# ============================================================
# REGRESI NONPARAMETRIK SPLINE TRUNCATED MULTIVARIABEL
# ============================================================
# LIBRARY
# ============================================================
library(Matrix)
library(pracma)
## Warning: package 'pracma' was built under R version 4.5.3
##
## Attaching package: 'pracma'
## The following objects are masked from 'package:Matrix':
##
## expm, lu, tril, triu
data=read.table(file.choose(),header=TRUE)
data
## Y X1 X2 X3 X4
## 1 4.52 67.88 13.00 14.86 72.04
## 2 4.97 71.02 12.89 14.38 51.19
## 3 5.70 61.98 13.58 18.56 73.59
## 4 5.45 68.96 12.78 29.61 43.00
## 5 5.08 67.40 13.31 14.89 74.71
## 6 6.22 69.04 12.55 55.70 71.41
## 7 3.49 76.22 12.50 10.46 67.09
## 8 9.00 62.90 14.13 15.59 80.01
## 9 8.26 65.16 14.70 75.04 30.11
## 10 9.46 69.24 12.90 31.21 80.02
## 11 3.71 74.28 12.60 20.67 67.03
## 12 3.91 75.81 12.08 8.67 47.87
## 13 3.38 71.78 12.39 10.74 65.98
## 14 7.55 64.14 12.33 8.54 25.74
## 15 3.52 70.38 11.56 19.95 65.77
## 16 7.30 60.75 11.79 28.13 67.17
## 17 4.50 75.57 12.02 14.71 36.88
## 18 4.02 74.09 12.04 10.28 65.69
## 19 3.39 77.53 11.57 6.56 64.76
## 20 2.70 73.93 11.15 25.23 25.55
## 21 3.71 65.53 11.81 4.21 22.68
## 22 7.14 67.71 13.64 28.93 67.95
## 23 12.36 60.05 13.64 37.68 79.44
## 24 8.78 63.84 12.89 10.14 41.94
## 25 3.57 72.03 11.96 10.16 69.38
## 26 4.96 64.68 11.92 17.31 68.86
## 27 3.87 72.55 12.28 11.73 59.18
## 28 2.93 74.61 12.38 5.76 66.22
## 29 3.73 70.17 11.86 6.35 70.11
## 30 2.24 73.15 12.10 4.65 48.85
## 31 3.90 71.15 12.19 4.83 68.84
## 32 4.49 70.08 12.88 3.30 65.59
## 33 3.07 69.27 12.59 14.48 72.19
## 34 6.95 70.16 12.36 15.39 50.71
## 35 2.46 76.50 12.37 9.17 68.82
## 36 8.32 62.07 13.92 21.93 77.10
## 37 5.54 66.82 14.80 6.11 79.10
## 38 5.08 66.44 13.29 11.21 71.94
## 39 4.45 67.38 12.99 18.72 41.10
## 40 4.83 67.81 12.20 5.75 66.97
## 41 4.14 66.91 12.63 26.30 45.79
## 42 5.86 65.65 13.73 38.11 75.83
## 43 4.76 73.01 12.71 33.79 72.87
## 44 5.25 67.41 12.69 56.63 71.31
## 45 4.98 70.04 12.90 45.81 69.48
## 46 4.21 64.68 12.54 45.53 70.22
## 47 5.29 71.54 12.48 51.50 30.59
## 48 4.70 65.50 12.11 66.27 68.03
## 49 2.83 70.50 12.47 67.99 70.51
## 50 4.30 65.04 11.98 40.96 37.58
## 51 5.69 64.55 12.51 48.22 68.68
## 52 2.63 72.77 12.40 43.84 68.45
## 53 2.49 71.22 11.77 51.25 70.81
## 54 2.91 77.73 12.82 54.56 21.39
## 55 3.10 63.93 11.74 62.92 67.98
## 56 5.95 62.71 14.94 61.01 80.77
# ============================================================
# SCATTERPLOT
# ============================================================
# X1 : Tingkat Partisipasi Angkatan Kerja
plot(data$X1,data$Y,
main="Scatterplot Tingkat Pengangguran Terbuka dan
Tingkat Partisipasi Angkatan Kerja",
xlab="Tingkat Partisipasi Angkatan Kerja (X1)",
ylab="Tingkat Pengangguran Terbuka (Y)",
col="black")
abline(lm(data$Y~data$X1), col="darkred", lwd=3)
# X2 : Harapan Lama Sekolah
plot(data$X2,data$Y,
main="Scatterplot Tingkat Pengangguran Terbuka dan
Harapan Lama Sekolah",
xlab="Harapan Lama Sekolah (X2)",
ylab="Tingkat Pengangguran Terbuka (Y)",
col="black")
abline(lm(data$Y~data$X2), col="darkred", lwd=3)
# X3 : PDRB Atas Dasar Harga Berlaku
plot(data$X3,data$Y,
main="Scatterplot Tingkat Pengangguran Terbuka dan
PDRB Atas Dasar Harga Berlaku",
xlab="PDRB Atas Dasar Harga Berlaku (X3)",
ylab="Tingkat Pengangguran Terbuka (Y)",
col="black")
abline(lm(data$Y~data$X3), col="darkred", lwd=3)
# X4 : Indeks Pembangunan Manusia
plot(data$X4,data$Y,
main="Scatterplot Tingkat Pengangguran Terbuka dan
Indeks Pembangunan Manusia",
xlab="Indeks Pembangunan Manusia (X4)",
ylab="Tingkat Pengangguran Terbuka (Y)",
col="black")
abline(lm(data$Y~data$X4), col="darkred", lwd=3)
# ============================================================
# PEMILIHAN 1 TITIK KNOT
# ============================================================
GCV1=function(data)
{
library(Matrix)
library(pracma)
para=0
data=as.matrix(data)
N=nrow(data)
M=ncol(data)
m=ncol(data)-para-1
dataA=data[,(para+2):M]
dataA=as.matrix(dataA)
F=diag(N)
nk=50
knot1=matrix(ncol=m,nrow=nk)
for (i in (1:m))
{
a=seq(min(dataA[,i]),max(dataA[,i]),length.out=nk)
knot1[,i]=t(as.matrix(a))
}
a1=length(knot1[,1])
knot1=as.matrix(knot1[2:(a1-1),])
aa=rep(1,N)
data1=matrix(ncol=m,nrow=N)
data2=data[,2:M]
nk1=nrow(knot1)
GCV=as.matrix(rep(NA,nk1),ncol=1)
colnames(GCV)<-"GCV"
MSE=as.matrix(rep(NA,nk1),ncol=1)
colnames(MSE)<-"MSE"
SSE=rep(NA,nk1)
SSR=rep(NA,nk1)
Rsq=as.matrix(rep(NA,nk1),ncol=1)
colnames(Rsq)<-"Rsq"
knotke=matrix(c(1:nk1),ncol=1)
colnames(knotke)<-"knot_ke"
for (i in 1:nk1)
{
for (j in 1:m)
{
for (k in 1:N)
{
if (data[k,(j+para+1)]<knot1[i,j])
data1[k,j]=0
else
data1[k,j]=data[k,(j+para+1)]-knot1[i,j]
}
}
mx=as.matrix(cbind(aa,data2,data1))
C=pinv(t(mx)%*%mx)
B=C%*%(t(mx)%*%data[,1])
yhat=mx%*%B
res=data[,1]-yhat
SSE[i]=sum((res)^2)
SSR[i]=sum((yhat-mean(data[,1]))^2)
MSE[i]=SSE[i]/(N)
Rsq[i]=(SSR[i]/(SSR[i]+SSE[i]))*100
A=mx%*%C%*%t(mx)
A1=(F-A)
A2=(sum(diag(A1))/N)^2
GCV[i]=MSE[i]/A2
}
dataAll=as.matrix(cbind(GCV,Rsq,knotke,knot1))
dataG=dataAll[order(GCV),-2]
write.csv(dataAll,file="DATA ALL KNOT 1.csv")
cat("==============================================","\n")
cat("HASIL GCV terkecil dengan 1 knot","\n")
cat("==============================================","\n")
print(((dataG[1,1:6])))
cat("Nilai GCV 10 terkecil pertama","\n")
print(dataG[1:10,])
mingcv=dataG[1,1]
# knot optimal = baris dengan GCV terkecil
knotke_opt=as.integer(dataG[1,2])
knotgcv=as.matrix(knot1[knotke_opt,])
knotgcv1=matrix(knotgcv,nrow=1)
# hitung kembali B tepat pada knot optimal
datagcv1=matrix(ncol=m,nrow=N)
for (j in 1:m)
{
for (k in 1:N)
{
if(data[k,(j+para+1)]<knotgcv[j,1])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(j+para+1)]-knotgcv[j,1]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
Cgcv=pinv(t(mxgcv)%*%mxgcv)
Bgcv=Cgcv%*%t(mxgcv)%*%data[,1]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 1","\n")
cat("==============================================","\n")
print(Bgcv)
cat("\n")
list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv,
B=Bgcv
)
}
hasil1=GCV1(data)
## ==============================================
## HASIL GCV terkecil dengan 1 knot
## ==============================================
## GCV knot_ke
## 1.508187 45.000000 76.286735 14.630612 69.183673 75.922653
## Nilai GCV 10 terkecil pertama
## GCV knot_ke
## [1,] 1.508187 45 76.28673 14.63061 69.183673 75.92265
## [2,] 1.515931 44 75.92592 14.55327 67.719592 74.71082
## [3,] 1.603414 46 76.64755 14.70796 70.647755 77.13449
## [4,] 1.615275 43 75.56510 14.47592 66.255510 73.49898
## [5,] 1.734461 42 75.20429 14.39857 64.791429 72.28714
## [6,] 1.763515 47 77.00837 14.78531 72.111837 78.34633
## [7,] 1.830095 3 61.13245 11.38204 7.692245 25.02551
## [8,] 1.861406 4 61.49327 11.45939 9.156327 26.23735
## [9,] 1.869770 41 74.84347 14.32122 63.327347 71.07531
## [10,] 1.912402 5 61.85408 11.53673 10.620408 27.44918
##
## ==============================================
## HASIL ESTIMASI PARAMETER TITIK KNOT KE 1
## ==============================================
## [,1]
## [1,] -0.160517930
## [2,] 1.319322478
## [3,] -0.006232983
## [4,] -0.008207276
## [5,] -0.066081304
# ============================================================
# UJI SIGNIFIKANSI 1 TITIK KNOT
# ============================================================
uji1=function(alpha,knot,data)
{
alpha=0.1
data=as.matrix(data)
knot=as.matrix(knot)
ybar=mean(data[,1])
m=2
n=nrow(data)
q=ncol(data)
dataA=cbind(data[,m],data[,m+1],
data[,m+2],data[,m+3])
dataA=as.matrix(dataA)
satu=rep(1,n)
n1=ncol(knot)
data.knot=matrix(ncol=n1,nrow=n)
for (i in 1:n1)
{
for (j in 1:n)
{
if(dataA[j,i]<knot[1,i])
data.knot[j,i]=0
else
data.knot[j,i]=dataA[j,i]-knot[1,i]
}
}
mx=cbind(satu,data[,2],data.knot[,1:1],
data[,3],data.knot[,2:2],
data[,4],data.knot[,3:3],
data[,5],data.knot[,4:4])
mx=as.matrix(mx)
B=(pinv(t(mx)%*%mx))%*%t(mx)%*%data[,1]
n1=nrow(B)
yhat=mx%*%B
ybar=mean(data[,1])
res=data[,1]-yhat
SSE=sum((data[,1]-yhat)^2)
SSR=sum((yhat-ybar)^2)
MSE=SSE/(n)
MSR=SSR/(n1-1)
SST=sum((data[,1]-ybar)^2)
Rsq=(SSR/(SSR+SSE))*100
#-------------------------------------------------------#
#SINTAKS UJI SIMULTAN DENGAN TITIK KNOT
#-------------------------------------------------------#
Fhit=MSR/MSE
pvalue=pf(Fhit,(n1-1),(n-n1),lower.tail=FALSE)
if(pvalue<=alpha)
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan','\n')
cat('','\n')
}
else
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan','\n')
cat('','\n')
}
#------------------------------------------------------#
#SINTAKS UJI PARSIAL DENGAN TITIK KNOT
#------------------------------------------------------#
thit=rep(NA,n1)
pval=rep(NA,n1)
SE=sqrt(diag(MSE*(pinv(t(mx)%*%mx))))
cat('---------------------------------------------','\n')
cat('Kesimpulan hasil uji parsial','\n')
cat('---------------------------------------------','\n')
thit=rep(NA,n1)
pval=rep(NA,n1)
for (i in 1:n1)
{
thit[i]=B[i,1]/SE[i]
pval[i]=2*(pt(abs(thit[i]),(n-n1),lower.tail=FALSE))
if (pval[i]<=alpha)
cat('Tolak Ho yakni variabel bebas signifikan dengan pvalue',pval[i],'\n')
else
cat('Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue',pval[i],'\n')
}
thit=as.matrix(thit)
cat('=============================================','\n')
cat('nilai t hitung','\n')
cat('=============================================','\n')
print(thit)
cat('Analysis of Variance','\n')
cat('=============================================','\n')
cat('Sumber df SS MS Fhit','\n')
cat('Regresi ',(n1-1),' ',SSR,' ',MSR,' ',Fhit,'\n')
cat('Error ',n-n1,' ',SSE,' ',MSE,'\n')
cat('Total ',n-1,' ',SST,'\n')
cat('=============================================','\n')
cat('s=',sqrt(MSE),' Rsq=',Rsq,'\n')
cat('pvalue(F)=',pvalue,'\n')
write.csv(res,file='OUTPUT UJI RESIDUAL KNOT 1.csv')
write.csv(mx,file='OUTPUT UJI MX KNOT 1.csv')
write.csv(yhat,file='UJI YHAT KNOT 1.csv')
list(
mx=mx,
residual=res,
yhat=yhat,
B=B,
SE=SE,
thit=thit,
pval=pval,
Fhit=Fhit,
pvalue=pvalue,
Rsq=Rsq
)
}
uji_hasil1=uji1(
alpha=0.1,
knot=hasil1$knotgcv,
data=data
)
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.04471309
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 6.825617e-06
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.9079879
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.006735878
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 2.184894e-06
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.5049048
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.07036832
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.09074499
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 4.259298e-07
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] 2.0624803
## [2,] -5.0617196
## [3,] 0.1162015
## [4,] 2.8350060
## [5,] -5.3953305
## [6,] -0.6719509
## [7,] 1.8516205
## [8,] -1.7269469
## [9,] 5.8681386
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 8 167.6864 20.9608 19.73027
## Error 47 59.49258 1.062368
## Total 55 227.1789
## =============================================
## s= 1.030712 Rsq= 73.81246
## pvalue(F)= 1.239e-12
# ============================================================
# PEMILIHAN 2 TITIK KNOT
# ============================================================
GCV2=function(data)
{
library(Matrix)
library(pracma)
para=0
data=as.matrix(data)
N=nrow(data)
M=ncol(data)
m=ncol(data)-para-1
dataA=data[,(para+2):M]
dataA=as.matrix(dataA)
F=diag(N)
nk=50
knot1=matrix(ncol=m,nrow=nk)
for (i in (1:m))
{
a=seq(min(dataA[,i]),max(dataA[,i]),length.out=nk)
knot1[,i]=t(as.matrix(a))
}
a1=length(knot1[,1])
knot1=as.matrix(knot1[2:(a1-1),])
a2=nk-2
z=(a2*(a2-1)/2)
knot2=cbind(rep(NA,(z+1)))
for (i in (1:m))
{
knot=rbind(rep(NA,2))
for (j in 1:(a2-1))
{
for (k in (j+1):a2)
{
xx=cbind(knot1[j,i],knot1[k,i])
knot=rbind(knot,xx)
}
}
knot2=cbind(knot2,knot)
}
knot2=knot2[2:(z+1),2:(2*m+1)]
a3=nrow(knot2)
aa=rep(1,N)
data1=matrix(ncol=2*m,nrow=N)
data2=data[,2:M]
nk1=nrow(knot2)
GCV=as.matrix(rep(NA,nk1),ncol=1)
colnames(GCV)<-"GCV"
MSE=as.matrix(rep(NA,nk1),ncol=1)
colnames(MSE)<-"MSE"
SSE=rep(NA,nk1)
SSR=rep(NA,nk1)
Rsq=as.matrix(rep(NA,nk1),ncol=1)
colnames(Rsq)<-"Rsq"
knotke=matrix(c(1:nk1),ncol=1)
colnames(knotke)<-"knot_ke"
for (i in 1:a3)
{
for (j in 1:(2*m))
{
if (mod(j,2)==1)
b=floor(j/2)+1
else
b=j/2
for (k in 1:N)
{
if (data[k,(b+para+1)]<knot2[i,j])
data1[k,j]=0
else
data1[k,j]=data[k,(b+para+1)]-knot2[i,j]
}
}
mx=as.matrix(cbind(aa,data2,data1))
C=pinv(t(mx)%*%mx)
B=C%*%(t(mx)%*%data[,1])
yhat=mx%*%B
res=data[,1]-yhat
SSE[i]=sum((res)^2)
SSR[i]=sum((yhat-mean(data[,1]))^2)
MSE[i]=SSE[i]/(N)
Rsq[i]=(SSR[i]/(SSR[i]+SSE[i]))*100
A=mx%*%C%*%t(mx)
A1=(F-A)
A2=(sum(diag(A1))/N)^2
GCV[i]=MSE[i]/A2
}
dataAll=as.matrix(cbind(GCV,Rsq,knotke,knot2))
dataG=dataAll[order(GCV),-2]
write.csv(dataAll,file="DATA ALL KNOT 2.csv")
cat("==============================================","\n")
cat("HASIL GCV terkecil dengan 2 knot","\n")
cat("==============================================","\n")
print(((dataG[1,1:10])))
cat("Nilai GCV 10 terkecil pertama","\n")
print(dataG[1:10,])
mingcv=dataG[1,1]
knotke_opt=as.integer(dataG[1,2])
knotgcv=as.matrix(knot2[knotke_opt,])
knotgcv1=matrix(knotgcv,nrow=2)
datagcv1=matrix(ncol=2*m,nrow=N)
for (j in 1:(2*m))
{
if (mod(j,2)==1)
b=floor(j/2)+1
else
b=j/2
for (k in 1:N)
{
if(data[k,(b+para+1)]<knotgcv[j,1])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(b+para+1)]-knotgcv[j,1]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
Cgcv=pinv(t(mxgcv)%*%mxgcv)
Bgcv=Cgcv%*%t(mxgcv)%*%data[,1]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 2","\n")
cat("==============================================","\n")
print(Bgcv)
cat("\n")
list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv,
B=Bgcv
)
}
hasil2=GCV2(data)
## ==============================================
## HASIL GCV terkecil dengan 2 knot
## ==============================================
## GCV knot_ke
## 1.316068 135.000000 61.132449 76.286735 11.382041 14.630612 7.692245
##
## 69.183673 25.025510 75.922653
## Nilai GCV 10 terkecil pertama
## GCV knot_ke
## [1,] 1.316068 135 61.13245 76.28673 11.38204 14.63061 7.692245 69.18367
## [2,] 1.317894 179 61.49327 76.28673 11.45939 14.63061 9.156327 69.18367
## [3,] 1.321114 178 61.49327 75.92592 11.45939 14.55327 9.156327 67.71959
## [4,] 1.321402 134 61.13245 75.92592 11.38204 14.55327 7.692245 67.71959
## [5,] 1.358738 221 61.85408 75.92592 11.53673 14.55327 10.620408 67.71959
## [6,] 1.359630 222 61.85408 76.28673 11.53673 14.63061 10.620408 69.18367
## [7,] 1.359989 138 61.13245 77.36918 11.38204 14.86265 7.692245 73.57592
## [8,] 1.388799 136 61.13245 76.64755 11.38204 14.70796 7.692245 70.64776
## [9,] 1.393180 180 61.49327 76.64755 11.45939 14.70796 9.156327 70.64776
## [10,] 1.396087 177 61.49327 75.56510 11.45939 14.47592 9.156327 66.25551
##
## [1,] 25.02551 75.92265
## [2,] 26.23735 75.92265
## [3,] 26.23735 74.71082
## [4,] 25.02551 74.71082
## [5,] 27.44918 74.71082
## [6,] 27.44918 75.92265
## [7,] 25.02551 79.55816
## [8,] 25.02551 77.13449
## [9,] 26.23735 77.13449
## [10,] 26.23735 73.49898
##
## ==============================================
## HASIL ESTIMASI PARAMETER TITIK KNOT KE 2
## ==============================================
## [,1]
## [1,] -0.078732767
## [2,] 0.975097952
## [3,] -0.008054519
## [4,] -0.009098772
## [5,] -0.149594082
# ============================================================
# UJI SIGNIFIKANSI 2 TITIK KNOT
# ============================================================
uji2=function(alpha,knot,data)
{
alpha=0.1
data=as.matrix(data)
knot=as.matrix(knot)
# HASIL GCV2 disimpan sebagai matriks 2 x 4.
# Untuk tahap uji, skripsi menggunakan knot dalam satu baris
# (8 nilai: 2 knot x 4 variabel).
knot=matrix(as.numeric(knot),nrow=1)
ybar=mean(data[,1])
m=2
n=nrow(data)
q=ncol(data)
dataA=cbind(
data[,m],data[,m],
data[,m+1],data[,m+1],
data[,m+2],data[,m+2],
data[,m+3],data[,m+3]
)
dataA=as.matrix(dataA)
satu=rep(1,n)
n1=ncol(knot)
data.knot=matrix(ncol=n1,nrow=n)
for (i in 1:n1)
{
for (j in 1:n)
{
if(dataA[j,i]<knot[1,i])
data.knot[j,i]=0
else
data.knot[j,i]=dataA[j,i]-knot[1,i]
}
}
mx=cbind(
satu,
data[,2],data.knot[,1:2],
data[,3],data.knot[,3:4],
data[,4],data.knot[,5:6],
data[,5],data.knot[,7:8]
)
mx=as.matrix(mx)
B=(pinv(t(mx)%*%mx))%*%t(mx)%*%data[,1]
n1=nrow(B)
yhat=mx%*%B
ybar=mean(data[,1])
res=data[,1]-yhat
SSE=sum((data[,1]-yhat)^2)
SSR=sum((yhat-ybar)^2)
MSE=SSE/(n)
MSR=SSR/(n1-1)
SST=sum((data[,1]-ybar)^2)
Rsq=(SSR/(SSR+SSE))*100
#-------------------------------------------------------#
#SINTAKS UJI SIMULTAN DENGAN TITIK KNOT
#-------------------------------------------------------#
Fhit=MSR/MSE
pvalue=pf(Fhit,(n1-1),(n-n1),lower.tail=FALSE)
if(pvalue<=alpha)
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan','\n')
cat('','\n')
}
else
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan','\n')
cat('','\n')
}
#------------------------------------------------------#
#SINTAKS UJI PARSIAL DENGAN TITIK KNOT
#------------------------------------------------------#
thit=rep(NA,n1)
pval=rep(NA,n1)
SE=sqrt(diag(MSE*(pinv(t(mx)%*%mx))))
cat('---------------------------------------------','\n')
cat('Kesimpulan hasil uji parsial','\n')
cat('---------------------------------------------','\n')
thit=rep(NA,n1)
pval=rep(NA,n1)
for (i in 1:n1)
{
thit[i]=B[i,1]/SE[i]
pval[i]=2*(pt(abs(thit[i]),(n-n1),lower.tail=FALSE))
if (pval[i]<=alpha)
cat('Tolak Ho yakni variabel bebas signifikan dengan pvalue',pval[i],'\n')
else
cat('Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue',pval[i],'\n')
}
thit=as.matrix(thit)
cat('=============================================','\n')
cat('nilai t hitung','\n')
cat('=============================================','\n')
print(thit)
cat('Analysis of Variance','\n')
cat('=============================================','\n')
cat('Sumber df SS MS Fhit','\n')
cat('Regresi ',(n1-1),' ',SSR,' ',MSR,' ',Fhit,'\n')
cat('Error ',n-n1,' ',SSE,' ',MSE,'\n')
cat('Total ',n-1,' ',SST,'\n')
cat('=============================================','\n')
cat('s=',sqrt(MSE),' Rsq=',Rsq,'\n')
cat('pvalue(F)=',pvalue,'\n')
write.csv(res,file='OUTPUT UJI RESIDUAL KNOT 2.csv')
write.csv(mx,file='OUTPUT UJI MX KNOT 2.csv')
write.csv(yhat,file='UJI YHAT KNOT 2.csv')
list(
mx=mx,
residual=res,
yhat=yhat,
B=B,
SE=SE,
thit=thit,
pval=pval,
Fhit=Fhit,
pvalue=pvalue,
Rsq=Rsq
)
}
uji_hasil2=uji2(
alpha=0.1,
knot=hasil2$knotgcv,
data=data
)
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2064143
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.002583234
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.004789845
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2422198
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1561285
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2229634
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 1.532736e-05
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1557346
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1498621
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1649558
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.02812549
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.02406025
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 3.439945e-06
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] 1.282856
## [2,] -3.199948
## [3,] 2.975107
## [4,] 1.185782
## [5,] 1.443491
## [6,] -1.236557
## [7,] -4.872993
## [8,] 1.444899
## [9,] -1.466226
## [10,] 1.412651
## [11,] 2.272317
## [12,] -2.338846
## [13,] 5.327626
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 12 183.7252 15.31043 19.73097
## Error 43 43.45373 0.7759595
## Total 55 227.1789
## =============================================
## s= 0.8808856 Rsq= 80.87246
## pvalue(F)= 1.075619e-13
# ============================================================
# PEMILIHAN 3 TITIK KNOT
# ============================================================
GCV3=function(data)
{
library(Matrix)
library(pracma)
para=0
data=as.matrix(data)
N=nrow(data)
M=ncol(data)
m=ncol(data)-para-1
dataA=data[,(para+2):M]
dataA=as.matrix(dataA)
F=diag(N)
nk=50
knot1=matrix(ncol=m,nrow=nk)
for (i in (1:m))
{
a=seq(min(dataA[,i]),max(dataA[,i]),length.out=nk)
knot1[,i]=t(as.matrix(a))
}
a1=length(knot1[,1])
knot1=as.matrix(knot1[2:(a1-1),])
a2=nk-2
z=(a2*(a2-1)*(a2-2)/6)
knot2=cbind(rep(NA,(z+1)))
for (i in (1:m))
{
knot=rbind(rep(NA,3))
for (j in 1:(a2-2))
{
for (k in (j+1):(a2-1))
{
for (g in (k+1):a2)
{
xx=cbind(
knot1[j,i],
knot1[k,i],
knot1[g,i]
)
knot=rbind(knot,xx)
}
}
}
knot2=cbind(knot2,knot)
}
knot2=knot2[2:(z+1),2:(3*m+1)]
a3=nrow(knot2)
aa=rep(1,N)
data1=matrix(ncol=3*m,nrow=N)
data2=data[,2:M]
nk1=nrow(knot2)
GCV=as.matrix(rep(NA,nk1),ncol=1)
colnames(GCV)<-"GCV"
MSE=as.matrix(rep(NA,nk1),ncol=1)
colnames(MSE)<-"MSE"
SSE=rep(NA,nk1)
SSR=rep(NA,nk1)
Rsq=as.matrix(rep(NA,nk1),ncol=1)
colnames(Rsq)<-"Rsq"
knotke=matrix(c(1:nk1),ncol=1)
colnames(knotke)<-"knot_ke"
for (i in 1:a3)
{
for (j in 1:(3*m))
{
b=ceiling(j/3)
for (k in 1:N)
{
if (data[k,(b+para+1)]<knot2[i,j])
data1[k,j]=0
else
data1[k,j]=data[k,(b+para+1)]-knot2[i,j]
}
}
mx=as.matrix(cbind(aa,data2,data1))
C=pinv(t(mx)%*%mx)
B=C%*%(t(mx)%*%data[,1])
yhat=mx%*%B
res=data[,1]-yhat
SSE[i]=sum((res)^2)
SSR[i]=sum((yhat-mean(data[,1]))^2)
MSE[i]=SSE[i]/(N)
Rsq[i]=(SSR[i]/(SSR[i]+SSE[i]))*100
A=mx%*%C%*%t(mx)
A1=(F-A)
A2=(sum(diag(A1))/N)^2
GCV[i]=MSE[i]/A2
}
dataAll=as.matrix(cbind(GCV,Rsq,knotke,knot2))
dataG=dataAll[order(GCV),-2]
write.csv(dataAll,file="DATA ALL KNOT 3.csv")
cat("==============================================","\n")
cat("HASIL GCV terkecil dengan 3 knot","\n")
cat("==============================================","\n")
print(((dataG[1,1:14])))
cat("Nilai GCV 10 terkecil pertama","\n")
print(dataG[1:10,])
mingcv=dataG[1,1]
knotke_opt=as.integer(dataG[1,2])
knotgcv=as.matrix(knot2[knotke_opt,])
knotgcv1=matrix(knotgcv,nrow=3)
datagcv1=matrix(ncol=3*m,nrow=N)
for (j in 1:(3*m))
{
b=ceiling(j/3)
for (k in 1:N)
{
if (data[k,(b+para+1)]<knotgcv[j,1])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(b+para+1)]-knotgcv[j,1]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
Cgcv=pinv(t(mxgcv)%*%mxgcv)
Bgcv=Cgcv%*%t(mxgcv)%*%data[,1]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 3","\n")
cat("==============================================","\n")
print(Bgcv)
cat("\n")
list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv,
B=Bgcv
)
}
hasil3=GCV3(data)
## ==============================================
## HASIL GCV terkecil dengan 3 knot
## ==============================================
## GCV knot_ke
## 1.444246 2200.000000 61.132449 61.854082 76.286735 11.382041
##
## 11.536735 14.630612 7.692245 10.620408 69.183673 25.025510
##
## 27.449184 75.922653
## Nilai GCV 10 terkecil pertama
## GCV knot_ke
## [1,] 1.444246 2200 61.13245 61.85408 76.28673 11.38204 11.53673 14.63061
## [2,] 1.445793 3146 61.49327 61.85408 76.28673 11.45939 11.53673 14.63061
## [3,] 1.447104 2157 61.13245 61.49327 76.28673 11.38204 11.45939 14.63061
## [4,] 1.452451 3106 61.13245 77.00837 77.36918 11.38204 14.78531 14.86265
## [5,] 1.453903 2199 61.13245 61.85408 75.92592 11.38204 11.53673 14.55327
## [6,] 1.454858 3145 61.49327 61.85408 75.92592 11.45939 11.53673 14.55327
## [7,] 1.458180 2156 61.13245 61.49327 75.92592 11.38204 11.45939 14.55327
## [8,] 1.458931 2242 61.13245 62.21490 76.28673 11.38204 11.61408 14.63061
## [9,] 1.464584 3037 61.13245 73.03939 76.28673 11.38204 13.93449 14.63061
## [10,] 1.465580 3101 61.13245 76.28673 76.64755 11.38204 14.63061 14.70796
##
## [1,] 7.692245 10.620408 69.18367 25.02551 27.44918 75.92265
## [2,] 9.156327 10.620408 69.18367 26.23735 27.44918 75.92265
## [3,] 7.692245 9.156327 69.18367 25.02551 26.23735 75.92265
## [4,] 7.692245 72.111837 73.57592 25.02551 78.34633 79.55816
## [5,] 7.692245 10.620408 67.71959 25.02551 27.44918 74.71082
## [6,] 9.156327 10.620408 67.71959 26.23735 27.44918 74.71082
## [7,] 7.692245 9.156327 67.71959 25.02551 26.23735 74.71082
## [8,] 7.692245 12.084490 69.18367 25.02551 28.66102 75.92265
## [9,] 7.692245 56.006939 69.18367 25.02551 65.01612 75.92265
## [10,] 7.692245 69.183673 70.64776 25.02551 75.92265 77.13449
##
## ==============================================
## HASIL ESTIMASI PARAMETER TITIK KNOT KE 3
## ==============================================
## [,1]
## [1,] -0.078732767
## [2,] 0.975097952
## [3,] -0.008054519
## [4,] -0.009098772
## [5,] -0.149594082
# ============================================================
# UJI SIGNIFIKANSI 3 TITIK KNOT
# ============================================================
uji3=function(alpha,knot,data)
{
alpha=0.1
data=as.matrix(data)
knot=as.matrix(knot)
# HASIL GCV3 disimpan sebagai matriks 3 x 4.
# Untuk tahap uji, knot diratakan menjadi 1 baris
# (12 nilai: 3 knot x 4 variabel).
knot=matrix(as.numeric(knot),nrow=1)
ybar=mean(data[,1])
m=2
n=nrow(data)
q=ncol(data)
dataA=cbind(
data[,m],data[,m],data[,m],
data[,m+1],data[,m+1],data[,m+1],
data[,m+2],data[,m+2],data[,m+2],
data[,m+3],data[,m+3],data[,m+3]
)
dataA=as.matrix(dataA)
satu=rep(1,n)
n1=ncol(knot)
data.knot=matrix(ncol=n1,nrow=n)
for (i in 1:n1)
{
for (j in 1:n)
{
if(dataA[j,i]<knot[1,i])
data.knot[j,i]=0
else
data.knot[j,i]=dataA[j,i]-knot[1,i]
}
}
mx=cbind(
satu,
data[,2],data.knot[,1:3],
data[,3],data.knot[,4:6],
data[,4],data.knot[,7:9],
data[,5],data.knot[,10:12]
)
mx=as.matrix(mx)
B=(pinv(t(mx)%*%mx))%*%t(mx)%*%data[,1]
n1=nrow(B)
yhat=mx%*%B
ybar=mean(data[,1])
res=data[,1]-yhat
SSE=sum((data[,1]-yhat)^2)
SSR=sum((yhat-ybar)^2)
MSE=SSE/(n)
MSR=SSR/(n1-1)
SST=sum((data[,1]-ybar)^2)
Rsq=(SSR/(SSR+SSE))*100
#-------------------------------------------------------#
#SINTAKS UJI SIMULTAN DENGAN TITIK KNOT
#-------------------------------------------------------#
Fhit=MSR/MSE
pvalue=pf(Fhit,(n1-1),(n-n1),lower.tail=FALSE)
if(pvalue<=alpha)
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan','\n')
cat('','\n')
}
else
{
cat('---------------------------------------','\n')
cat('Kesimpulan hasil uji simultan','\n')
cat('---------------------------------------','\n')
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan','\n')
cat('','\n')
}
#------------------------------------------------------#
#SINTAKS UJI PARSIAL DENGAN TITIK KNOT
#------------------------------------------------------#
thit=rep(NA,n1)
pval=rep(NA,n1)
SE=sqrt(diag(MSE*(pinv(t(mx)%*%mx))))
cat('---------------------------------------------','\n')
cat('Kesimpulan hasil uji parsial','\n')
cat('---------------------------------------------','\n')
thit=rep(NA,n1)
pval=rep(NA,n1)
for (i in 1:n1)
{
thit[i]=B[i,1]/SE[i]
pval[i]=2*(pt(abs(thit[i]),(n-n1),lower.tail=FALSE))
if (pval[i]<=alpha)
cat('Tolak Ho yakni variabel bebas signifikan dengan pvalue',pval[i],'\n')
else
cat('Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue',pval[i],'\n')
}
thit=as.matrix(thit)
cat('=============================================','\n')
cat('nilai t hitung','\n')
cat('=============================================','\n')
print(thit)
cat('Analysis of Variance','\n')
cat('=============================================','\n')
cat('Sumber df SS MS Fhit','\n')
cat('Regresi ',(n1-1),' ',SSR,' ',MSR,' ',Fhit,'\n')
cat('Error ',n-n1,' ',SSE,' ',MSE,'\n')
cat('Total ',n-1,' ',SST,'\n')
cat('=============================================','\n')
cat('s=',sqrt(MSE),' Rsq=',Rsq,'\n')
cat('pvalue(F)=',pvalue,'\n')
write.csv(res,file='OUTPUT UJI RESIDUAL KNOT 3.csv')
write.csv(mx,file='OUTPUT UJI MX KNOT 3.csv')
write.csv(yhat,file='UJI YHAT KNOT 3.csv')
list(
mx=mx,
residual=res,
yhat=yhat,
B=B,
SE=SE,
thit=thit,
pval=pval,
Fhit=Fhit,
pvalue=pvalue,
Rsq=Rsq
)
}
uji_hasil3=uji3(
alpha=0.1,
knot=hasil3$knotgcv,
data=data
)
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6087605
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.7734961
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.5228609
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1758342
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.3014451
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.8976796
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6190703
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.4479088
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 1.040868e-05
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.4567152
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6607985
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.9315849
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2034532
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.04980339
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1138228
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2996611
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 2.587599e-06
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] -0.51601044
## [2,] -0.28981099
## [3,] -0.64475471
## [4,] 1.37873374
## [5,] 1.04722022
## [6,] 0.12943381
## [7,] 0.50116758
## [8,] -0.76664478
## [9,] -5.05857856
## [10,] 0.75174871
## [11,] -0.44218412
## [12,] 0.08640707
## [13,] 1.29348236
## [14,] 2.02451772
## [15,] -1.61753943
## [16,] 1.05114669
## [17,] 5.49666947
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 16 185.9148 11.61967 15.76917
## Error 39 41.26416 0.7368601
## Total 55 227.1789
## =============================================
## s= 0.8584055 Rsq= 81.83627
## pvalue(F)= 2.762142e-12