Syntax Project
Cindy Indriyani
2024-04-22
library(readxl)
df <- read_excel("C:/Users/DEVINA/OneDrive/DOKUMEN EJA/ANREG/PROJECT ANREG/DATA PROJEK 2021.xlsx")
df## # A tibble: 27 × 12
## Y `Nama Kab/Kota` X1 X2 X3 X4 X5 X6 X7 X8 X9
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 16821 KABUPATEN BOGOR 2585 1.3 53.0 59040 4.22e6 573352 62.4 74.4 87.5
## 2 6543 KABUPATEN SUKA… 1650 4.9 82.3 32883 3.13e6 362219 57.7 99.7 100
## 3 5146 KABUPATEN CIAN… 2929 2.4 87.2 35113 2.53e6 442503 57.3 92.9 100
## 4 9596 KABUPATEN BAND… 4238 2.3 95.4 40368 3.24e6 367264 65.5 90.3 74.6
## 5 5150 KABUPATEN GARUT 4194 3 89.1 19828 1.96e6 282908 58.5 96.6 81.5
## 6 4606 KABUPATEN TASI… 1641 4.2 90.5 6815 2.25e6 206987 59.8 79.3 84.6
## 7 1977 KABUPATEN CIAM… 1515 4 93.8 6602 1.88e6 96743 65.8 85.5 95.4
## 8 2461 KABUPATEN KUNI… 1346 5.5 77 11602 1.88e6 187029 60.0 90.1 80.3
## 9 7876 KABUPATEN CIRE… 1791 3.6 81.4 23029 2.27e6 189083 57.8 91.3 23.9
## 10 2471 KABUPATEN MAJA… 716 3.8 92.9 15717 2.01e6 211474 58.3 88.8 53.8
## # ℹ 17 more rows
## # ℹ 1 more variable: X10 <dbl>data.projek <- df
data.projek## # A tibble: 27 × 12
## Y `Nama Kab/Kota` X1 X2 X3 X4 X5 X6 X7 X8 X9
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 16821 KABUPATEN BOGOR 2585 1.3 53.0 59040 4.22e6 573352 62.4 74.4 87.5
## 2 6543 KABUPATEN SUKA… 1650 4.9 82.3 32883 3.13e6 362219 57.7 99.7 100
## 3 5146 KABUPATEN CIAN… 2929 2.4 87.2 35113 2.53e6 442503 57.3 92.9 100
## 4 9596 KABUPATEN BAND… 4238 2.3 95.4 40368 3.24e6 367264 65.5 90.3 74.6
## 5 5150 KABUPATEN GARUT 4194 3 89.1 19828 1.96e6 282908 58.5 96.6 81.5
## 6 4606 KABUPATEN TASI… 1641 4.2 90.5 6815 2.25e6 206987 59.8 79.3 84.6
## 7 1977 KABUPATEN CIAM… 1515 4 93.8 6602 1.88e6 96743 65.8 85.5 95.4
## 8 2461 KABUPATEN KUNI… 1346 5.5 77 11602 1.88e6 187029 60.0 90.1 80.3
## 9 7876 KABUPATEN CIRE… 1791 3.6 81.4 23029 2.27e6 189083 57.8 91.3 23.9
## 10 2471 KABUPATEN MAJA… 716 3.8 92.9 15717 2.01e6 211474 58.3 88.8 53.8
## # ℹ 17 more rows
## # ℹ 1 more variable: X10 <dbl>Eksplorasi Data Matriks Korelasi Data
model <- lm(Y ~ X1+X2+X3+X4+X5+X6+X7+X8+X9+X10 ,data= data.projek)
library(corrplot)## corrplot 0.92 loadedcor_mat <- cor(model$model[, -1])
corrplot(cor_mat, method = 'number')
Box Plot
par(mfrow=c(1,3))
boxplot(data.projek$Y,
ylab = "Jumlah Balita Kurang Gizi",
main = "Boxplot Jumlah Balita Kurang Gizi di Jawa Barat 2021", col="light blue")
boxplot(data.projek$X1,
ylab = "Jumlah Posyandu Aktif (unit)",
main = "Boxplot Jumlah Posyandu Aktif", col="light blue")
boxplot(data.projek$X2,
ylab = "BBLR (%)",
main = "Boxplot BBLR", col="light blue")
boxplot(data.projek$X3,
ylab = "Inisiasi Menyusui Dini (%)",
main = "Boxplot Inisiasi Menyusui Dini", col="light blue")
boxplot(data.projek$X4,
ylab = "Bayi Penerima ASI Eksklusif (orang)",
main = "Boxplot Bayi Penerima ASI Eksklusif", col="light blue")
boxplot(data.projek$X5,
ylab = "Upah Minimum (Rp)",
main = "Boxplot Upah Minimum", col="light blue")
boxplot(data.projek$X6,
ylab = "Perilaku Hidup Bersih",
main = "Boxplot Perilaku Hidup Bersih", col="light blue")
boxplot(data.projek$X7,
ylab = "Indeks Pendidikan",
main = "Boxplot Indeks Pendidikan", col="light blue")
boxplot(data.projek$X8,
ylab = "Sanitasi Layak (%)",
main = "Boxplot Sanitasi Layak", col="light blue")
boxplot(data.projek$X9,
ylab = "Air Minum Memenuhi Syarat (%)",
main = "Boxplot Air Minum Memenuhi SYarat", col="light blue")
boxplot(data.projek$X10,
ylab = "TPM Memenuhi Syarat (%)",
main = "Tempat Pengelolaan Makanan Memnuhi SYarat", col="light blue")
dataprojek <- read_xlsx("C:\\Users\\DEVINA\\OneDrive\\DOKUMEN EJA\\ANREG\\PROJECT ANREG\\DATA PROJEK 2021.xlsx", sheet = "Lembar2")
dataprojek## # A tibble: 27 × 11
## Y X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 16821 2585 1.3 53.0 59040 4217206 573352 62.4 74.4 87.5 23.8
## 2 6543 1650 4.9 82.3 32883 3125445. 362219 57.7 99.7 100 39.6
## 3 5146 2929 2.4 87.2 35113 2534799. 442503 57.3 92.9 100 60.3
## 4 9596 4238 2.3 95.4 40368 3241930. 367264 65.5 90.3 74.6 30.5
## 5 5150 4194 3 89.1 19828 1961086. 282908 58.5 96.6 81.5 55.1
## 6 4606 1641 4.2 90.5 6815 2251788. 206987 59.8 79.3 84.6 38.0
## 7 1977 1515 4 93.8 6602 1880655. 96743 65.8 85.5 95.4 55.6
## 8 2461 1346 5.5 77 11602 1882642. 187029 60.0 90.1 80.3 77
## 9 7876 1791 3.6 81.4 23029 2269557. 189083 57.8 91.3 23.9 62.8
## 10 2471 716 3.8 92.9 15717 2009000 211474 58.3 88.8 53.8 62.1
## # ℹ 17 more rowslibrary(GGally)## Loading required package: ggplot2## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggpairs(dataprojek)
Model Regresi Awal
model <- lm(Y ~ X1+X2+X3+X4+X5+X6+X7+X8+X9+X10 ,data= data.projek)
model##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 +
## X10, data = data.projek)
##
## Coefficients:
## (Intercept) X1 X2 X3 X4 X5
## 5.334e+03 7.590e-01 -3.143e+01 -8.180e+01 1.624e-01 3.793e-04
## X6 X7 X8 X9 X10
## -1.763e-03 3.973e+01 9.542e+00 -4.724e-01 -3.182e+01summary(model)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 +
## X10, data = data.projek)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2281.4 -959.2 -433.6 856.5 3151.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.334e+03 5.945e+03 0.897 0.38291
## X1 7.590e-01 5.770e-01 1.315 0.20696
## X2 -3.143e+01 1.235e+02 -0.255 0.80230
## X3 -8.180e+01 5.439e+01 -1.504 0.15210
## X4 1.624e-01 5.338e-02 3.042 0.00777 **
## X5 3.793e-04 6.079e-04 0.624 0.54142
## X6 -1.763e-03 4.790e-03 -0.368 0.71768
## X7 3.973e+01 8.138e+01 0.488 0.63207
## X8 9.542e+00 3.471e+01 0.275 0.78692
## X9 -4.724e-01 2.115e+01 -0.022 0.98246
## X10 -3.182e+01 2.450e+01 -1.299 0.21240
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1871 on 16 degrees of freedom
## Multiple R-squared: 0.8296, Adjusted R-squared: 0.7232
## F-statistic: 7.792 on 10 and 16 DF, p-value: 0.0001825Eksplorasi Data -> masih error peubah y nya ga bisa masuk
library(corrplot)
cor_mat <- cor(model$model[, -1])
corrplot(cor_mat, method = 'number')
Pemeriksaan Multikolinieritas
library(car)## Loading required package: carDatavif(model)## X1 X2 X3 X4 X5 X6 X7 X8
## 2.773863 1.584947 1.794022 3.982359 2.810331 4.149471 2.290315 1.515883
## X9 X10
## 1.636167 1.354969multikolinieritas terjadi saat VIF > 10. Dalam kasus ini, tidak ada multikolinieritas antarvariabel. Oleh karena itu, dapat dilanjutkan ke tahap analisis berikutnya.
Regresi Klasik Regresi klasik tanpa peubah X4 dan X6
model2 <- lm(Y ~ X1+X2+X3+X5+X7+X8+X9+X10 ,data= data.projek)
model2##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X5 + X7 + X8 + X9 + X10, data = data.projek)
##
## Coefficients:
## (Intercept) X1 X2 X3 X5 X7
## 1.055e+04 2.049e+00 -7.167e+00 -1.619e+02 6.523e-04 4.022e+01
## X8 X9 X10
## 1.530e+01 -5.979e+00 -2.114e+01summary(model2)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X5 + X7 + X8 + X9 + X10, data = data.projek)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3284.3 -1324.2 -330.3 1554.2 4180.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.055e+04 7.150e+03 1.476 0.15720
## X1 2.049e+00 5.582e-01 3.671 0.00175 **
## X2 -7.167e+00 1.544e+02 -0.046 0.96349
## X3 -1.619e+02 6.079e+01 -2.664 0.01581 *
## X5 6.523e-04 6.296e-04 1.036 0.31388
## X7 4.022e+01 9.005e+01 0.447 0.66050
## X8 1.530e+01 4.352e+01 0.352 0.72925
## X9 -5.979e+00 2.569e+01 -0.233 0.81862
## X10 -2.114e+01 3.046e+01 -0.694 0.49657
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2354 on 18 degrees of freedom
## Multiple R-squared: 0.6968, Adjusted R-squared: 0.5621
## F-statistic: 5.172 on 8 and 18 DF, p-value: 0.001837Regresi Gulud (Ridge) Korelasi terkuat ada di peubah X4 dan X6, jadi kita coba ilangin kedua peubah itu terus pake regresi gulud (ridge)
library(glmnet)## Loading required package: Matrix## Loaded glmnet 4.1-8library(lmridge)##
## Attaching package: 'lmridge'## The following object is masked from 'package:car':
##
## viflapply(c("glmnet","lmridge"),library,character.only=T)[[1]]## [1] "lmridge" "glmnet" "Matrix" "car" "carData" "GGally"
## [7] "ggplot2" "corrplot" "readxl" "stats" "graphics" "grDevices"
## [13] "utils" "datasets" "methods" "base"Y <- data.projek$Y
X1 <- data.projek$X1
X2 <- data.projek$X2
X3 <- data.projek$X3
X4 <- data.projek$X4
X5 <- data.projek$X5
X6 <- data.projek$X6
X7 <- data.projek$X7
X8 <- data.projek$X8
X9 <- data.projek$X9
X10 <- data.projek$X10
x <- cbind(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10)
y <- data.projek$Ycv.r <- cv.glmnet(x,y,alpha=0);plot(cv.r)## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
Best Model
best.lr <- cv.r$lambda.min
bestridge <- glmnet(x,y,alpha=0,lambda=best.lr);coef(bestridge)## 11 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 6.916611e+03
## X1 6.477050e-01
## X2 -4.212534e+01
## X3 -7.035041e+01
## X4 8.206597e-02
## X5 2.754074e-04
## X6 2.534253e-03
## X7 1.184373e+01
## X8 2.552332e+00
## X9 3.587638e+00
## X10 -2.678597e+01Fungsi R square
rsq <- function(bestmodel,bestlambda,x,y) {
# y duga
y.duga <- predict(bestmodel, s = bestlambda, newx = x)
#JKG dan JKT
jkt <- sum((y-mean(y))^2)
jkg <- sum((y.duga-y)^2)
#find R-Squared
rsq <- 1-jkg/jkt
return(rsq)
}Rsquare Ridge
rsq(bestridge,best.lr,x,y)## [1] 0.7732472Regresi Lasso
cv.l <- cv.glmnet(x,y,alpha=1);plot(cv.l)## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
best.ll <- cv.l$lambda.min
bestlasso <- glmnet(x,y,alpha=1,lambda=best.ll);coef(bestlasso)## 11 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 6.403101e+03
## X1 4.213773e-01
## X2 .
## X3 -5.154793e+01
## X4 1.516273e-01
## X5 2.390044e-04
## X6 .
## X7 .
## X8 .
## X9 .
## X10 -2.590867e+01MOdel yang kosong dikeluarkan sepenuhnya karena tidak cukup berpengaruh
rsq(bestlasso,best.ll ,x,y)## [1] 0.8026896Regresi Ridge (lmridge)
lmr <- lmridge(y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10,data=data.projek,scaling="centered")
plot(lmr)
summary(lmr)##
## Call:
## lmridge.default(formula = y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 +
## X8 + X9 + X10, data = data.projek, scaling = "centered")
##
##
## Coefficients: for Ridge parameter K= 0
## Estimate Estimate (Sc) StdErr (Sc) t-value (Sc) Pr(>|t|)
## Intercept 5333.9841 5333.9841 8019.0705 0.6652 0.5154
## X1 0.7590 0.7590 0.5598 1.3557 0.1940
## X2 -31.4330 -31.4330 119.7921 -0.2624 0.7964
## X3 -81.7988 -81.7988 52.7681 -1.5502 0.1407
## X4 0.1624 0.1624 0.0518 3.1352 0.0064 **
## X5 0.0004 0.0004 0.0006 0.6432 0.5292
## X6 -0.0018 -0.0018 0.0046 -0.3793 0.7094
## X7 39.7266 39.7266 78.9519 0.5032 0.6217
## X8 9.5423 9.5423 33.6762 0.2834 0.7805
## X9 -0.4724 -0.4724 20.5217 -0.0230 0.9819
## X10 -31.8211 -31.8211 23.7676 -1.3388 0.1993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Ridge Summary
## R2 adj-R2 DF ridge F AIC BIC
## 0.829600 0.739500 10.000010 8.279126 412.729254 514.675231
## Ridge minimum MSE= 25488.47 at K= 0
## P-value for F-test ( 10.00001 , 17 ) = 9.04721e-05
## -------------------------------------------------------------------summary(model2)$r.squared## [1] 0.6968431rsq(bestridge,best.lr,x,y)## [1] 0.7732472rsq(bestlasso,best.ll ,x,y)## [1] 0.8026896summary(model2)$sigma## [1] 2353.544# Prediksi model ridge pada data pelatihan
train_predictionsridge <- predict(bestridge,newx = x)
# Hitung residu (selisih antara prediksi dan nilai sebenarnya)
residualsridge <- y - train_predictionsridge
# Hitung varian residu
dfridge <- length(y) - length(bestridge$beta)
residual_varianceridge <- sum(residualsridge^2) / dfridge
# Hitung RSE
rseridge <- sqrt(residual_varianceridge)
# Tampilkan hasil RSE
print(paste("Residual Standard Error (RSE):",rseridge))## [1] "Residual Standard Error (RSE): 2094.48207564246"# Prediksi model Lasso pada data pelatihan
train_predictionsLasso <- predict(bestlasso,newx = x)
# Hitung residu (selisih antara prediksi dan nilai sebenarnya)
residualsLasso <- y - train_predictionsLasso
# Hitung varian residu
dfLasso <- length(y) - length(bestlasso$beta)
residual_varianceLasso <- sum(residualsLasso^2) / dfLasso
# Hitung RSE
rseLasso <- sqrt(residual_varianceLasso)
# Tampilkan hasil RSE
print(paste("Residual Standard Error (RSE):",rseLasso))## [1] "Residual Standard Error (RSE): 1953.77805136955"Model Regresi Lasso memiliki R-Square paling besar dan RSE paling kecil. Jadi, model terbaik adalah Model Regresi Lasso (x1,x3,x4,x5,x10). Tapi x1,x4,x5 ga sesuai hiks
Pemeriksaan 𝜀(𝑖~𝑁)
Plot antara sisaan dan peluang normal Plot quantil quantil Pemeriksaan 𝐸[𝜀𝑖] = 0
Plot sisaan dan Y duga Plot sisaan dan X (Regresi linear sederhana)
plot(model,1) 
plot sisaan vs urutan sisaan saling bebas
plot(x = 1:dim(data.projek)[1],
y = model$residuals,
type = 'b',
ylab = "Residuals",
xlab = "Observation")
Eksplorasi Normalitas Sisaan - qq-plot sisaan menyebar normal
plot(model,2)
Uji Formal Kondisi Gauss-Markov p-value < 0.05 tolak h0
1 Nilai harapan sisaan sama dengan nol
t.test(model$residuals,mu = 0,conf.level = 0.95)##
## One Sample t-test
##
## data: model$residuals
## t = -1.043e-16, df = 26, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -580.7084 580.7084
## sample estimates:
## mean of x
## -2.946614e-142 Ragam sisaan homogen
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericbptest(model)##
## studentized Breusch-Pagan test
##
## data: model
## BP = 7.2485, df = 10, p-value = 0.7018library(car)ncvTest(model)## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.1938274, Df = 1, p = 0.659753 Sisaan saling bebas
library(randtests)
runs.test(model$residuals)##
## Runs Test
##
## data: model$residuals
## statistic = 0.40032, runs = 15, n1 = 13, n2 = 13, n = 26, p-value =
## 0.6889
## alternative hypothesis: nonrandomnesslibrary(lmtest)
dwtest(model)##
## Durbin-Watson test
##
## data: model
## DW = 2.1037, p-value = 0.244
## alternative hypothesis: true autocorrelation is greater than 0Uji Formal Normalitas Sisaan
ks.test(model$residuals, "pnorm", mean=mean(model$residuals), sd=sd(model$residuals))##
## Exact one-sample Kolmogorov-Smirnov test
##
## data: model$residuals
## D = 0.13468, p-value = 0.6624
## alternative hypothesis: two-sidedlibrary(car)
shapiro.test(model$residuals)##
## Shapiro-Wilk normality test
##
## data: model$residuals
## W = 0.93972, p-value = 0.1199H0: miu = 0
Interpretasi : p-value > \(\alpha\), maka tak Tolak H0, nilai harapan sisaan sama dengan nol.
H0: Saling bebas
Interpretasi : p-value > \(\alpha\), tak tolak H0, maka sisaan saling bebas.
H0: homogen
Interpretasi : p-value > \(\alpha\), maka tak tolak H0. Ragam sisaan homogen.
H0: Menyebar normal
Interpratsi : p-value > \(\alpha\), maka tak tolak Ho. Sisaan menyebar normal.
Pemeriksaan Amatan Berpengaruh Tabel hii, ri, Di
s <- sqrt(anova(model)["Residuals", "Mean Sq"])
n = dim(data.projek)[1]
p = length(model$coefficients)
hii=hatvalues(model)
Obs = c(1:n)
ei = model$residuals
ri = ei/(s*sqrt(1-hii))
Di = (ri^2/p)*(hii/(1-hii))
summ <- cbind.data.frame(Obs, data.projek, hii, ri, Di)Pendeteksian Titik Laverage
for (i in 1:dim(summ)[1]){
cutoff <- 2*p/n
titik_leverage <- which(hii > cutoff)
}
titik_leverage## 15 27
## 15 27summ_leverage <- subset(summ, Obs %in% titik_leverage)
summ_leverage <- subset(summ, Obs %in% titik_leverage, select = c("Obs","Nama Kab/Kota", "hii", "ri", "Di"))
summ_leverage## Obs Nama Kab/Kota hii ri Di
## 15 15 KABUPATEN KARAWANG 0.8151566 -1.9185287 1.475642
## 27 27 KOTA BANJAR 0.9630320 0.3837571 0.348767library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionsumm_leverage_sorted <- summ_leverage %>%
arrange(desc(hii))
summ_leverage_sorted## Obs Nama Kab/Kota hii ri Di
## 27 27 KOTA BANJAR 0.9630320 0.3837571 0.348767
## 15 15 KABUPATEN KARAWANG 0.8151566 -1.9185287 1.475642Pendeteksian Pencilan
for (i in 1:dim(summ)[1]){
absri <- abs(summ$ri)
pencilan <- which(absri > 2)
}
pencilan## [1] 16summ_pencilan <- subset(summ, Obs %in% pencilan)
summ_pencilan <- subset(summ, Obs %in% pencilan, select = c("Obs","Nama Kab/Kota", "hii", "ri", "Di"))
summ_pencilan## Obs Nama Kab/Kota hii ri Di
## 16 16 KABUPATEN BEKASI 0.4945943 2.369059 0.4993073library(dplyr)
summ_pencilan_sorted <- summ_pencilan %>%
arrange(desc(hii))
summ_pencilan_sorted## Obs Nama Kab/Kota hii ri Di
## 16 16 KABUPATEN BEKASI 0.4945943 2.369059 0.4993073Pendeteksian Amatan Berpengaruh (Jarak COOK)
for (i in 1:dim(summ)[1]){
fcrit = qf(p=0.95, df1=p, df2=n-p)
amatan_berpengaruh <- which(Di > fcrit)
}
amatan_berpengaruh## named integer(0)summ_sorted <- summ %>%
arrange(desc(Di))
summ_sorted## Obs Y Nama Kab/Kota X1 X2 X3 X4 X5 X6
## 15 15 2914 KABUPATEN KARAWANG 1595 2.8 78.47 13938 4798312 326480
## 1 1 16821 KABUPATEN BOGOR 2585 1.3 52.95 59040 4217206 573352
## 16 16 7548 KABUPATEN BEKASI 1752 0.5 88.85 17141 4791844 554077
## 27 27 727 KOTA BANJAR 200 21.0 84.59 1826 1831885 46517
## 9 9 7876 KABUPATEN CIREBON 1791 3.6 81.43 23029 2269557 189083
## 12 12 5973 KABUPATEN INDRAMAYU 1985 3.4 85.94 3656 2373073 45951
## 14 14 1228 KABUPATEN PURWAKARTA 704 2.3 78.68 7157 4173569 178321
## 23 23 7343 KOTA BEKASI 1357 1.9 78.99 13228 4782936 40596
## 3 3 5146 KABUPATEN CIANJUR 2929 2.4 87.23 35113 2534799 442503
## 5 5 5150 KABUPATEN GARUT 4194 3.0 89.12 19828 1961086 282908
## 6 6 4606 KABUPATEN TASIKMALAYA 1641 4.2 90.46 6815 2251788 206987
## 4 4 9596 KABUPATEN BANDUNG 4238 2.3 95.44 40368 3241930 367264
## 24 24 2397 KOTA DEPOK 1022 0.7 96.15 12379 4339515 347237
## 2 2 6543 KABUPATEN SUKABUMI 1650 4.9 82.26 32883 3125445 362219
## 26 26 2477 KOTA TASIKMALAYA 639 3.4 85.00 2628 2264093 73447
## 18 18 347 KABUPATEN PANGANDARAN 531 5.4 84.27 5120 1860591 94504
## 21 21 3941 KOTA BANDUNG 1423 1.6 78.84 4081 3742276 97979
## 25 25 1221 KOTA CIMAHI 391 2.4 85.18 3173 3241929 65195
## 20 20 621 KOTA SUKABUMI 378 3.8 100.00 1788 2530183 54842
## 13 13 2390 KABUPATEN SUBANG 1372 1.4 82.10 9488 3064218 266437
## 19 19 2824 KOTA BOGOR 203 1.7 95.85 7431 4169807 145792
## 17 17 5164 KABUPATEN BANDUNG BARAT 1858 1.8 78.46 8412 3248283 363351
## 8 8 2461 KABUPATEN KUNINGAN 1346 5.5 77.00 11602 1882642 187029
## 11 11 2381 KABUPATEN SUMEDANG 1264 2.5 88.11 9791 3241930 193165
## 10 10 2471 KABUPATEN MAJALENGKA 716 3.8 92.88 15717 2009000 211474
## 22 22 1108 KOTA CIREBON 264 4.9 81.69 2267 2271202 46322
## 7 7 1977 KABUPATEN CIAMIS 1515 4.0 93.79 6602 1880655 96743
## X7 X8 X9 X10 hii ri Di
## 15 59.54 43.90 39.11 58.25 0.81515661 -1.91852868 1.475642e+00
## 1 62.39 74.45 87.52 23.76 0.77766868 1.50869238 7.237735e-01
## 16 67.39 91.33 95.49 66.35 0.49459430 2.36905861 4.993073e-01
## 27 66.01 97.97 86.40 54.78 0.96303205 0.38375708 3.487670e-01
## 9 57.75 91.32 23.89 62.75 0.47452090 1.86709469 2.861804e-01
## 12 55.79 82.06 74.30 33.36 0.35030627 1.95820886 1.879596e-01
## 14 60.67 94.45 48.58 49.34 0.36071511 -1.52478312 1.192596e-01
## 23 76.87 99.30 90.72 46.04 0.56496438 0.90440801 9.656781e-02
## 3 57.30 92.89 100.00 60.26 0.25620507 -1.41302478 6.252323e-02
## 5 58.52 96.65 81.47 55.12 0.50942403 -0.68807807 4.469469e-02
## 6 59.77 79.26 84.64 37.97 0.19209598 1.23649624 3.304848e-02
## 4 65.51 90.30 74.60 30.49 0.55611699 -0.53763262 3.292124e-02
## 24 76.89 90.29 59.31 56.69 0.39500031 -0.65524511 2.548339e-02
## 2 57.67 99.72 100.00 39.61 0.36884373 -0.65999434 2.314159e-02
## 26 69.12 57.86 22.91 9.17 0.62915620 -0.38053678 2.233408e-02
## 18 59.72 88.34 96.55 52.17 0.25054290 -0.74521605 1.687746e-02
## 21 76.11 78.49 96.36 24.45 0.36653852 -0.55872280 1.642100e-02
## 25 75.29 80.91 63.57 43.87 0.18155486 -0.78784080 1.251707e-02
## 20 70.42 83.20 72.17 72.89 0.26166010 0.56476172 1.027588e-02
## 13 56.23 100.00 72.17 51.79 0.22970855 -0.58737206 9.353108e-03
## 19 72.38 76.33 47.40 53.04 0.28328953 0.50812220 9.277489e-03
## 17 60.33 100.00 88.17 20.82 0.47709354 0.21443490 3.813974e-03
## 8 59.97 90.11 80.30 77.00 0.31516923 -0.28759930 3.460537e-03
## 11 64.46 95.84 78.98 51.82 0.08274138 -0.49903223 2.042187e-03
## 10 58.34 88.84 53.75 62.10 0.27533971 0.12905062 5.752570e-04
## 22 70.21 97.49 80.47 80.79 0.35560901 0.10066383 5.083672e-04
## 7 65.78 85.51 95.36 55.57 0.21295206 0.03629982 3.241134e-05library(openxlsx)
# Tulis data frame ke file Excel
write.xlsx(summ_leverage_sorted, "summ_leverage_sorted.xlsx", rowNames = FALSE)
write.xlsx(summ_pencilan_sorted, "summ_pencilan_sorted.xlsx", rowNames = FALSE)
write.xlsx(amatan_berpengaruh, "amatan_berpengaruh.xlsx", rowNames = FALSE)
write.xlsx(summ_sorted, "summ_sorted.xlsx", rowNames = FALSE)Plot Titik leverage dan pencilan
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_plot_resid_lev(model)
hapus titik leverage dan pencilan
# Mendeteksi titik leverage, pencilan, dan amatan berpengaruh
cutoff <- 2*p/n
titik_leverage <- which(hii > cutoff)
absri <- abs(summ$ri)
pencilan <- which(absri > 2)
fcrit = qf(p=0.95, df1=p, df2=n-p)
amatan_berpengaruh <- which(Di > fcrit)
# Menggabungkan indeks titik leverage dan pencilan
observasi_kecuali_leverage_pencilan <- setdiff(1:n, c(titik_leverage, pencilan))
# Membuat data baru dengan menghapus titik leverage dan pencilan
data_regresi_no_leverage_pencilan <- data.projek[observasi_kecuali_leverage_pencilan,]
# Membuat model
model2 <- lm(Y ~ X1+X2+X3+X4+X5+X6+X7+X8+X9+X10 ,data= data_regresi_no_leverage_pencilan)
model2##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 +
## X10, data = data_regresi_no_leverage_pencilan)
##
## Coefficients:
## (Intercept) X1 X2 X3 X4 X5
## 1.395e+04 9.696e-01 -2.967e+01 -9.073e+01 1.913e-01 7.378e-04
## X6 X7 X8 X9 X10
## -8.149e-03 -3.271e+01 -3.340e+01 -4.460e+00 -2.461e+01summary(model2)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 +
## X10, data = data_regresi_no_leverage_pencilan)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2618.7 -766.3 -136.3 934.2 2037.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.395e+04 7.857e+03 1.775 0.0993 .
## X1 9.696e-01 6.561e-01 1.478 0.1633
## X2 -2.967e+01 5.728e+02 -0.052 0.9595
## X3 -9.073e+01 4.738e+01 -1.915 0.0778 .
## X4 1.913e-01 6.681e-02 2.864 0.0133 *
## X5 7.378e-04 9.896e-04 0.746 0.4692
## X6 -8.149e-03 5.747e-03 -1.418 0.1798
## X7 -3.271e+01 8.621e+01 -0.379 0.7105
## X8 -3.340e+01 5.858e+01 -0.570 0.5783
## X9 -4.460e+00 1.990e+01 -0.224 0.8261
## X10 -2.461e+01 3.098e+01 -0.794 0.4413
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1621 on 13 degrees of freedom
## Multiple R-squared: 0.8876, Adjusted R-squared: 0.8011
## F-statistic: 10.26 on 10 and 13 DF, p-value: 0.0001193Alternatif Pemilihan Model Terbaik (OLS): Pemilihan Model Terbaik - Forward
library(olsrr)
##== Forward selection
fw.hc <- ols_step_forward_p(model2)
fw.hc##
##
## Stepwise Summary
## -------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## -------------------------------------------------------------------------
## 0 Base Model 464.609 466.965 393.659 0.00000 0.00000
## 1 X4 435.964 439.498 366.701 0.72109 0.70842
## 2 X10 429.459 434.172 361.707 0.80431 0.78567
## 3 X6 427.831 433.721 361.483 0.83177 0.80653
## 4 X3 426.193 433.261 362.062 0.85543 0.82500
## 5 X1 425.470 433.717 363.921 0.87093 0.83508
## 6 X2 425.391 434.815 366.699 0.88165 0.83987
## -------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------------
## R 0.939 RMSE 1224.198
## R-Squared 0.882 MSE 2115757.867
## Adj. R-Squared 0.840 Coef. Var 34.204
## Pred R-Squared 0.737 AIC 425.391
## MAE 1048.809 SBC 434.815
## ----------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 267931050.094 6 44655175.016 21.106 0.0000
## Residual 35967883.739 17 2115757.867
## Total 303898933.833 23
## --------------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------------
## (Intercept) 12591.068 3358.965 3.748 0.002 5504.270 19677.865
## X4 0.222 0.046 0.874 4.863 0.000 0.125 0.318
## X10 -38.296 19.859 -0.190 -1.928 0.071 -80.196 3.603
## X6 -0.009 0.004 -0.372 -2.266 0.037 -0.018 -0.001
## X3 -90.296 39.104 -0.235 -2.309 0.034 -172.798 -7.793
## X1 0.624 0.401 0.187 1.554 0.139 -0.223 1.470
## X2 -324.317 261.468 -0.121 -1.240 0.232 -875.966 227.332
## ------------------------------------------------------------------------------------------------Pemilihan Model Terbaik - Backward
##== Backward selection
bw.hc <- ols_step_backward_p(model2)
bw.hc##
##
## Stepwise Summary
## -------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## -------------------------------------------------------------------------
## 0 Full Model 432.160 446.297 381.235 0.88756 0.80107
## 1 X2 430.165 443.124 377.541 0.88754 0.81524
## 2 X9 428.287 440.067 373.835 0.88697 0.82668
## 3 X7 426.712 437.314 370.177 0.88495 0.83461
## 4 X8 425.403 434.828 366.702 0.88159 0.83979
## -------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------------
## R 0.939 RMSE 1224.507
## R-Squared 0.882 MSE 2116825.919
## Adj. R-Squared 0.840 Coef. Var 34.213
## Pred R-Squared 0.723 AIC 425.403
## MAE 1052.349 SBC 434.828
## ----------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 267912893.204 6 44652148.867 21.094 0.0000
## Residual 35986040.629 17 2116825.919
## Total 303898933.833 23
## --------------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------------
## (Intercept) 9644.555 3601.144 2.678 0.016 2046.806 17242.304
## X1 0.782 0.428 0.235 1.829 0.085 -0.120 1.684
## X3 -85.934 39.032 -0.224 -2.202 0.042 -168.283 -3.585
## X4 0.205 0.046 0.809 4.489 0.000 0.109 0.301
## X5 0.000 0.000 0.119 1.237 0.233 0.000 0.001
## X6 -0.008 0.004 -0.327 -2.097 0.051 -0.017 0.000
## X10 -39.282 19.599 -0.195 -2.004 0.061 -80.631 2.068
## -----------------------------------------------------------------------------------------------Pemilihan Model Terbaik - Stepwise
##== Stepwise
sw.hc <- ols_step_both_p(model2, details = T)## Stepwise Selection Method
## -------------------------
##
## Candidate Terms:
##
## 1. X1
## 2. X2
## 3. X3
## 4. X4
## 5. X5
## 6. X6
## 7. X7
## 8. X8
## 9. X9
## 10. X10
##
##
## Step => 0
## Model => Y ~ 1
## R2 => 0
##
## Initiating stepwise selection...
##
## Step => 1
## Selected => X4
## Model => Y ~ X4
## R2 => 0.721
##
## Step => 2
## Selected => X10
## Model => Y ~ X4 + X10
## R2 => 0.804
##
## Step => 3
## Selected => X6
## Model => Y ~ X4 + X10 + X6
## R2 => 0.832
##
## Step => 4
## Selected => X3
## Model => Y ~ X4 + X10 + X6 + X3
## R2 => 0.855
##
##
## No more variables to be added or removed.sw.hc##
##
## Stepwise Summary
## -------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## -------------------------------------------------------------------------
## 0 Base Model 464.609 466.965 393.659 0.00000 0.00000
## 1 X4 (+) 435.964 439.498 366.701 0.72109 0.70842
## 2 X10 (+) 429.459 434.172 361.707 0.80431 0.78567
## 3 X6 (+) 427.831 433.721 361.483 0.83177 0.80653
## 4 X3 (+) 426.193 433.261 362.062 0.85543 0.82500
## -------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------------
## R 0.925 RMSE 1352.994
## R-Squared 0.855 MSE 2312328.588
## Adj. R-Squared 0.825 Coef. Var 35.758
## Pred R-Squared 0.757 AIC 426.193
## MAE 1130.762 SBC 433.261
## ----------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 259964690.668 4 64991172.667 28.106 0.0000
## Residual 43934243.165 19 2312328.588
## Total 303898933.833 23
## --------------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------------
## (Intercept) 10645.648 3340.833 3.187 0.005 3653.205 17638.092
## X4 0.244 0.042 0.962 5.763 0.000 0.155 0.332
## X10 -54.169 18.741 -0.268 -2.890 0.009 -93.394 -14.945
## X6 -0.007 0.004 -0.285 -1.766 0.093 -0.016 0.001
## X3 -67.988 38.554 -0.177 -1.763 0.094 -148.682 12.706
## ------------------------------------------------------------------------------------------------Best Subset Regression # Hald Cement data
bs.hc <- ols_step_best_subset(model2)
bs.hc## Best Subsets Regression
## ---------------------------------------------
## Model Index Predictors
## ---------------------------------------------
## 1 X4
## 2 X4 X10
## 3 X4 X6 X10
## 4 X3 X4 X6 X10
## 5 X1 X3 X4 X6 X10
## 6 X1 X2 X3 X4 X6 X10
## 7 X1 X3 X4 X5 X6 X8 X10
## 8 X1 X3 X4 X5 X6 X7 X8 X10
## 9 X1 X3 X4 X5 X6 X7 X8 X9 X10
## 10 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## ---------------------------------------------
##
## Subsets Regression Summary
## --------------------------------------------------------------------------------------------------------------------------------------------------
## Adj. Pred
## Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
## --------------------------------------------------------------------------------------------------------------------------------------------------
## 1 0.7211 0.7084 0.61 12.2468 435.9635 366.7007 439.4977 92495138.1121 4173747.5545 183461.4310 0.3296
## 2 0.8043 0.7857 0.7109 4.6255 429.4593 361.7074 434.1716 68142700.1078 3185892.4726 141595.2210 0.2516
## 3 0.8318 0.8065 0.7019 3.4507 427.8306 361.4833 433.7209 61664068.5078 2982298.5860 134539.7858 0.2355
## 4 0.8554 0.8250 0.7569 2.7149 426.1927 362.0622 433.2610 55934800.3260 2794063.7101 128462.6993 0.2207
## 5 0.8709 0.8351 0.7213 2.9225 425.4703 363.9209 433.7167 52874162.0640 2723820.4700 128179.7868 0.2151
## 6 0.8816 0.8399 0.7372 3.6841 425.3910 366.6995 434.8155 51516500.1468 2732853.9115 132234.8667 0.2158
## 7 0.8849 0.8346 0.6484 5.3022 426.7118 370.1766 437.3143 53417565.5674 2913685.3946 145684.2697 0.2301
## 8 0.8870 0.8267 0.586 7.0687 428.2867 373.8345 440.0672 56228185.5918 3148778.3931 163572.9035 0.2487
## 9 0.8875 0.8152 0.4643 9.0027 430.1652 377.5410 443.1238 60247762.4880 3458378.0545 187785.2337 0.2731
## 10 0.8876 0.8011 0.3962 11.0000 432.1603 381.2346 446.2969 65254944.3940 3833157.5728 219037.5756 0.3027
## --------------------------------------------------------------------------------------------------------------------------------------------------
## AIC: Akaike Information Criteria
## SBIC: Sawa's Bayesian Information Criteria
## SBC: Schwarz Bayesian Criteria
## MSEP: Estimated error of prediction, assuming multivariate normality
## FPE: Final Prediction Error
## HSP: Hocking's Sp
## APC: Amemiya Prediction Criteriabest_model <- lm(Y~ X3 + X4+ X6 + X10 , data = data_regresi_no_leverage_pencilan)
best_model##
## Call:
## lm(formula = Y ~ X3 + X4 + X6 + X10, data = data_regresi_no_leverage_pencilan)
##
## Coefficients:
## (Intercept) X3 X4 X6 X10
## 1.065e+04 -6.799e+01 2.436e-01 -7.196e-03 -5.417e+01summary(best_model)##
## Call:
## lm(formula = Y ~ X3 + X4 + X6 + X10, data = data_regresi_no_leverage_pencilan)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2310.6 -992.8 -147.7 815.6 2417.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.065e+04 3.341e+03 3.187 0.00486 **
## X3 -6.799e+01 3.855e+01 -1.763 0.09390 .
## X4 2.436e-01 4.227e-02 5.763 1.49e-05 ***
## X6 -7.196e-03 4.074e-03 -1.766 0.09345 .
## X10 -5.417e+01 1.874e+01 -2.890 0.00937 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1521 on 19 degrees of freedom
## Multiple R-squared: 0.8554, Adjusted R-squared: 0.825
## F-statistic: 28.11 on 4 and 19 DF, p-value: 9.572e-08Uji Asumsi Model Terbaik
# ===== Eksplorasi asumsi =====
plot(best_model,1) # plot sisaan vs yduga
plot(best_model,2) # qq-plot
plot(x = 1:dim(data_regresi_no_leverage_pencilan)[1],
y = best_model$residuals,
type = 'b',
ylab = "Residuals",
xlab = "Observation") # plot sisaan vs urutan
Regresi Gulud
Uji Asumsi: Metode Formal
# Asumsi Gauss-Markov: Nilai harapan sisaan sama dengan nol
t.test(best_model$residuals,
mu = 0,
conf.level = 0.95)##
## One Sample t-test
##
## data: best_model$residuals
## t = 1.805e-16, df = 23, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -583.6072 583.6072
## sample estimates:
## mean of x
## 5.092223e-14# Asumsi Gauss-Markov: Sisaan saling bebas
library(randtests)
runs.test(best_model$residuals)##
## Runs Test
##
## data: best_model$residuals
## statistic = 0.41742, runs = 14, n1 = 12, n2 = 12, n = 24, p-value =
## 0.6764
## alternative hypothesis: nonrandomness# Asumsi Gauss-Markov: Ragam Sisaan Homogen
ncvTest(best_model)## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.008171531, Df = 1, p = 0.92797# Asumsi Normalitas Sisaan
shapiro.test(best_model$residuals)##
## Shapiro-Wilk normality test
##
## data: best_model$residuals
## W = 0.95503, p-value = 0.3469H0: miu = 0
Interpretasi : p-value > \(\alpha\), maka tak Tolak H0, nilai harapan sisaan sama dengan nol.
H0: Saling bebas
Interpretasi : p-value > \(\alpha\), tak tolak H0, maka sisaan saling bebas.
H0: homogen
Interpretasi : p-value > \(\alpha\), maka tak tolak H0. Ragam sisaan homogen.
H0: Menyebar normal
Interpratsi : p-value > \(\alpha\), maka tak tolak Ho. Sisaan menyebar normal.
Pengujian Kelayakan Model
summary.lm(best_model)##
## Call:
## lm(formula = Y ~ X3 + X4 + X6 + X10, data = data_regresi_no_leverage_pencilan)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2310.6 -992.8 -147.7 815.6 2417.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.065e+04 3.341e+03 3.187 0.00486 **
## X3 -6.799e+01 3.855e+01 -1.763 0.09390 .
## X4 2.436e-01 4.227e-02 5.763 1.49e-05 ***
## X6 -7.196e-03 4.074e-03 -1.766 0.09345 .
## X10 -5.417e+01 1.874e+01 -2.890 0.00937 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1521 on 19 degrees of freedom
## Multiple R-squared: 0.8554, Adjusted R-squared: 0.825
## F-statistic: 28.11 on 4 and 19 DF, p-value: 9.572e-08anova(best_model)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X3 1 101803395 101803395 44.0264 2.393e-06 ***
## X4 1 134295208 134295208 58.0779 3.421e-07 ***
## X6 1 4546766 4546766 1.9663 0.176967
## X10 1 19319322 19319322 8.3549 0.009372 **
## Residuals 19 43934243 2312329
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1aov(best_model)## Call:
## aov(formula = best_model)
##
## Terms:
## X3 X4 X6 X10 Residuals
## Sum of Squares 101803395 134295208 4546766 19319322 43934243
## Deg. of Freedom 1 1 1 1 19
##
## Residual standard error: 1520.634
## Estimated effects may be unbalanced