Tugas Skripsi regresi spline
Elvira Aurelia Aisya Putri
2026-10-04
# ============================================================
# REGRESI SPLINE TRUNCATED MULTIVARIABEL
# Adaptasi dari Skripsi Rewani Ega Tanaty
# Data: Tingkat Pengangguran Terbuka di Kabupaten/Kota Kalimantan
# ============================================================
# Perubahan dari versi awal:
# 1. Knot optimal diambil dengan which.min(GCV)
# 2. Parameter yang dicetak adalah parameter di knot OPTIMAL
# 3. Uji signifikansi memakai knot optimal (bukan knot ke-1)
# 4. MSE di uji signifikansi = SSE/(n - n1)
# 5. Nama file output diganti (akhiran _v2) supaya tidak menimpa file lama
# ============================================================
# ============================================================
# BAGIAN 1: STATISTIKA DESKRIPTIF & DETEKSI MULTIKOLINIERITAS
# ============================================================
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(MASS)
library(car)## Loading required package: carDatalibrary(pastecs)
library(pracma)##
## Attaching package: 'pracma'## The following object is masked from 'package:car':
##
## logitlibrary(ggplot2)
library(gridExtra)
data = read.table("Data_Kabupaten_Kota_Kalimantan.txt", 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 80.77nrow(data) # harus 56## [1] 56# Statistika deskriptif
stat.desc(data) # ada SD, varians, dll## 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 0.2696148library(ggplot2)
library(gridExtra)
sp1 = ggplot(data, aes(x=x1, y=y)) + geom_point() + stat_smooth()
sp2 = ggplot(data, aes(x=x2, y=y)) + geom_point() + stat_smooth()
sp3 = ggplot(data, aes(x=x3, y=y)) + geom_point() + stat_smooth()
sp4 = ggplot(data, aes(x=x4, y=y)) + geom_point() + stat_smooth()
grid.arrange(sp1, sp2, sp3, sp4, ncol=2)## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
# Deteksi multikolinieritas
model_lm = lm(formula = y ~ x1 + x2 + x3 + x4, data = data)
summary(model_lm)##
## 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-08vif(model_lm)## x1 x2 x3 x4
## 1.304895 1.316581 1.083064 1.099406# ============================================================
# REGRESI SPLINE TRUNCATED MULTIVARIABEL - 1, 2, DAN 3 KNOT
# Data: Tingkat Pengangguran Terbuka di Kabupaten/Kota Kalimantan
# (y, x1, x2, x3, x4; n = 56)
# ============================================================
# Isi:
# BAGIAN 1 : statistika deskriptif & deteksi multikolinieritas
# BAGIAN A : persiapan (fungsi bantu)
# BAGIAN B : fungsi pemilihan knot optimal (GCV) untuk k knot
# BAGIAN C : fungsi uji signifikansi (simultan & parsial) untuk k knot
# BAGIAN D : jalankan 1, 2, 3 knot sekaligus + tabel perbandingan
#
# Skema knot (sama untuk 1, 2, 3 knot):
# - tiap variabel punya grid nk = 50 titik dari min sampai max,
# titik min & max dibuang (jadi 48 kandidat)
# - 1 knot : 48 kandidat -> C(48,1) = 48 kombinasi
# - 2 knot : semua pasangan (i<j) -> C(48,2) = 1128 kombinasi
# - 3 knot : semua tripel (i<j<l) -> C(48,3) = 17296 kombinasi
# ============================================================
# ============================================================
# BAGIAN A: FUNGSI BANTU
# ============================================================
# Membentuk matriks desain
# knot : matriks k x m (baris = knot ke-s, kolom = variabel ke-j)
# urut = "gcv" -> 1, x1..xm, lalu semua (x-k1)+, semua (x-k2)+, ...
# urut = "uji" -> 1, x1, (x1-k1)+, (x1-k2)+, x2, (x2-k1)+, ...
buat_mx = function(X, knot, urut = "gcv")
{
N = nrow(X); m = ncol(X); k = nrow(knot)
if (urut == "gcv") {
trunc = do.call(cbind, lapply(1:k, function(s)
sapply(1:m, function(j) pmax(X[, j] - knot[s, j], 0))))
mx = cbind(1, X, trunc)
nama = c("b0", paste0("x", 1:m),
unlist(lapply(1:k, function(s) paste0("(x", 1:m, "-k", s, ")+"))))
} else {
kol = list(rep(1, N)); nama = "b0"
for (j in 1:m) {
kol[[length(kol) + 1]] = X[, j]
nama = c(nama, paste0("x", j))
for (s in 1:k) {
kol[[length(kol) + 1]] = pmax(X[, j] - knot[s, j], 0)
nama = c(nama, paste0("(x", j, "-k", s, ")+"))
}
}
mx = do.call(cbind, kol)
}
colnames(mx) = nama
mx
}
# ============================================================
# BAGIAN B: PEMILIHAN KNOT OPTIMAL DENGAN GCV (k = 1, 2, atau 3)
# ============================================================
GCVk = function(data, k = 2, nk = 50)
{
data = as.matrix(data)
N = nrow(data)
y = data[, 1]
X = data[, 2:ncol(data), drop = FALSE]
m = ncol(X)
# grid kandidat knot per variabel (buang titik min & max)
grid = sapply(1:m, function(j) seq(min(X[, j]), max(X[, j]), length.out = nk))
grid = grid[2:(nk - 1), , drop = FALSE]
ng = nrow(grid)
# tiap baris = indeks kandidat (naik); matrix() menjaga bentuk saat k = 1
komb = matrix(t(combn(ng, k)), ncol = k)
nkomb = nrow(komb)
cat("\n>>> Jumlah kombinasi knot (k =", k, "):", nkomb, "\n")
GCV = rep(NA, nkomb)
Rsq = rep(NA, nkomb)
knotmat = matrix(NA, nkomb, k * m)
nama.knot = as.vector(t(outer(1:k, 1:m, function(s, j) paste0("k", s, "_x", j))))
for (i in 1:nkomb)
{
knot = matrix(0, k, m)
for (s in 1:k) knot[s, ] = grid[komb[i, s], ]
knotmat[i, ] = as.vector(t(knot))
mx = buat_mx(X, knot, "gcv")
C = pinv(t(mx) %*% mx)
B = C %*% (t(mx) %*% y)
yhat = mx %*% B
SSE = sum((y - yhat)^2)
SSR = sum((yhat - mean(y))^2)
trA = sum((mx %*% C) * mx) # trace matriks hat
GCV[i] = (SSE / N) / (((N - trA) / N)^2)
Rsq[i] = SSR / (SSR + SSE) * 100
if (i %% 2000 == 0) cat(" selesai", i, "dari", nkomb, "\n")
}
dataAll = cbind(GCV = GCV, Rsq = Rsq, komb_ke = 1:nkomb, knotmat)
colnames(dataAll)[4:ncol(dataAll)] = nama.knot
file.out = paste0("dataAll_knot", k, "_v2.csv")
write.csv(dataAll, file = file.out)
dataG = dataAll[order(GCV), -2, drop = FALSE] # GCV, komb_ke, knot...
cat("\n==============================================\n")
cat("HASIL GCV terkecil dengan", k, "knot\n")
cat("==============================================\n")
print(dataG[1, ])
cat("\nNilai GCV 10 terkecil pertama\n")
print(dataG[1:min(10, nkomb), ])
# ---- estimasi parameter pada knot OPTIMAL ----
best = which.min(GCV)
knotopt = matrix(knotmat[best, ], nrow = k, byrow = TRUE,
dimnames = list(paste0("knot_", 1:k), paste0("x", 1:m)))
mxopt = buat_mx(X, knotopt, "gcv")
Bopt = pinv(t(mxopt) %*% mxopt) %*% t(mxopt) %*% y
rownames(Bopt) = colnames(mxopt)
cat("\nKombinasi knot optimal ke-", best, " GCV =", min(GCV), "\n")
print(knotopt)
cat("\n==============================================\n")
cat("HASIL ESTIMASI PARAMETER", k, "TITIK KNOT (OPTIMAL)\n")
cat("==============================================\n")
print(Bopt)
cat("\nFile knot tersimpan di:", file.out, "\n")
invisible(list(k = k, knotopt = knotopt, mingcv = min(GCV), B = Bopt, dataAll = dataAll))
}
# ============================================================
# BAGIAN C: UJI SIGNIFIKANSI SIMULTAN & PARSIAL (k = 1, 2, atau 3)
# ============================================================
uji_k = function(data, k = 2, alpha = 0.1)
{
data = as.matrix(data)
y = data[, 1]
X = data[, 2:ncol(data), drop = FALSE]
n = nrow(data); m = ncol(X)
# ambil knot dengan GCV minimum dari file hasil GCVk
file.knot = paste0("dataAll_knot", k, "_v2.csv")
knot_all = read.csv(file.knot, header = TRUE, row.names = 1)
best = which.min(knot_all$GCV)
knot = matrix(as.numeric(knot_all[best, 4:ncol(knot_all)]), nrow = k, byrow = TRUE,
dimnames = list(paste0("knot_", 1:k), paste0("x", 1:m)))
cat("\n>>> UJI SIGNIFIKANSI,", k, "KNOT\n")
cat("Kombinasi knot optimal ke-", best, " GCV =", knot_all$GCV[best], "\n")
print(knot)
cat("\n")
mx = buat_mx(X, knot, "uji")
B = pinv(t(mx) %*% mx) %*% t(mx) %*% y
p = nrow(B)
yhat = mx %*% B
ybar = mean(y)
res = y - yhat
SSE = sum(res^2)
SSR = sum((yhat - ybar)^2)
SST = sum((y - ybar)^2)
MSE = SSE / (n - p)
MSR = SSR / (p - 1)
Rsq = SSR / (SSR + SSE) * 100
# --- Uji simultan ---
Fhit = MSR / MSE
pvalue = pf(Fhit, p - 1, n - p, lower.tail = FALSE)
cat('---------------------------------------\n')
cat('Kesimpulan hasil uji simultan\n')
cat('---------------------------------------\n')
if (pvalue <= alpha) {
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan\n\n')
} else {
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan\n\n')
}
# --- Uji parsial ---
SE = sqrt(diag(MSE * pinv(t(mx) %*% mx)))
thit = B[, 1] / SE
pval = 2 * pt(abs(thit), n - p, lower.tail = FALSE)
cat('---------------------------------------------\n')
cat('Kesimpulan hasil uji parsial\n')
cat('---------------------------------------------\n')
for (i in 1:p)
{
if (pval[i] <= alpha)
cat('Parameter', i - 1, colnames(mx)[i], ': Tolak Ho, signifikan, pvalue =', pval[i], '\n') else
cat('Parameter', i - 1, colnames(mx)[i], ': Gagal tolak Ho, tidak signifikan, pvalue =', pval[i], '\n')
}
cat('=============================================\n')
cat('Estimasi parameter, t hitung, p-value\n')
cat('=============================================\n')
tab = cbind(Beta = B[, 1], SE = SE, t_hitung = thit, p_value = pval)
rownames(tab) = colnames(mx)
print(tab)
cat('\nAnalysis of Variance\n')
cat('=============================================\n')
cat('Sumber df SS MS Fhit\n')
cat('Regresi ', p - 1, ' ', SSR, ' ', MSR, ' ', Fhit, '\n')
cat('Error ', n - p, ' ', 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 = paste0('output_uji_residual_knot', k, '_v2.csv'))
write.csv(mx, file = paste0('output_uji_mx_knot', k, '_v2.csv'))
write.csv(yhat, file = paste0('output_uji_yhat_knot', k, '_v2.csv'))
invisible(list(k = k, B = B, tab = tab, Rsq = Rsq, MSE = MSE, pvalueF = pvalue, p = p))
}
# ============================================================
# BAGIAN D: JALANKAN 1, 2, 3 KNOT SEKALIGUS + PERBANDINGAN
# ============================================================
K_set = 1:3
alpha = 0.1
m = ncol(data) - 1
hasil = list()
uji = list()
for (k in K_set)
{
cat("\n\n############################################################\n")
cat("# ", k, "TITIK KNOT\n")
cat("############################################################\n")
hasil[[k]] = GCVk(data, k = k) # knot optimal + estimasi parameter
uji[[k]] = uji_k(data, k = k, alpha = alpha) # uji simultan & parsial
}##
##
## ############################################################
## # 1 TITIK KNOT
## ############################################################
##
## >>> Jumlah kombinasi knot (k = 1 ): 48
##
## ==============================================
## HASIL GCV terkecil dengan 1 knot
## ==============================================
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4
## 1.508187 45.000000 76.286735 14.630612 69.183673 75.922653
##
## Nilai GCV 10 terkecil pertama
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4
## [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
##
## Kombinasi knot optimal ke- 45 GCV = 1.508187
## x1 x2 x3 x4
## knot_1 76.28673 14.63061 69.18367 75.92265
##
## ==============================================
## HASIL ESTIMASI PARAMETER 1 TITIK KNOT (OPTIMAL)
## ==============================================
## [,1]
## b0 10.122393144
## x1 -0.200697922
## x2 0.762874047
## x3 -0.005244856
## x4 -0.017306261
## (x1-k1)+ 0.072850412
## (x2-k1)+ -21.843749933
## (x3-k1)+ 0.415138942
## (x4-k1)+ 1.053106627
##
## File knot tersimpan di: dataAll_knot1_v2.csv
##
## >>> UJI SIGNIFIKANSI, 1 KNOT
## Kombinasi knot optimal ke- 45 GCV = 1.508187
## x1 x2 x3 x4
## knot_1 76.28673 14.63061 69.18367 75.92265
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 b0 : Tolak Ho, signifikan, pvalue = 0.06500353
## Parameter 1 x1 : Tolak Ho, signifikan, pvalue = 2.835411e-05
## Parameter 2 (x1-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.9156743
## Parameter 3 x2 : Tolak Ho, signifikan, pvalue = 0.01250812
## Parameter 4 (x2-k1)+ : Tolak Ho, signifikan, pvalue = 1.020449e-05
## Parameter 5 x3 : Gagal tolak Ho, tidak signifikan, pvalue = 0.541134
## Parameter 6 (x3-k1)+ : Tolak Ho, signifikan, pvalue = 0.09644074
## Parameter 7 x4 : Gagal tolak Ho, tidak signifikan, pvalue = 0.1203336
## Parameter 8 (x4-k1)+ : Tolak Ho, signifikan, pvalue = 2.335269e-06
## =============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## b0 10.122393144 5.35720770 1.8894905 6.500353e-02
## x1 -0.200697922 0.04328026 -4.6371698 2.835411e-05
## (x1-k1)+ 0.072850412 0.68432960 0.1064552 9.156743e-01
## x2 0.762874047 0.29372705 2.5972210 1.250812e-02
## (x2-k1)+ -21.843749933 4.41930754 -4.9427992 1.020449e-05
## x3 -0.005244856 0.00852003 -0.6155913 5.411340e-01
## (x3-k1)+ 0.415138942 0.24472964 1.6963165 9.644074e-02
## x4 -0.017306261 0.01093879 -1.5820999 1.203336e-01
## (x4-k1)+ 1.053106627 0.19589216 5.3759508 2.335269e-06
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 8 167.6864 20.9608 16.55933
## Error 47 59.49258 1.2658
## Total 55 227.1789
## =============================================
## s = 1.125078 Rsq = 73.81246
## pvalue(F) = 2.451288e-11
##
##
## ############################################################
## # 2 TITIK KNOT
## ############################################################
##
## >>> Jumlah kombinasi knot (k = 2 ): 1128
##
## ==============================================
## HASIL GCV terkecil dengan 2 knot
## ==============================================
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k2_x1
## 1.316068 135.000000 61.132449 11.382041 7.692245 25.025510 76.286735
## k2_x2 k2_x3 k2_x4
## 14.630612 69.183673 75.922653
##
## Nilai GCV 10 terkecil pertama
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k2_x1 k2_x2
## [1,] 1.316068 135 61.13245 11.38204 7.692245 25.02551 76.28673 14.63061
## [2,] 1.317894 179 61.49327 11.45939 9.156327 26.23735 76.28673 14.63061
## [3,] 1.321114 178 61.49327 11.45939 9.156327 26.23735 75.92592 14.55327
## [4,] 1.321402 134 61.13245 11.38204 7.692245 25.02551 75.92592 14.55327
## [5,] 1.358738 221 61.85408 11.53673 10.620408 27.44918 75.92592 14.55327
## [6,] 1.359630 222 61.85408 11.53673 10.620408 27.44918 76.28673 14.63061
## [7,] 1.359989 138 61.13245 11.38204 7.692245 25.02551 77.36918 14.86265
## [8,] 1.388799 136 61.13245 11.38204 7.692245 25.02551 76.64755 14.70796
## [9,] 1.393180 180 61.49327 11.45939 9.156327 26.23735 76.64755 14.70796
## [10,] 1.396087 177 61.49327 11.45939 9.156327 26.23735 75.56510 14.47592
## k2_x3 k2_x4
## [1,] 69.18367 75.92265
## [2,] 69.18367 75.92265
## [3,] 67.71959 74.71082
## [4,] 67.71959 74.71082
## [5,] 67.71959 74.71082
## [6,] 69.18367 75.92265
## [7,] 73.57592 79.55816
## [8,] 70.64776 77.13449
## [9,] 70.64776 77.13449
## [10,] 66.25551 73.49898
##
## Kombinasi knot optimal ke- 135 GCV = 1.316068
## x1 x2 x3 x4
## knot_1 61.13245 11.38204 7.692245 25.02551
## knot_2 76.28673 14.63061 69.183673 75.92265
##
## ==============================================
## HASIL ESTIMASI PARAMETER 2 TITIK KNOT (OPTIMAL)
## ==============================================
## [,1]
## b0 95.3587177
## x1 -2.9213119
## x2 6.1469387
## x3 0.2059982
## x4 0.7283636
## (x1-k1)+ 2.7449916
## (x2-k1)+ -5.3197766
## (x3-k1)+ -0.2144538
## (x4-k1)+ -0.7619877
## (x1-k2)+ 0.7954129
## (x2-k2)+ -18.0705567
## (x3-k2)+ 0.2853691
## (x4-k2)+ 0.9034632
##
## File knot tersimpan di: dataAll_knot2_v2.csv
##
## >>> UJI SIGNIFIKANSI, 2 KNOT
## Kombinasi knot optimal ke- 135 GCV = 1.316068
## x1 x2 x3 x4
## knot_1 61.13245 11.38204 7.692245 25.02551
## knot_2 76.28673 14.63061 69.183673 75.92265
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 b0 : Gagal tolak Ho, tidak signifikan, pvalue = 0.2671925
## Parameter 1 x1 : Tolak Ho, signifikan, pvalue = 0.007544198
## Parameter 2 (x1-k1)+ : Tolak Ho, signifikan, pvalue = 0.01250391
## Parameter 3 (x1-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3045796
## Parameter 4 x2 : Gagal tolak Ho, tidak signifikan, pvalue = 0.2127214
## Parameter 5 (x2-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2845971
## Parameter 6 (x2-k2)+ : Tolak Ho, signifikan, pvalue = 0.0001058266
## Parameter 7 x3 : Gagal tolak Ho, tidak signifikan, pvalue = 0.2122837
## Parameter 8 (x3-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2057346
## Parameter 9 (x3-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2224808
## Parameter 10 x4 : Tolak Ho, signifikan, pvalue = 0.05283963
## Parameter 11 (x4-k1)+ : Tolak Ho, signifikan, pvalue = 0.0465475
## Parameter 12 (x4-k2)+ : Tolak Ho, signifikan, pvalue = 2.97441e-05
## =============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## b0 95.3587180 84.8285642 1.124135 0.2671924572
## x1 -2.9213119 1.0418249 -2.804034 0.0075441984
## (x1-k1)+ 2.7449916 1.0529268 2.607011 0.0125039144
## (x1-k2)+ 0.7954129 0.7655043 1.039070 0.3045796349
## x2 6.1469387 4.8596443 1.264895 0.2127214060
## (x2-k1)+ -5.3197766 4.9095217 -1.083563 0.2845971101
## (x2-k2)+ -18.0705567 4.2319010 -4.270080 0.0001058266
## x3 0.2059982 0.1626993 1.266128 0.2122837024
## (x3-k1)+ -0.2144538 0.1669140 -1.284816 0.2057346472
## (x3-k2)+ 0.2853691 0.2305324 1.237870 0.2224808174
## x4 0.7283636 0.3657962 1.991173 0.0528396322
## (x4-k1)+ -0.7619877 0.3717972 -2.049471 0.0465474966
## (x4-k2)+ 0.9034632 0.1935247 4.668464 0.0000297441
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 12 183.7252 15.31043 15.15057
## Error 43 43.45373 1.010552
## Total 55 227.1789
## =============================================
## s = 1.005262 Rsq = 80.87246
## pvalue(F) = 9.568368e-12
##
##
## ############################################################
## # 3 TITIK KNOT
## ############################################################
##
## >>> Jumlah kombinasi knot (k = 3 ): 17296
## selesai 2000 dari 17296
## selesai 4000 dari 17296
## selesai 6000 dari 17296
## selesai 8000 dari 17296
## selesai 10000 dari 17296
## selesai 12000 dari 17296
## selesai 14000 dari 17296
## selesai 16000 dari 17296
##
## ==============================================
## HASIL GCV terkecil dengan 3 knot
## ==============================================
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4
## 1.444246 2200.000000 61.132449 11.382041 7.692245 25.025510
## k2_x1 k2_x2 k2_x3 k2_x4 k3_x1 k3_x2
## 61.854082 11.536735 10.620408 27.449184 76.286735 14.630612
## k3_x3 k3_x4
## 69.183673 75.922653
##
## Nilai GCV 10 terkecil pertama
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k2_x1 k2_x2
## [1,] 1.444246 2200 61.13245 11.38204 7.692245 25.02551 61.85408 11.53673
## [2,] 1.445793 3146 61.49327 11.45939 9.156327 26.23735 61.85408 11.53673
## [3,] 1.447104 2157 61.13245 11.38204 7.692245 25.02551 61.49327 11.45939
## [4,] 1.452451 3106 61.13245 11.38204 7.692245 25.02551 77.00837 14.78531
## [5,] 1.453903 2199 61.13245 11.38204 7.692245 25.02551 61.85408 11.53673
## [6,] 1.454858 3145 61.49327 11.45939 9.156327 26.23735 61.85408 11.53673
## [7,] 1.458180 2156 61.13245 11.38204 7.692245 25.02551 61.49327 11.45939
## [8,] 1.458931 2242 61.13245 11.38204 7.692245 25.02551 62.21490 11.61408
## [9,] 1.464584 3037 61.13245 11.38204 7.692245 25.02551 73.03939 13.93449
## [10,] 1.465580 3101 61.13245 11.38204 7.692245 25.02551 76.28673 14.63061
## k2_x3 k2_x4 k3_x1 k3_x2 k3_x3 k3_x4
## [1,] 10.620408 27.44918 76.28673 14.63061 69.18367 75.92265
## [2,] 10.620408 27.44918 76.28673 14.63061 69.18367 75.92265
## [3,] 9.156327 26.23735 76.28673 14.63061 69.18367 75.92265
## [4,] 72.111837 78.34633 77.36918 14.86265 73.57592 79.55816
## [5,] 10.620408 27.44918 75.92592 14.55327 67.71959 74.71082
## [6,] 10.620408 27.44918 75.92592 14.55327 67.71959 74.71082
## [7,] 9.156327 26.23735 75.92592 14.55327 67.71959 74.71082
## [8,] 12.084490 28.66102 76.28673 14.63061 69.18367 75.92265
## [9,] 56.006939 65.01612 76.28673 14.63061 69.18367 75.92265
## [10,] 69.183673 75.92265 76.64755 14.70796 70.64776 77.13449
##
## Kombinasi knot optimal ke- 2200 GCV = 1.444246
## x1 x2 x3 x4
## knot_1 61.13245 11.38204 7.692245 25.02551
## knot_2 61.85408 11.53673 10.620408 27.44918
## knot_3 76.28673 14.63061 69.183673 75.92265
##
## ==============================================
## HASIL ESTIMASI PARAMETER 3 TITIK KNOT (OPTIMAL)
## ==============================================
## [,1]
## b0 -4.87954771
## x1 -0.57070096
## x2 1.29861829
## x3 0.20162854
## x4 1.23897093
## (x1-k1)+ -2.60712938
## (x2-k1)+ 13.80910089
## (x3-k1)+ -0.22960609
## (x4-k1)+ -1.94377922
## (x1-k2)+ 3.03208075
## (x2-k2)+ -14.12188190
## (x3-k2)+ 0.02361872
## (x4-k2)+ 0.67438515
## (x1-k3)+ 0.76491110
## (x2-k3)+ -19.59971920
## (x3-k3)+ 0.25980650
## (x4-k3)+ 0.92445503
##
## File knot tersimpan di: dataAll_knot3_v2.csv
##
## >>> UJI SIGNIFIKANSI, 3 KNOT
## Kombinasi knot optimal ke- 2200 GCV = 1.444246
## x1 x2 x3 x4
## knot_1 61.13245 11.38204 7.692245 25.02551
## knot_2 61.85408 11.53673 10.620408 27.44918
## knot_3 76.28673 14.63061 69.183673 75.92265
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 b0 : Gagal tolak Ho, tidak signifikan, pvalue = 0.6691134
## Parameter 1 x1 : Gagal tolak Ho, tidak signifikan, pvalue = 0.8101606
## Parameter 2 (x1-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.5935914
## Parameter 3 (x1-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2569091
## Parameter 4 (x1-k3)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3875066
## Parameter 5 x2 : Gagal tolak Ho, tidak signifikan, pvalue = 0.9145372
## Parameter 6 (x2-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.6780688
## Parameter 7 (x2-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.5260547
## Parameter 8 (x2-k3)+ : Tolak Ho, signifikan, pvalue = 0.0001404269
## Parameter 9 x3 : Gagal tolak Ho, tidak signifikan, pvalue = 0.5340848
## Parameter 10 (x3-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.7141141
## Parameter 11 (x3-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.942884
## Parameter 12 (x3-k3)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2870221
## Parameter 13 x4 : Tolak Ho, signifikan, pvalue = 0.09910266
## Parameter 14 (x4-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.1848397
## Parameter 15 (x4-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3857466
## Parameter 16 (x4-k3)+ : Tolak Ho, signifikan, pvalue = 4.564589e-05
## =============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## b0 -4.87954767 11.3313796 -0.43062256 6.691134e-01
## x1 -0.57070097 2.3596928 -0.24185393 8.101606e-01
## (x1-k1)+ -2.60712937 4.8454015 -0.53806261 5.935914e-01
## (x1-k2)+ 3.03208075 2.6352515 1.15058497 2.569091e-01
## (x1-k3)+ 0.76491110 0.8752551 0.87392932 3.875066e-01
## x2 1.29861830 12.0225195 0.10801549 9.145372e-01
## (x2-k1)+ 13.80910084 33.0174968 0.41823585 6.780688e-01
## (x2-k2)+ -14.12188187 22.0729359 -0.63978267 5.260547e-01
## (x2-k3)+ -19.59971920 4.6428330 -4.22149996 1.404269e-04
## x3 0.20162854 0.3213964 0.62735156 5.340848e-01
## (x3-k1)+ -0.22960609 0.6222171 -0.36901280 7.141141e-01
## (x3-k2)+ 0.02361872 0.3275433 0.07210868 9.428840e-01
## (x3-k3)+ 0.25980650 0.2406862 1.07944073 2.870221e-01
## x4 1.23897093 0.7333330 1.68950652 9.910266e-02
## (x4-k1)+ -1.94377922 1.4399711 -1.34987380 1.848397e-01
## (x4-k2)+ 0.67438515 0.7687876 0.87720604 3.857466e-01
## (x4-k3)+ 0.92445502 0.2015338 4.58709688 4.564589e-05
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 16 185.9148 11.61967 10.9821
## Error 39 41.26416 1.058056
## Total 55 227.1789
## =============================================
## s = 1.028618 Rsq = 81.83627
## pvalue(F) = 7.291165e-10# ---- Tabel perbandingan 1, 2, 3 knot ----
perbandingan = data.frame(
Knot = K_set,
Kombinasi = sapply(K_set, function(k) choose(48, k)),
Parameter = sapply(K_set, function(k) uji[[k]]$p),
GCV_min = sapply(K_set, function(k) hasil[[k]]$mingcv),
MSE = sapply(K_set, function(k) uji[[k]]$MSE),
Rsq = sapply(K_set, function(k) uji[[k]]$Rsq),
pvalue_F = sapply(K_set, function(k) uji[[k]]$pvalueF)
)
cat("\n\n==============================================\n")##
##
## ==============================================cat("PERBANDINGAN MODEL 1, 2, 3 TITIK KNOT\n")## PERBANDINGAN MODEL 1, 2, 3 TITIK KNOTcat("==============================================\n")## ==============================================print(perbandingan)## Knot Kombinasi Parameter GCV_min MSE Rsq pvalue_F
## 1 1 48 9 1.508187 1.265800 73.81246 2.451288e-11
## 2 2 1128 13 1.316068 1.010552 80.87246 9.568368e-12
## 3 3 17296 17 1.444246 1.058056 81.83627 7.291165e-10cat("\nModel terbaik (GCV minimum): knot =",
perbandingan$Knot[which.min(perbandingan$GCV_min)], "\n")##
## Model terbaik (GCV minimum): knot = 2write.csv(perbandingan, file = "perbandingan_knot_1_2_3.csv", row.names = FALSE)R Markdown
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