Analisis Regresi - Teknik Pembelajaran Mesin
Hakim Zoelva Mahesa - G1401211039
2024-05-31
Library
# memuat library yang dibutuhkan
library(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(ggplot2)
library(corrplot)## corrplot 0.92 loadedlibrary(cowplot)
library(glmnet)## Loading required package: Matrix## Loaded glmnet 4.1-8library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varEksplorasi Data
# Membaca data
library(readxl)
data <- read_xlsx("C:/Users/HAKIM/Downloads/Data TPM.xlsx", sheet = "Gabungan")
# Melihat Struktur data
str(data)## tibble [119 × 6] (S3: tbl_df/tbl/data.frame)
## $ Y : num [1:119] 13.67 9.82 11.17 9.18 9.72 ...
## $ X1: num [1:119] 97.1 98.4 97.4 97 95.6 ...
## $ X2: num [1:119] 2.28 1.84 1.91 2.18 2.21 2.11 2.1 1.71 2.02 1.9 ...
## $ X3: num [1:119] 74.2 85.4 82.8 82.2 82.3 ...
## $ X4: num [1:119] 14.87 3.43 4.16 4.51 4.25 ...
## $ X5: num [1:119] 98.7 99.2 99 99.7 98.7 ...| Variabel | Keterangan |
|---|---|
| Y | Angka Kematian Bayi — jumlah kematian bayi per 1.000 kelahiran hidup dalam satu tahun di suatu wilayah. |
| X1 | Angka Harapan Hidup — rata-rata perkiraan lama hidup seseorang sejak lahir. |
| X2 | Total Fertility Rate — rata-rata jumlah anak yang dilahirkan oleh seorang wanita selama masa suburnya. |
| X3 | Indeks Pembangunan Manusia — indeks komposit yang mencerminkan kualitas hidup manusia melalui pendidikan, kesehatan, dan pendapatan. |
| X4 | Persentase Kemiskinan — persentase penduduk yang berada di bawah garis kemiskinan di suatu wilayah. |
| X5 | Angka Melek Huruf Ibu — persentase ibu yang dapat membaca dan menulis di suatu wilayah. |
# Melihat summary data
summary(data)## Y X1 X2 X3
## Min. : 9.18 Min. :77.60 Min. :1.540 Min. :64.75
## 1st Qu.:11.71 1st Qu.:93.01 1st Qu.:1.915 1st Qu.:69.61
## Median :13.24 Median :96.07 Median :2.050 Median :72.48
## Mean :13.39 Mean :95.04 Mean :2.034 Mean :73.54
## 3rd Qu.:14.71 3rd Qu.:98.58 3rd Qu.:2.160 3rd Qu.:76.53
## Max. :19.66 Max. :99.95 Max. :2.450 Max. :86.93
## X4 X5
## Min. : 2.290 Min. :77.60
## 1st Qu.: 7.170 1st Qu.:93.01
## Median : 9.940 Median :96.07
## Mean : 9.927 Mean :95.04
## 3rd Qu.:12.430 3rd Qu.:98.58
## Max. :22.780 Max. :99.95# Melihat nilai NA
colSums(is.na(data))## Y X1 X2 X3 X4 X5
## 0 0 0 0 0 0# menghitung korelasi antar kolom
corr_matrix <- round(cor(data), 2)
# membuat plot korelasi
corrplot(corr_matrix,
type="lower",
method = "color",
tl.cex = 0.5,
tl.col = "black",
addCoef.col = "#2F2F2F",
addCoefasPercent = FALSE,
number.cex = 0.5,
diag = FALSE)
Pembagian Data
set.seed(039)
# Menentukan proporsi data untuk training (misalnya, 80%) dan testing (misalnya, 20%)
prop_train <- 0.8
index <- createDataPartition(data$Y, p = prop_train, list = FALSE)
# Membagi dataset
training_data <- data[index, ]
testing_data <- data[-index, ]Pemodelan
# Melatih model regresi linear
model_reg <- lm(Y ~ ., data = training_data)
car::vif(model_reg)## X1 X2 X3 X4 X5
## 1.241477 1.027043 1.798745 1.929327 1.322506summary(model_reg)##
## Call:
## lm(formula = Y ~ ., data = training_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2134 -0.9348 -0.0071 0.6620 5.1071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.47614 5.86404 4.686 9.86e-06 ***
## X1 -0.03783 0.03629 -1.043 0.3000
## X2 1.00793 0.87529 1.152 0.2526
## X3 -0.26834 0.03865 -6.943 5.78e-10 ***
## X4 0.09469 0.05273 1.796 0.0759 .
## X5 0.06521 0.04741 1.375 0.1724
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.434 on 90 degrees of freedom
## Multiple R-squared: 0.5829, Adjusted R-squared: 0.5597
## F-statistic: 25.16 on 5 and 90 DF, p-value: 8.776e-16Deteksi Pencilan dan outlier
#titik pencilan
sisaan<-residuals(model_reg)
stdr.sisaan<-rstandard(model_reg)
mut.stdr.sisaan<-abs(stdr.sisaan)
pencilll <- data.frame(sort(mut.stdr.sisaan))
pencilan <- data.frame(pencilll, pencilll>2)
pencilan## sort.mut.stdr.sisaan. sort.mut.stdr.sisaan..1
## 52 2.934199e-05 FALSE
## 29 1.020845e-02 FALSE
## 33 2.387866e-02 FALSE
## 4 2.692892e-02 FALSE
## 49 2.706920e-02 FALSE
## 45 5.058162e-02 FALSE
## 10 5.547483e-02 FALSE
## 9 6.777830e-02 FALSE
## 57 7.428544e-02 FALSE
## 59 9.271648e-02 FALSE
## 22 9.432184e-02 FALSE
## 21 1.071630e-01 FALSE
## 95 1.344607e-01 FALSE
## 88 1.483334e-01 FALSE
## 7 1.670029e-01 FALSE
## 14 1.861112e-01 FALSE
## 6 1.878320e-01 FALSE
## 43 1.922635e-01 FALSE
## 25 2.019830e-01 FALSE
## 74 2.128772e-01 FALSE
## 68 2.308358e-01 FALSE
## 34 2.356360e-01 FALSE
## 96 2.415794e-01 FALSE
## 77 2.420103e-01 FALSE
## 2 2.443759e-01 FALSE
## 30 2.591992e-01 FALSE
## 1 2.675704e-01 FALSE
## 20 2.834002e-01 FALSE
## 26 2.852262e-01 FALSE
## 89 2.922638e-01 FALSE
## 83 3.048645e-01 FALSE
## 48 3.075783e-01 FALSE
## 23 3.217419e-01 FALSE
## 24 3.251137e-01 FALSE
## 11 3.360381e-01 FALSE
## 5 3.503375e-01 FALSE
## 16 4.124900e-01 FALSE
## 61 4.525938e-01 FALSE
## 60 4.772302e-01 FALSE
## 55 4.956599e-01 FALSE
## 42 4.971182e-01 FALSE
## 71 5.033830e-01 FALSE
## 18 5.114785e-01 FALSE
## 66 5.376247e-01 FALSE
## 76 5.474967e-01 FALSE
## 13 5.491789e-01 FALSE
## 87 5.555210e-01 FALSE
## 62 5.727714e-01 FALSE
## 15 5.745755e-01 FALSE
## 17 5.827126e-01 FALSE
## 56 5.849224e-01 FALSE
## 86 6.663865e-01 FALSE
## 81 6.753652e-01 FALSE
## 92 6.783020e-01 FALSE
## 12 6.848629e-01 FALSE
## 47 6.850604e-01 FALSE
## 28 6.908164e-01 FALSE
## 51 7.052784e-01 FALSE
## 39 7.248910e-01 FALSE
## 58 7.579051e-01 FALSE
## 8 7.861058e-01 FALSE
## 27 8.122294e-01 FALSE
## 73 8.184426e-01 FALSE
## 75 8.370506e-01 FALSE
## 54 8.657657e-01 FALSE
## 19 8.658475e-01 FALSE
## 41 8.878073e-01 FALSE
## 63 9.109013e-01 FALSE
## 72 9.562364e-01 FALSE
## 53 9.873582e-01 FALSE
## 85 1.005506e+00 FALSE
## 31 1.020415e+00 FALSE
## 37 1.025272e+00 FALSE
## 40 1.076151e+00 FALSE
## 36 1.100870e+00 FALSE
## 65 1.116616e+00 FALSE
## 82 1.162571e+00 FALSE
## 69 1.210410e+00 FALSE
## 3 1.213325e+00 FALSE
## 80 1.231850e+00 FALSE
## 46 1.278879e+00 FALSE
## 67 1.342223e+00 FALSE
## 64 1.431922e+00 FALSE
## 94 1.446401e+00 FALSE
## 44 1.453913e+00 FALSE
## 35 1.610470e+00 FALSE
## 93 1.624643e+00 FALSE
## 50 1.973746e+00 FALSE
## 32 2.031145e+00 TRUE
## 79 2.069946e+00 TRUE
## 90 2.144115e+00 TRUE
## 84 2.159584e+00 TRUE
## 91 2.235606e+00 TRUE
## 38 2.260498e+00 TRUE
## 78 2.359825e+00 TRUE
## 70 3.716813e+00 TRUE#titik leverage
hi<-hatvalues(model_reg, infl = influence(model_reg))
ambang_batas<-2*(10/34) #2p/n, p=10, n=34
leveragee <- data.frame(hi, hi>ambang_batas)
leveragee## hi hi...ambang_batas
## 1 0.08415773 FALSE
## 2 0.08289759 FALSE
## 3 0.05785058 FALSE
## 4 0.04871496 FALSE
## 5 0.09778723 FALSE
## 6 0.04767867 FALSE
## 7 0.03433197 FALSE
## 8 0.10253424 FALSE
## 9 0.06031376 FALSE
## 10 0.07324402 FALSE
## 11 0.05882564 FALSE
## 12 0.03492227 FALSE
## 13 0.09876190 FALSE
## 14 0.06009103 FALSE
## 15 0.04697435 FALSE
## 16 0.04703569 FALSE
## 17 0.04562092 FALSE
## 18 0.04406433 FALSE
## 19 0.03827881 FALSE
## 20 0.03081689 FALSE
## 21 0.08799578 FALSE
## 22 0.01645603 FALSE
## 23 0.05837341 FALSE
## 24 0.07978175 FALSE
## 25 0.04753211 FALSE
## 26 0.05535826 FALSE
## 27 0.04654154 FALSE
## 28 0.04282208 FALSE
## 29 0.04475618 FALSE
## 30 0.04923337 FALSE
## 31 0.11550119 FALSE
## 32 0.03780361 FALSE
## 33 0.09466140 FALSE
## 34 0.04166758 FALSE
## 35 0.03676084 FALSE
## 36 0.04574993 FALSE
## 37 0.03972319 FALSE
## 38 0.01738378 FALSE
## 39 0.02382388 FALSE
## 40 0.03098018 FALSE
## 41 0.05670686 FALSE
## 42 0.05595835 FALSE
## 43 0.04171766 FALSE
## 44 0.13475185 FALSE
## 45 0.10390278 FALSE
## 46 0.07237469 FALSE
## 47 0.09068451 FALSE
## 48 0.10740095 FALSE
## 49 0.02719486 FALSE
## 50 0.04832489 FALSE
## 51 0.03001109 FALSE
## 52 0.04567590 FALSE
## 53 0.06132746 FALSE
## 54 0.08511344 FALSE
## 55 0.05773588 FALSE
## 56 0.06003468 FALSE
## 57 0.08287526 FALSE
## 58 0.21481991 FALSE
## 59 0.11018171 FALSE
## 60 0.09296809 FALSE
## 61 0.11174571 FALSE
## 62 0.03849529 FALSE
## 63 0.02600452 FALSE
## 64 0.03651257 FALSE
## 65 0.02651001 FALSE
## 66 0.02494046 FALSE
## 67 0.02412986 FALSE
## 68 0.05460983 FALSE
## 69 0.04416452 FALSE
## 70 0.08195865 FALSE
## 71 0.01945827 FALSE
## 72 0.06327741 FALSE
## 73 0.03235638 FALSE
## 74 0.06116080 FALSE
## 75 0.03440819 FALSE
## 76 0.02127041 FALSE
## 77 0.04650627 FALSE
## 78 0.06808932 FALSE
## 79 0.09654514 FALSE
## 80 0.15873875 FALSE
## 81 0.10010824 FALSE
## 82 0.18317253 FALSE
## 83 0.06243881 FALSE
## 84 0.03429651 FALSE
## 85 0.03883731 FALSE
## 86 0.04450664 FALSE
## 87 0.05842917 FALSE
## 88 0.04715074 FALSE
## 89 0.05444424 FALSE
## 90 0.05147024 FALSE
## 91 0.06951863 FALSE
## 92 0.04341517 FALSE
## 93 0.11356305 FALSE
## 94 0.12434776 FALSE
## 95 0.04911384 FALSE
## 96 0.06673529 FALSE# Plot titik pencilan dan leverage
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_plot_resid_lev(model_reg)
# Jarak Cook
di<-cooks.distance(model_reg)
f<-qf(0.05,10,24, lower.tail = F) # qf(p,db1,db2, lower.tail=F). db1=n-p, db2=n-p, lower.tail=F untuk p=taraf nyata(alpha) dan sebaliknya untuk p= (1-alpha)
data.frame(di, di>f)## di di...f
## 1 1.096474e-03 FALSE
## 2 8.996828e-04 FALSE
## 3 1.506576e-02 FALSE
## 4 6.189255e-06 FALSE
## 5 2.217150e-03 FALSE
## 6 2.943936e-04 FALSE
## 7 1.652601e-04 FALSE
## 8 1.176689e-02 FALSE
## 9 4.914322e-05 FALSE
## 10 4.053662e-05 FALSE
## 11 1.176312e-03 FALSE
## 12 2.828760e-03 FALSE
## 13 5.508411e-03 FALSE
## 14 3.690775e-04 FALSE
## 15 2.712059e-03 FALSE
## 16 1.399672e-03 FALSE
## 17 2.705209e-03 FALSE
## 18 2.009842e-03 FALSE
## 19 4.973256e-03 FALSE
## 20 4.256298e-04 FALSE
## 21 1.846730e-04 FALSE
## 22 2.480873e-05 FALSE
## 23 1.069548e-03 FALSE
## 24 1.527327e-03 FALSE
## 25 3.393244e-04 FALSE
## 26 7.945896e-04 FALSE
## 27 5.367168e-03 FALSE
## 28 3.558354e-03 FALSE
## 29 8.137799e-07 FALSE
## 30 5.798313e-04 FALSE
## 31 2.266167e-02 FALSE
## 32 2.701470e-02 FALSE
## 33 9.936432e-06 FALSE
## 34 4.023593e-04 FALSE
## 35 1.649700e-02 FALSE
## 36 9.683868e-03 FALSE
## 37 7.247275e-03 FALSE
## 38 1.506667e-02 FALSE
## 39 2.137364e-03 FALSE
## 40 6.170875e-03 FALSE
## 41 7.897235e-03 FALSE
## 42 2.441416e-03 FALSE
## 43 2.682064e-04 FALSE
## 44 5.486808e-02 FALSE
## 45 4.944317e-05 FALSE
## 46 2.126776e-02 FALSE
## 47 7.800545e-03 FALSE
## 48 1.897194e-03 FALSE
## 49 3.413978e-06 FALSE
## 50 3.296958e-02 FALSE
## 51 2.564985e-03 FALSE
## 52 6.867823e-12 FALSE
## 53 1.061547e-02 FALSE
## 54 1.162199e-02 FALSE
## 55 2.508936e-03 FALSE
## 56 3.641963e-03 FALSE
## 57 8.310988e-05 FALSE
## 58 2.619290e-02 FALSE
## 59 1.774070e-04 FALSE
## 60 3.890594e-03 FALSE
## 61 4.294964e-03 FALSE
## 62 2.189110e-03 FALSE
## 63 3.692184e-03 FALSE
## 64 1.295041e-02 FALSE
## 65 5.658941e-03 FALSE
## 66 1.232198e-03 FALSE
## 67 7.424390e-03 FALSE
## 68 5.129971e-04 FALSE
## 69 1.128247e-02 FALSE
## 70 2.055524e-01 FALSE
## 71 8.380771e-04 FALSE
## 72 1.029478e-02 FALSE
## 73 3.733101e-03 FALSE
## 74 4.920269e-04 FALSE
## 75 4.161217e-03 FALSE
## 76 1.085738e-03 FALSE
## 77 4.761130e-04 FALSE
## 78 6.781302e-02 FALSE
## 79 7.631161e-02 FALSE
## 80 4.772175e-02 FALSE
## 81 8.456792e-03 FALSE
## 82 5.051465e-02 FALSE
## 83 1.031615e-03 FALSE
## 84 2.760546e-02 FALSE
## 85 6.808796e-03 FALSE
## 86 3.447453e-03 FALSE
## 87 3.191732e-03 FALSE
## 88 1.814642e-04 FALSE
## 89 8.197161e-04 FALSE
## 90 4.157672e-02 FALSE
## 91 6.223471e-02 FALSE
## 92 3.480270e-03 FALSE
## 93 5.635776e-02 FALSE
## 94 4.951449e-02 FALSE
## 95 1.556377e-04 FALSE
## 96 6.955356e-04 FALSE# Jarak Cook
library(ggplot2)
cooks_crit = f
model_cooks <- cooks.distance(model_reg)
df <- data.frame(obs = names(model_cooks),
cooks = model_cooks)
ggplot(df, aes(y = cooks, x = obs)) +
geom_point() +
geom_hline(yintercept = cooks_crit, linetype="dashed") +
labs(title = "Cook's Distance",
subtitle = "Influential Observation ",
x = "Observation Number",
y = "Cook's")
tidak terdapat pencilan
#Deteksi amatan berpengaruh (dfbetas)
ols_plot_dfbetas(model_reg)
amatan yang berada di luar batas garis merah adalah amatan berpengaruh
#Deteksi amatan berpengaruh (dffits)
ols_plot_dffits(model_reg)
44, 70, 78, 79, 80, 82, 90, 91, 93, 94 amatan berpengaruh (amatan yang berada di luar batas garis merah adalah amatan berpengaruh)
Pemodelan Regresi Sementara
amatan 38 dihapuskan karena titik leverage yang bukan amatan berpengaruh Setelah mencoba berbagai kombinasi, diperoleh kombinasi terbaik didapatkan dari menghapus amatan 38, 58, 80.
#model_reg <- lm(Y ~ ., data = training_data[-c(84,90,78,91,70,79,50,44,82),])
#summary(model_reg)Uji Asumsi
# Asumsi GAUSS MARKOV
# 1 Nilai harapan sisaan sama dengan nol
t.test(model_reg$residuals,
mu = 0,
conf.level = 0.95) #asumsi nilai harapan sama dengan 0 terpenuhi##
## One Sample t-test
##
## data: model_reg$residuals
## t = 1.6411e-16, df = 95, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.2828185 0.2828185
## sample estimates:
## mean of x
## 2.337896e-17terpenuhi
# 2 Sisaan saling bebas
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(randtests)
runs.test(model_reg$residuals) #asumsi sisaan saling bebas terpenuhi##
## Runs Test
##
## data: model_reg$residuals
## statistic = -1.8469, runs = 40, n1 = 48, n2 = 48, n = 96, p-value =
## 0.06477
## alternative hypothesis: nonrandomnessterpenuhi
# 3 Ragam sisaan homogen
library(lmtest)
bptest(model_reg)##
## studentized Breusch-Pagan test
##
## data: model_reg
## BP = 10.402, df = 5, p-value = 0.06461terpenuhi
# ASUMSI NORMALITAS SISAAN
shapiro.test(model_reg$residuals)##
## Shapiro-Wilk normality test
##
## data: model_reg$residuals
## W = 0.96836, p-value = 0.02019nortest::ad.test(model_reg$residuals)##
## Anderson-Darling normality test
##
## data: model_reg$residuals
## A = 0.78116, p-value = 0.04116asumsi normalitas terpenuhi
# Multikolinearitas
car::vif(model_reg)## X1 X2 X3 X4 X5
## 1.241477 1.027043 1.798745 1.929327 1.322506VIF<10, tidak ada multikolinearitas
Regresi Stepwise
model_stepwise <- MASS::stepAIC(model_reg, direction="both")## Start: AIC=75.02
## Y ~ X1 + X2 + X3 + X4 + X5
##
## Df Sum of Sq RSS AIC
## - X1 1 2.235 187.32 74.175
## - X2 1 2.727 187.82 74.427
## - X5 1 3.891 188.98 75.020
## <none> 185.09 75.023
## - X4 1 6.633 191.72 76.403
## - X3 1 99.126 284.21 114.196
##
## Step: AIC=74.18
## Y ~ X2 + X3 + X4 + X5
##
## Df Sum of Sq RSS AIC
## - X5 1 2.196 189.52 73.294
## - X2 1 3.377 190.70 73.890
## <none> 187.32 74.175
## + X1 1 2.235 185.09 75.023
## - X4 1 6.269 193.59 75.335
## - X3 1 101.253 288.58 113.659
##
## Step: AIC=73.29
## Y ~ X2 + X3 + X4
##
## Df Sum of Sq RSS AIC
## - X2 1 3.578 193.10 73.089
## <none> 189.52 73.294
## - X4 1 4.836 194.35 73.713
## + X5 1 2.196 187.32 74.175
## + X1 1 0.540 188.98 75.020
## - X3 1 103.765 293.29 113.212
##
## Step: AIC=73.09
## Y ~ X3 + X4
##
## Df Sum of Sq RSS AIC
## <none> 193.10 73.089
## + X2 1 3.578 189.52 73.294
## + X5 1 2.396 190.70 73.890
## - X4 1 5.740 198.84 73.901
## + X1 1 0.817 192.28 74.682
## - X3 1 102.701 295.80 112.032best_model <- summary(model_stepwise)Uji Asumsi
# Asumsi GAUSS MARKOV
# 1 Nilai harapan sisaan sama dengan nol
t.test(model_stepwise$residuals,
mu = 0,
conf.level = 0.95) #asumsi nilai harapan sama dengan 0 terpenuhi##
## One Sample t-test
##
## data: model_stepwise$residuals
## t = 4.471e-16, df = 95, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.2888724 0.2888724
## sample estimates:
## mean of x
## 6.505665e-17terpenuhi
# 2 Sisaan saling bebas
library(lmtest)
library(randtests)
runs.test(model_stepwise$residuals) #asumsi sisaan saling bebas terpenuhi##
## Runs Test
##
## data: model_stepwise$residuals
## statistic = -2.0521, runs = 39, n1 = 48, n2 = 48, n = 96, p-value =
## 0.04016
## alternative hypothesis: nonrandomnessterpenuhi
# 3 Ragam sisaan homogen
library(lmtest)
bptest(model_stepwise)##
## studentized Breusch-Pagan test
##
## data: model_stepwise
## BP = 6.0411, df = 2, p-value = 0.04878terpenuhi
# ASUMSI NORMALITAS SISAAN
shapiro.test(model_stepwise$residuals)##
## Shapiro-Wilk normality test
##
## data: model_stepwise$residuals
## W = 0.97495, p-value = 0.06264nortest::ad.test(model_stepwise$residuals)##
## Anderson-Darling normality test
##
## data: model_stepwise$residuals
## A = 0.72783, p-value = 0.05586asumsi normalitas terpenuhi
# Multikolinearitas
car::vif(model_stepwise)## X3 X4
## 1.782551 1.782551tidak ada multikol
Evaluasi Model
preds_reg <- predict(model_stepwise, newdata = testing_data)
# Package Metrics
# install.packages("Metrics")
MAE<-Metrics::mae(testing_data$Y, preds_reg)
MSE<-Metrics::mse(testing_data$Y, preds_reg)
RMSE<-Metrics::rmse(testing_data$Y, preds_reg)
MAPE<-Metrics::mape(testing_data$Y, preds_reg)*100
print(paste("MAE:", MAE))## [1] "MAE: 1.51049841843366"print(paste("MSE:", MSE))## [1] "MSE: 4.06428413333408"print(paste("RMSE:", RMSE))## [1] "RMSE: 2.01600697750134"print(paste("MAPE:", MAPE))## [1] "MAPE: 10.7251890322102"# Hitung R-squared
r_squared <- 1 - sum((preds_reg - testing_data$Y)^2) / sum((testing_data$Y - mean(testing_data$Y))^2)
print(paste("R-squared:", r_squared))## [1] "R-squared: 0.448767949592585"