27 27 11.4.3 4 -1 1 -1 1 -1 1 -1
## 28 28 13.4.4 4 -1 1 1 -1 -1 -1 1
## 29 29 17.4.5 4 1 -1 -1 -1 -1 1 1
## 30 30 23.4.6 4 1 -1 1 1 -1 -1 -1
## 31 31 26.4.7 4 1 1 -1 -1 1 -1 -1
## 32 32 32.4.8 4 1 1 1 1 1 1 1
## class=design, type= FrF2.blocked
## NOTE: columns run.no and run.no.std.rp are annotation,
## not part of the data frameThe confounded blocks are ACE, BFG, ABCEFG
8.28: Manufacturing Plant
The experimenter used a \(2^4\) design. It initially was a \(2^6\) design. After fractioning it is a \(2^{6-2}\) design.
## Df Sum Sq Mean Sq F value Pr(>F)
## temp 1 0.0002422 0.0002422 27.793 3.17e-06 ***
## time 1 0.0000053 0.0000053 0.614 0.43725
## pressure 1 0.0005023 0.0005023 57.644 9.14e-10 ***
## firingTemp 1 0.0000323 0.0000323 3.712 0.05995 .
## cycleTime 1 0.0001901 0.0001901 21.815 2.45e-05 ***
## dewPonit 1 0.0009602 0.0009602 110.192 5.05e-14 ***
## temp:time 1 0.0000587 0.0000587 6.738 0.01249 *
## temp:pressure 1 0.0000803 0.0000803 9.218 0.00387 **
## time:pressure 1 0.0000527 0.0000527 6.053 0.01754 *
## temp:firingTemp 1 0.0000239 0.0000239 2.741 0.10431
## time:firingTemp 1 0.0000849 0.0000849 9.739 0.00305 **
## pressure:firingTemp 1 0.0000622 0.0000622 7.139 0.01027 *
## firingTemp:cycleTime 1 0.0000088 0.0000088 1.007 0.32062
## temp:time:firingTemp 1 0.0000000 0.0000000 0.005 0.94291
## time:pressure:firingTemp 1 0.0000481 0.0000481 5.523 0.02293 *
## Residuals 48 0.0004183 0.0000087
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Call:
## FrF2(nfactors = 6, resolution = NULL, randomize = FALSE, nruns = 16)
##
## Experimental design of type FrF2
## 16 runs
##
## Factor settings (scale ends):
## A B C D E F
## 1 -1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1 1
##
## Responses:
## [1] rep1 rep2 rep3 rep4
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E F=F
##
## $generators
## [1] E=ABC F=ABD
##
##
## Alias structure:
## $fi2
## [1] AB=CE=DF AC=BE AD=BF AE=BC AF=BD CD=EF CF=DE
##
##
## The design itself:
## A B C D E F rep1 rep2 rep3 rep4
## 1 -1 -1 -1 -1 -1 -1 0.0167 0.0128 0.0149 0.0185
## 2 1 -1 -1 -1 1 1 0.0062 0.0066 0.0044 0.0020
## 3 -1 1 -1 -1 1 1 0.0041 0.0043 0.0042 0.0050
## 4 1 1 -1 -1 -1 -1 0.0073 0.0081 0.0039 0.0030
## 5 -1 -1 1 -1 1 -1 0.0047 0.0047 0.0040 0.0089
## 6 1 -1 1 -1 -1 1 0.0219 0.0258 0.0147 0.0296
## 7 -1 1 1 -1 -1 1 0.0121 0.0090 0.0092 0.0086
## 8 1 1 1 -1 1 -1 0.0255 0.0250 0.0226 0.0169
## 9 -1 -1 -1 1 -1 1 0.0032 0.0023 0.0077 0.0069
## 10 1 -1 -1 1 1 -1 0.0078 0.0158 0.0060 0.0045
## 11 -1 1 -1 1 1 -1 0.0043 0.0027 0.0028 0.0028
## 12 1 1 -1 1 -1 1 0.0186 0.0137 0.0158 0.0159
## 13 -1 -1 1 1 1 1 0.0110 0.0086 0.0101 0.0158
## 14 1 -1 1 1 -1 -1 0.0065 0.0109 0.0126 0.0071
## 15 -1 1 1 1 -1 -1 0.0155 0.0158 0.0145 0.0145
## 16 1 1 1 1 1 1 0.0093 0.0124 0.0110 0.0133
## class=design, type= FrF2## $legend
## [1] A=A B=B C=C D=D E=E F=F
##
## $main
## character(0)
##
## $fi2
## [1] AB=CE=DF AC=BE AD=BF AE=BC AF=BD CD=EF CF=DE8.40
## A B C D y
## 1 -1 -1 -1 -1 8
## 2 1 -1 -1 1 10
## 3 -1 1 -1 1 12
## 4 1 1 -1 -1 7
## 5 -1 -1 1 1 13
## 6 1 -1 1 -1 6
## 7 -1 1 1 -1 5
## 8 1 1 1 1 11
## class=design, type= FrF2## $legend
## [1] A=A B=B C=C D=D
##
## $main
## character(0)
##
## $fi2
## [1] AB=CD AC=BD AD=BC## Call:
## FrF2(nfactors = 4, resolution = NULL, randomize = FALSE, nruns = 8)
##
## Experimental design of type FrF2
## 8 runs
##
## Factor settings (scale ends):
## A B C D
## 1 -1 -1 -1 -1
## 2 1 1 1 1
##
## Responses:
## [1] y
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D
##
## $generators
## [1] D=ABC
##
##
## Alias structure:
## $fi2
## [1] AB=CD AC=BD AD=BC
##
##
## The design itself:
## A B C D y
## 1 -1 -1 -1 -1 8
## 2 1 -1 -1 1 10
## 3 -1 1 -1 1 12
## 4 1 1 -1 -1 7
## 5 -1 -1 1 1 13
## 6 1 -1 1 -1 6
## 7 -1 1 1 -1 5
## 8 1 1 1 1 11
## class=design, type= FrF2There are four (4) factors investigated in this experiment. The resolution of the design is a type four (IV). The defining relation for this design is I = ABCD.
A =
\(-(1)+ad-bd+ab-cd+ac-bc+abcd\)
$ = (-8+10-12+7-13+6-5+11)$
\(= -1\)
B =
\(-(1)-ad+bd+ab-cd-ac+bc+abcd\)
$ =(-8-10+12+7-13-6+5+11)$
\(= -0.5\)
C =
\(-(1)+ad+bd-ab+cd-ac-bc+abcd\)
\(=\frac{1}{4}(-8-10-12-7+13+6+5+11)\)
\(= -0.5\)
D =
\(-(1)+ad-bd+ab-cd+ac-bc+abcd\)
\(=\frac{1}{4}(-8+10+12-7+13-6-5+11)\)
\(= 5\)
8.48 Folded over Design and Column Generator
## $legend
## [1] A=A B=B C=C D=D E=E
##
## $main
## [1] A=BD=CE B=AD C=AE D=AB E=AC
##
## $fi2
## [1] BC=DE BE=CD## Call:
## FrF2(nfactors = 5, nruns = 8, randomize = FALSE)
##
## Experimental design of type FrF2
## 8 runs
##
## Factor settings (scale ends):
## A B C D E
## 1 -1 -1 -1 -1 -1
## 2 1 1 1 1 1
##
## Responses:
## [1] yields
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=D E=E
##
## $generators
## [1] D=AB E=AC
##
##
## Alias structure:
## $main
## [1] A=BD=CE B=AD C=AE D=AB E=AC
##
## $fi2
## [1] BC=DE BE=CD
##
##
## The design itself:
## A B C D E yields
## 1 -1 -1 -1 1 1 40
## 2 1 -1 -1 -1 -1 10
## 3 -1 1 -1 -1 1 30
## 4 1 1 -1 1 -1 20
## 5 -1 -1 1 1 -1 40
## 6 1 -1 1 -1 1 30
## 7 -1 1 1 -1 -1 20
## 8 1 1 1 1 1 30
## class=design, type= FrF2## Multi-step-call:
## [[1]]
## FrF2(nfactors = 5, nruns = 8, randomize = FALSE)
##
## $fold
## [1] full
##
##
## Experimental design of type FrF2.folded
## 16 runs
##
## Factor settings (scale ends):
## A B C fold D E
## 1 -1 -1 -1 original -1 -1
## 2 1 1 1 mirror 1 1
##
## Responses:
## [1] yields
##
## Design generating information:
## $legend
## [1] A=A B=B C=C D=fold E=D F=E
##
##
## Alias structure:
## $fi2
## [1] AB=-DE AC=-DF AD=-BE=-CF AE=-BD AF=-CD BC=EF BF=CE
##
##
## The design itself:
## A B C fold D E yields
## 1 -1 -1 -1 original 1 1 40
## 2 1 -1 -1 original -1 -1 10
## 3 -1 1 -1 original -1 1 30
## 4 1 1 -1 original 1 -1 20
## 5 -1 -1 1 original 1 -1 40
## 6 1 -1 1 original -1 1 30
## 7 -1 1 1 original -1 -1 20
## 8 1 1 1 original 1 1 30
## 9 1 1 1 mirror -1 -1 NA
## 10 -1 1 1 mirror 1 1 NA
## 11 1 -1 1 mirror 1 -1 NA
## 12 -1 -1 1 mirror -1 1 NA
## 13 1 1 -1 mirror -1 1 NA
## 14 -1 1 -1 mirror 1 -1 NA
## 15 1 -1 -1 mirror 1 1 NA
## 16 -1 -1 -1 mirror -1 -1 NA
## class=design, type= FrF2.foldedThe generator for column D = -ABC The generator for column E = BC The resolution of the original design and the folded over design is Resolution 4 (IV).
8.60 Aliasing
## $legend
## [1] A=A B=B C=C D=fold E=D F=E G=F H=G
##
## $main
## [1] B=CG=FH C=BG=EH E=CH=FG F=BH=EG G=BC=EF H=BF=CE
##
## $fi2
## [1] AB=-DE AC=-DF AD=-BE=-CF=-GH AE=-BD AF=-CD
## [6] AG=-DH AH=-DGThe alias factors can be seen on output above
All Code
library(FrF2)
library(dplyr)
library(GAD)
question2 <- FrF2(resolution = 4, nfactors = 4, randomize = FALSE)
results <- c(7.037, 14.707, 11.635, 17.273, 10.403, 4.368, 9.360, 13.440)
# 8.561, 16.867, 13.876, 19.824, 11.846, 6.125, 11.190, 15.653)
question2<-add.response(question2, results)
DanielPlot(question2,half=TRUE)
question2
#summary(question2)
question24 <- FrF2( nruns = 16, nfactors = 5, randomize = FALSE, resolution = 5, blocks = 2)
question24
summary(question24)
question25 <- FrF2(nruns = 32, nfactors = 7, randomize = FALSE, blocks = 4)
question25
summary(question25)
run <-seq(1,16)
#temp <-rep(c(55,75),8)
#time<-rep(c(rep(10,2),rep(25,2)),4)
#pressure <-rep(c(rep(5,4),rep(10,4)),2)
#firingTemp<-c(rep(1580,8),rep(1620,8))
#cycleTime <-c(17.5,29,29,17.5,29,17.5,17.5,29,17.5,29,29,17.5,29,17.5,17.5,29)
#dewPonit <-c(20,26,20,26,26,20,26,20,26,20,26,20,20,26,20,26)
temp <-rep(c(-1,1),8)
time<-rep(c(rep(-1,2),rep(1,2)),4)
pressure <-rep(c(rep(-1,4),rep(1,4)),2)
firingTemp<-c(rep(-1,8),rep(1,8))
cycleTime <-c(-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1)
dewPonit <-c(-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1)
temp<-as.fixed(temp)
time<-as.fixed(time)
pressure<-as.fixed(pressure)
firingTemp<-as.fixed(firingTemp)
cycleTime<-as.fixed(cycleTime)
dewPonit<-as.fixed(dewPonit)
yield <- c(0.0167,0.0062,0.0041,0.0073,0.0047,0.0219,0.0121,0.0255,0.0032,0.0078,0.0043,0.0186,0.011,0.0065,0.0155,0.0093,0.0128,0.0066,0.0043,0.0081,0.0047,0.0258,0.009,0.025,0.0023,0.0158,0.0027,0.0137,0.0086,0.0109,0.0158,0.0124,0.0149,0.0044,0.0042,0.0039,0.004,0.0147,0.0092,0.0226,0.0077,0.006,0.0028,0.0158,0.0101,0.0126,0.0145,0.011,0.0185,0.002,0.005,0.003,0.0089,0.0296,0.0086,0.0169,0.0069,0.0045,0.0028,0.0159,0.0158,0.0071,0.0145,0.0133)
total<- c(629,192,176,223,223,920,389,900,201,341,126,640,455,371,603,460)
meanX<- c(157.25,48,44,55.75,55.75,230,97.25,225,50.25,85.25,31.5,160,113.75,92.75,150.75,115)
standardDeviation <- c(24.418,20.976,4.083,25.025,22.41,63.639,16.029,39.42,26.725,50.341,7.681,20.083,31.12,29.51,6.75,17.45)
dat28<-cbind.data.frame(run,temp,time,pressure,firingTemp,cycleTime,dewPonit,yield,total,meanX,standardDeviation)
mod <-aov(yield~temp*time*pressure*firingTemp*cycleTime*dewPonit, data=dat28)
summary(mod)
question28<-FrF2(nfactors=6, resolution=NULL, randomize=FALSE, nruns =16)
rep1 <-c(0.0167,0.0062,0.0041,0.0073,0.0047,0.0219,0.0121,0.0255,0.0032,0.0078,0.0043,0.0186,0.0110,0.0065,0.0155,0.0093)
rep2<-c(0.0128,0.0066,0.0043,0.0081,0.0047,0.0258,0.0090,0.0250,0.0023,0.0158,0.0027,0.0137,0.0086, 0.0109, 0.0158,0.0124)
rep3 <- c( 0.0149,0.0044,0.0042,0.0039,0.0040,0.0147,0.0092,0.0226,0.0077,0.0060,0.0028,0.0158,0.0101,0.0126,0.0145,0.0110)
rep4<-c(0.0185,0.0020,0.0050,0.0030,0.0089,0.0296,0.0086,0.0169,0.0069,0.0045,0.0028,0.0159,0.0158,0.0071, 0.0145,0.0133)
question28<-add.response(question28,rep1)
question28<-add.response(question28,rep2)
question28<-add.response(question28,rep3)
question28<-add.response(question28,rep4)
summary(question28)
aliasprint(question28)
y <- c(8, 10, 12, 7, 13, 6, 5,11)
question40<-FrF2(nfactors=4, resolution=NULL, randomize=FALSE, nruns =8)
question40<-add.response(question40,y)
question40
aliasprint(question40)
summary(question40)
question60 <- FrF2(nfactors = 7, resolution = 3)
final <- fold.design(question60, columns = 1:1)
aliasprint(final)