Finalsrm11

Question 11

#Hypothesis:Null Hypothesis
#αγ)i,k=0

#(αλ)i,l=0

#αi=0

#γk=0

#λl=0

#Alternate Hypothesis
#(αγ)i,k≠0

#(αλ)i,l≠0

#αi≠0

#γk≠0

#λl≠0



f <- c(12,18,13,16,17,15,20,15,10,25,13,24,19,21,17,23)
a <- c(-1,1)
b <- c(-1,-1,1,1)
c <- c(-1,-1,-1,-1,1,1,1,1)
d <- c(-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1)
A <- c(rep(a,8))
B <- c(rep(b,4))
C <- c(rep(c,2))
D <- c(rep(d,1))

Data <- data.frame(A,B,C,D,f)
Data

##     A  B  C  D  f
## 1  -1 -1 -1 -1 12
## 2   1 -1 -1 -1 18
## 3  -1  1 -1 -1 13
## 4   1  1 -1 -1 16
## 5  -1 -1  1 -1 17
## 6   1 -1  1 -1 15
## 7  -1  1  1 -1 20
## 8   1  1  1 -1 15
## 9  -1 -1 -1  1 10
## 10  1 -1 -1  1 25
## 11 -1  1 -1  1 13
## 12  1  1 -1  1 24
## 13 -1 -1  1  1 19
## 14  1 -1  1  1 21
## 15 -1  1  1  1 17
## 16  1  1  1  1 23

Model <- lm(f~A*B*C*D,data = Data)
coef(Model)

##   (Intercept)             A             B             C             D 
##  1.737500e+01  2.250000e+00  2.500000e-01  1.000000e+00  1.625000e+00 
##           A:B           A:C           B:C           A:D           B:D 
## -3.750000e-01 -2.125000e+00  1.250000e-01  2.000000e+00 -8.543513e-17 
##           C:D         A:B:C         A:B:D         A:C:D         B:C:D 
##  1.110223e-16  5.000000e-01  3.750000e-01 -1.250000e-01 -3.750000e-01 
##       A:B:C:D 
##  5.000000e-01

#Halfnormal Plot

library(DoE.base)

## Warning: package 'DoE.base' was built under R version 4.2.2

## Loading required package: grid

## Loading required package: conf.design

## Registered S3 method overwritten by 'DoE.base':
##   method           from       
##   factorize.factor conf.design

## 
## Attaching package: 'DoE.base'

## The following objects are masked from 'package:stats':
## 
##     aov, lm

## The following object is masked from 'package:graphics':
## 
##     plot.design

## The following object is masked from 'package:base':
## 
##     lengths

halfnormal(Model)

## 
## Significant effects (alpha=0.05, Lenth method):

## [1] A   A:C A:D D

#Therefore significant effects are A,A:C, A:D,D
Model1 <- aov(f~A+C+D+A*C+A*D,data = Data)
summary(Model1)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## A            1  81.00   81.00  49.846 3.46e-05 ***
## C            1  16.00   16.00   9.846 0.010549 *  
## D            1  42.25   42.25  26.000 0.000465 ***
## A:C          1  72.25   72.25  44.462 5.58e-05 ***
## A:D          1  64.00   64.00  39.385 9.19e-05 ***
## Residuals   10  16.25    1.62                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(ggfortify)

## Warning: package 'ggfortify' was built under R version 4.2.2

## Loading required package: ggplot2

library(ggplot2)
autoplot(Model1)

interaction.plot(A,D,f)

#By analysis A,C,D appears to be significant