SINTAKS ANALISIS STATISTIKA DESKRIPTIF & DETEKSI
MULTIKOLINIERITAS
library(lmtest)
library(MASS)
library(car)
library(pastecs)
library(Matrix)
library(pracma)
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
stat.desc(data)
## Y X1 X2 X3 X4
## nbr.val 56.0000000 5.600000e+01 56.00000000 56.0000000 56.0000000
## nbr.null 0.0000000 0.000000e+00 0.00000000 0.0000000 0.0000000
## nbr.na 0.0000000 0.000000e+00 0.00000000 0.0000000 0.0000000
## min 2.2400000 6.005000e+01 11.15000000 3.3000000 21.3900000
## max 12.3600000 7.773000e+01 14.94000000 75.0400000 80.7700000
## range 10.1200000 1.768000e+01 3.79000000 71.7400000 59.3800000
## sum 277.6000000 3.863250e+03 708.36000000 1476.2800000 3422.8700000
## median 4.5100000 6.914000e+01 12.50500000 18.6400000 67.9650000
## mean 4.9571429 6.898661e+01 12.64928571 26.3621429 61.1226786
## SE.mean 0.2715868 6.008087e-01 0.10790865 2.6750203 2.2021767
## CI.mean.0.95 0.5442721 1.204048e+00 0.21625376 5.3608606 4.4132607
## var 4.1305262 2.021438e+01 0.65207948 400.7210935 271.5766018
## std.dev 2.0323696 4.496041e+00 0.80751438 20.0180192 16.4795814
## coef.var 0.4099881 6.517266e-02 0.06383873 0.7593472 0.2696148
model=(lm(formula=Y~X1+X2+X3+X4,data=data))
summary(model)
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1296 -0.9922 -0.1119 0.7639 4.6374
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.498612 5.796395 1.811 0.07600 .
## X1 -0.237422 0.049782 -4.769 1.59e-05 ***
## X2 0.919839 0.278410 3.304 0.00175 **
## X3 -0.008344 0.010186 -0.819 0.41651
## X4 -0.009455 0.012466 -0.758 0.45170
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.453 on 51 degrees of freedom
## Multiple R-squared: 0.526, Adjusted R-squared: 0.4888
## F-statistic: 14.15 on 4 and 51 DF, p-value: 7.786e-08
vif(model)
## X1 X2 X3 X4
## 1.304895 1.316581 1.083064 1.099406
SCATTER PLOT
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")
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")
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")
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")
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="dataAll 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]
knotgcv=as.matrix(knot1[dataG[1,4],])
knotgcv1=matrix(knotgcv,nrow=1)
datagcv1=matrix(ncol=m,nrow=N)
for (j in 1:m)
{
for (k in 1:N)
{
if (data[k,(j+para+1)]<knotgcv1[1,j])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(j+para+1)]-knotgcv1[1,j]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 1","\n")
cat("==============================================","\n")
print(B)
cat("\n")
return(list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv
))
}
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,] 1.100168e+01
## [2,] -2.352118e-01
## [3,] 8.683805e-01
## [4,] -5.401921e-03
## [5,] -1.233868e-02
## [6,] 5.699848e-01
## [7,] -1.336717e+02
## [8,] 4.073604e-01
## [9,] 6.923471e+00
knot=hasil1$knotgcv
knot
## [,1] [,2] [,3] [,4]
## [1,] 65.10143 12.23286 23.79714 38.35571
satu knot Uji signifikansi
uji=function(alpha,para)
{
alpha=0.1
para=0
data=as.matrix(data)
knot=as.matrix(knot)
knot=matrix(knot,nrow=1)
ybar=mean(data[,1])
m=para+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],
data[,3],
data.knot[,2],
data[,4],
data.knot[,3],
data[,5],
data.knot[,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")
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 knot1.csv")
write.csv(mx,file="output uji mx knot1.csv")
write.csv(yhat,file="output uji yhat knot1.csv")
}
uji(alpha,0)
## ---------------------------------------
## 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 0.04427686
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.0001707978
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.005038743
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.02686655
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.213757
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1991707
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1367919
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.7717169
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.9934183
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] 2.066896081
## [2,] -4.084126012
## [3,] 2.942793329
## [4,] 2.285060178
## [5,] -1.260371839
## [6,] 1.302267679
## [7,] -1.513724730
## [8,] -0.291808832
## [9,] 0.008293006
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 8 140.7515 17.59393 11.39985
## Error 47 86.42746 1.543348
## Total 55 227.1789
## =============================================
## s= 1.242315 Rsq= 61.95622
## pvalue(F)= 8.305017e-09
PEMILIHAN DUA 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="dataAll 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]
knotgcv=as.matrix(knot2[dataG[1,4],])
# Dibuat 1 baris dan 8 kolom
knotgcv1=matrix(knotgcv,nrow=1)
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)]<knotgcv1[1,j])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(b+para+1)]-knotgcv1[1,j]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 2","\n")
cat("==============================================","\n")
print(B)
cat("\n")
return(list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv
))
}
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,] 6.044955e+00
## [2,] -1.859007e-01
## [3,] 1.031486e+00
## [4,] -4.170952e-03
## [5,] -2.228411e-02
## [6,] 9.154406e+00
## [7,] -2.164657e+01
## [8,] -3.547727e+02
## [9,] 6.943980e+02
## [10,] 4.083286e-02
## [11,] 2.041643e-02
## [12,] 4.845712e+00
## [13,] -1.020433e+01
knot=hasil2$knotgcv
knot
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 60.77163 71.23531 11.30469 13.54776 6.228163 48.68653 23.81367 58.95694
dua knot Uji signifikansi
uji=function(alpha,para)
{
alpha=0.1
para=0
data=as.matrix(data)
knot=as.matrix(knot)
knot=matrix(knot,nrow=1)
ybar=mean(data[,1])
m=para+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")
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 knot2.csv")
write.csv(mx,file="output uji mx knot2.csv")
write.csv(yhat,file="output uji yhat knot2.csv")
}
uji(alpha,0)
## ---------------------------------------
## 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 0.1022024
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.0005926891
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.0009161883
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6124512
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2418797
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2975987
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1812606
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2071626
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.2051428
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.9447404
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.06747531
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.06002954
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1327567
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] 1.66990918
## [2,] -3.70862471
## [3,] 3.56150342
## [4,] 0.51029970
## [5,] 1.18665239
## [6,] -1.05437766
## [7,] -1.35891029
## [8,] 1.28070401
## [9,] -1.28652722
## [10,] -0.06971916
## [11,] 1.87584852
## [12,] -1.93149727
## [13,] 1.53236796
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 12 156.176 13.01466 10.26466
## Error 43 71.00298 1.26791
## Total 55 227.1789
## =============================================
## s= 1.126015 Rsq= 68.74579
## pvalue(F)= 4.212632e-09
PEMILIHAN TIGA 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="dataAll 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]
knotgcv=as.matrix(knot2[dataG[1,4],])
# Dibuat 1 baris dan 12 kolom
knotgcv1=matrix(knotgcv,nrow=1)
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)]<knotgcv1[1,j])
datagcv1[k,j]=0
else
datagcv1[k,j]=data[k,(b+para+1)]-knotgcv1[1,j]
}
}
mxgcv=as.matrix(cbind(aa,data2,datagcv1))
mxgcv=mxgcv[,c(2:6)]
cat("\n")
cat("==============================================","\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 3","\n")
cat("==============================================","\n")
print(B)
cat("\n")
return(list(
knotgcv=knotgcv1,
mingcv=mingcv,
mxgcv=mxgcv
))
}
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,] 6.072786922
## [2,] -0.185927169
## [3,] 1.029244397
## [4,] -0.004126666
## [5,] -0.022270952
## [6,] 6.655420960
## [7,] -4.161967634
## [8,] -14.979356227
## [9,] -6.028540779
## [10,] 14.203131537
## [11,] 9.970360436
## [12,] 0.022331619
## [13,] 0.014887746
## [14,] 0.007443873
## [15,] -12.848704041
## [16,] 31.920041594
## [17,] -28.068467337
knot=hasil3$knotgcv
knot
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 60.41082 61.13245 66.54469 11.22735 11.38204 12.54224 4.764082 7.692245
## [,9] [,10] [,11] [,12]
## [1,] 29.65347 22.60184 25.02551 43.20306
tiga knot Uji signifikansi
uji=function(alpha,para)
{
alpha=0.1
para=0
data=as.matrix(data)
knot=as.matrix(knot)
knot=matrix(knot,nrow=1)
ybar=mean(data[,1])
m=para+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")
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 knot3.csv")
write.csv(mx,file="output uji mx knot3.csv")
write.csv(yhat,file="output uji yhat knot3.csv")
}
uji(alpha,0)
## ---------------------------------------
## 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 0.4533707
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.3190536
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.7012486
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.4351769
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.5126893
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.3157713
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.4840213
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.8992993
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6159084
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.8873461
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.7603281
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.5576516
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.1216471
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.9794123
## Gagal tolak Ho yakni variabel tidak signifikan dengan pvalue 0.6124465
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.08233747
## Tolak Ho yakni variabel bebas signifikan dengan pvalue 0.07580495
## =============================================
## nilai t hitung
## =============================================
## [,1]
## [1,] 0.75738580
## [2,] -1.00929668
## [3,] 0.38647078
## [4,] 0.78849029
## [5,] 0.66069924
## [6,] 1.01625518
## [7,] -0.70659057
## [8,] 0.12737347
## [9,] -0.50570757
## [10,] -0.14259262
## [11,] 0.30719669
## [12,] -0.59142019
## [13,] -1.58234778
## [14,] 0.02597174
## [15,] 0.51069056
## [16,] -1.78320409
## [17,] 1.82410706
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 16 161.9062 10.11914 8.681598
## Error 39 65.27274 1.165585
## Total 55 227.1789
## =============================================
## s= 1.079622 Rsq= 71.26814
## pvalue(F)= 2.097291e-08