REGRESI PCA
NUR AISYAH
2023-12-14
Analisis Regresi Linier Berganda
#install.packages("readxl")
library(readxl) #Memasukkan Data ke R (Excel)
Data <- read_excel("D:/STATISTIKA 2021/SEMESTER 5/DATA MINING/Pertumbuhan Ekonomi SS.xlsx")
View(Data)
str(Data)## tibble [32 × 5] (S3: tbl_df/tbl/data.frame)
## $ PertumbuhanEkonomi : num [1:32] 24407 25836 26565 27807 26831 ...
## $ Ekspor : num [1:32] 15444 18961 19065 19400 20312 ...
## $ Investasi : num [1:32] 6070 5997 6695 7165 4577 ...
## $ KonsumsiRT : num [1:32] 11920 12058 12361 12394 12415 ...
## $ PengeluaranPemerintah: num [1:32] 1388 2083 2268 3244 1265 ...dim(Data)## [1] 32 5#Histogram Peubah Respons dan Peubah Penjelas
#install.packages("RColorBrewer")
library(RColorBrewer) #Warna Histogram
display.brewer.all()
hist(Data$PertumbuhanEkonomi, las=1, breaks=8,
main = "Histogram Pertumbuhan Ekonomi",
xlab = "Miliar",
ylab = "Frekuensi",
border = "black",
col = brewer.pal(n = 10, name = "RdBu"))
hist(Data$Ekspor, las=1, breaks=8,
main = "Histogram Ekspor",
xlab = "Miliar",
ylab = "Frekuensi",
border = "black",
col = brewer.pal(n = 10, name = "Set3"))
hist(Data$Investasi, las=1, breaks=8,
main = "Histogram Investasi",
xlab = "Miliar",
ylab = "Frekuensi",
border = "black",
col = brewer.pal(n = 10, name = "Paired"))
hist(Data$KonsumsiRT, las=1, breaks=8,
main = "Histogram Konsumsi Rumah Tangga",
xlab = "Miliar",
ylab = "Frekuensi",
border = "black",
col = brewer.pal(n = 10, name = "RdBu"))
hist(Data$PengeluaranPemerintah, las=1, breaks=8,
main = "Histogram Pengeluaran Pemerintah",
xlab = "Miliar",
ylab = "Frekuensi",
border = "black",
col = brewer.pal(n = 10, name = "PRGn"))
boxplot(Data, las=1,
ylab="Miliar", xlab="Peubah",
main = "Boxplot Peubah Respons dan Peubah Penjelas")
# Plot Peubah Respons dengan Peubah Penjelas
plot(Data$Ekspor, Data$PertumbuhanEkonomi, type="p",
main = "Plot antara Pertumbuhan Ekonomi dan Ekspor (Miliar)")
plot(Data$Investasi, Data$PertumbuhanEkonomi, type="p",
main = "Plot antara Pertumbuhan Ekonomi dan Investasi (Miliar)")
plot(Data$KonsumsiRT, Data$PertumbuhanEkonomi, type="p",
main = "Plot antara Pertumbuhan Ekonomi dan Konsumsi Rumah Tangga (Miliar)")
plot(Data$PengeluaranPemerintah, Data$PertumbuhanEkonomi, type="p",
main = "Plot antara Pertumbuhan Ekonomi dan Pengeluaran Pemerintah (Miliar)")
summary(Data)## PertumbuhanEkonomi Ekspor Investasi KonsumsiRT
## Min. :24407 Min. :15444 Min. : 4577 Min. :11920
## 1st Qu.:29102 1st Qu.:20191 1st Qu.: 6549 1st Qu.:12937
## Median :31706 Median :22804 Median : 7291 Median :14045
## Mean :31895 Mean :22845 Mean : 7249 Mean :14168
## 3rd Qu.:34815 3rd Qu.:25492 3rd Qu.: 7957 3rd Qu.:15278
## Max. :38420 Max. :29358 Max. :10047 Max. :16632
## PengeluaranPemerintah
## Min. :1265
## 1st Qu.:1735
## Median :2311
## Mean :2502
## 3rd Qu.:3192
## Max. :4059cor(Data)## PertumbuhanEkonomi Ekspor Investasi KonsumsiRT
## PertumbuhanEkonomi 1.0000000 0.9468991 0.5139441 0.9898244
## Ekspor 0.9468991 1.0000000 0.3243939 0.9450304
## Investasi 0.5139441 0.3243939 1.0000000 0.5045237
## KonsumsiRT 0.9898244 0.9450304 0.5045237 1.0000000
## PengeluaranPemerintah 0.3854982 0.2415247 0.7759085 0.3446699
## PengeluaranPemerintah
## PertumbuhanEkonomi 0.3854982
## Ekspor 0.2415247
## Investasi 0.7759085
## KonsumsiRT 0.3446699
## PengeluaranPemerintah 1.0000000# Korelasi Peubah Respons dengan Peubah Penjelas
cor.test (Data$Ekspor, Data$PertumbuhanEkonomi)##
## Pearson's product-moment correlation
##
## data: Data$Ekspor and Data$PertumbuhanEkonomi
## t = 16.13, df = 30, p-value = 2.504e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8930807 0.9739998
## sample estimates:
## cor
## 0.9468991cor.test (Data$Investasi, Data$PertumbuhanEkonomi)##
## Pearson's product-moment correlation
##
## data: Data$Investasi and Data$PertumbuhanEkonomi
## t = 3.2815, df = 30, p-value = 0.002622
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2013304 0.7315395
## sample estimates:
## cor
## 0.5139441cor.test (Data$KonsumsiRT, Data$PertumbuhanEkonomi)##
## Pearson's product-moment correlation
##
## data: Data$KonsumsiRT and Data$PertumbuhanEkonomi
## t = 38.1, df = 30, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9790429 0.9950731
## sample estimates:
## cor
## 0.9898244cor.test (Data$PengeluaranPemerintah, Data$PertumbuhanEkonomi)##
## Pearson's product-moment correlation
##
## data: Data$PengeluaranPemerintah and Data$PertumbuhanEkonomi
## t = 2.2883, df = 30, p-value = 0.02934
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.04251973 0.64719554
## sample estimates:
## cor
## 0.3854982# Korelasi Antar Peubah Penjelas
cor(as.matrix(Data[,c("Ekspor","Investasi", "KonsumsiRT","PengeluaranPemerintah")]))## Ekspor Investasi KonsumsiRT PengeluaranPemerintah
## Ekspor 1.0000000 0.3243939 0.9450304 0.2415247
## Investasi 0.3243939 1.0000000 0.5045237 0.7759085
## KonsumsiRT 0.9450304 0.5045237 1.0000000 0.3446699
## PengeluaranPemerintah 0.2415247 0.7759085 0.3446699 1.0000000# Analisis Regresi Berganda
Model_ARLB <- lm (PertumbuhanEkonomi ~ Ekspor + Investasi + KonsumsiRT + PengeluaranPemerintah, data=Data)
summary (Model_ARLB)##
## Call:
## lm(formula = PertumbuhanEkonomi ~ Ekspor + Investasi + KonsumsiRT +
## PengeluaranPemerintah, data = Data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1152.85 -204.86 50.33 316.81 858.18
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.990e+03 1.312e+03 -2.279 0.0308 *
## Ekspor 1.594e-01 9.108e-02 1.750 0.0914 .
## Investasi -9.160e-03 1.668e-01 -0.055 0.9566
## KonsumsiRT 2.161e+00 2.589e-01 8.347 5.89e-09 ***
## PengeluaranPemerintah 2.763e-01 1.612e-01 1.714 0.0980 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 496.4 on 27 degrees of freedom
## Multiple R-squared: 0.9845, Adjusted R-squared: 0.9822
## F-statistic: 428.3 on 4 and 27 DF, p-value: < 2.2e-16# Uji Asumsi Klasik
#install.packages("performance")
library(performance)
# Uji Normalitas
check_normality(Model_ARLB)## OK: residuals appear as normally distributed (p = 0.255).# Uji Heteroskedastisitas
check_heteroscedasticity(Model_ARLB)## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.010).# Uji Multikolinieritas
multicollinearity(Model_ARLB)## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## Investasi 4.11 [ 2.67, 6.82] 2.03 0.24
## PengeluaranPemerintah 2.67 [ 1.83, 4.36] 1.63 0.38
## Tolerance 95% CI
## [0.15, 0.38]
## [0.23, 0.55]
##
## High Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## Ekspor 13.90 [ 8.37, 23.57] 3.73 0.07 [0.04, 0.12]
## KonsumsiRT 16.80 [10.07, 28.55] 4.10 0.06 [0.04, 0.10]# Uji Autokorelasi
check_autocorrelation(Model_ARLB)## Warning: Autocorrelated residuals detected (p < .001).# Cek Performa/Kinerja Model
model_performance(Model_ARLB,metrics = "all")## # Indices of model performance
##
## AIC | AICc | BIC | R2 | R2 (adj.) | RMSE | Sigma
## -------------------------------------------------------------------
## 494.643 | 498.003 | 503.438 | 0.984 | 0.982 | 455.939 | 496.364# Hasil Prediksi Model (y_dugaARLB)
y_dugaARLB <- predict(Model_ARLB)
y_dugaARLB## 1 2 3 4 5 6 7 8
## 25559.95 26612.30 27327.46 27719.54 27386.12 27826.94 28248.08 28627.45
## 9 10 11 12 13 14 15 16
## 28625.26 29074.28 29813.50 30256.38 30187.60 30561.75 31348.18 31667.47
## 17 18 19 20 21 22 23 24
## 31415.20 31921.87 32823.21 33344.30 32878.19 33748.02 34958.60 35064.54
## 25 26 27 28 29 30 31 32
## 34537.17 35607.88 36457.24 37139.89 36140.98 37152.21 38010.90 38603.36# Korelasi Antara Pertumbuhan Ekonomi dan Y Duga
cor.test (Data$PertumbuhanEkonomi, y_dugaARLB)##
## Pearson's product-moment correlation
##
## data: Data$PertumbuhanEkonomi and y_dugaARLB
## t = 43.63, df = 30, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9839397 0.9962314
## sample estimates:
## cor
## 0.9922119Analisis Komponen Utama
x <- data.matrix(Data[, c('Ekspor', 'Investasi', 'KonsumsiRT','PengeluaranPemerintah')])
head(x)## Ekspor Investasi KonsumsiRT PengeluaranPemerintah
## [1,] 15443.83 6070.14 11919.53 1388.04
## [2,] 18961.48 5996.57 12057.78 2083.34
## [3,] 19064.53 6694.59 12360.51 2267.53
## [4,] 19400.01 7164.88 12394.40 3243.64
## [5,] 20312.28 4576.75 12414.77 1265.14
## [6,] 20089.67 5706.60 12528.48 2137.20y <- Data$PertumbuhanEkonomi
head(y)## [1] 24407.10 25835.93 26564.60 27807.45 26831.47 28066.35model_coba <- lm (y~x)
summary (model_coba)##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1152.85 -204.86 50.33 316.81 858.18
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.990e+03 1.312e+03 -2.279 0.0308 *
## xEkspor 1.594e-01 9.108e-02 1.750 0.0914 .
## xInvestasi -9.160e-03 1.668e-01 -0.055 0.9566
## xKonsumsiRT 2.161e+00 2.589e-01 8.347 5.89e-09 ***
## xPengeluaranPemerintah 2.763e-01 1.612e-01 1.714 0.0980 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 496.4 on 27 degrees of freedom
## Multiple R-squared: 0.9845, Adjusted R-squared: 0.9822
## F-statistic: 428.3 on 4 and 27 DF, p-value: < 2.2e-16Pembentukan Komponen Utama
PCA <- prcomp (x, center=TRUE)
PCA## Standard deviations (1, .., p=4):
## [1] 3916.7451 1273.6103 500.4547 293.9267
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Ekspor 0.92927908 0.1862035 0.1671404 0.2717218
## Investasi 0.10668145 -0.7563804 -0.4698159 0.4424712
## KonsumsiRT 0.34723229 -0.1483787 -0.4463423 -0.8112904
## PengeluaranPemerintah 0.06700139 -0.6092625 0.7430449 -0.2686902summary (PCA)## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 3916.7451 1.274e+03 500.45472 293.92666
## Proportion of Variance 0.8868 9.376e-02 0.01448 0.00499
## Cumulative Proportion 0.8868 9.805e-01 0.99501 1.00000DataPCA <- PCA$x
View(DataPCA)
PC1 <- data.matrix(DataPCA[, c('PC1')])
head(PC1)## [,1]
## [1,] -7858.967
## [2,] -4503.346
## [3,] -4215.660
## [4,] -3776.565
## [5,] -3330.407
## [6,] -3318.826#PC2 <- data.matrix(DataPCA[, c('PC2')])
#head(PC2)Analisis Regresi Komponen Utama
Model_ARKU <- lm (y ~ PC1)
summary (Model_ARKU)##
## Call:
## lm(formula = y ~ PC1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2012.7 -668.1 232.3 864.5 1355.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.190e+04 1.757e+02 181.6 <2e-16 ***
## PC1 9.161e-01 4.557e-02 20.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 993.7 on 30 degrees of freedom
## Multiple R-squared: 0.9309, Adjusted R-squared: 0.9286
## F-statistic: 404.2 on 1 and 30 DF, p-value: < 2.2e-16# Uji Asumsi Klasik
# Package "performance"
#install.packages("performance")
library(performance)
# Uji Normalitas
check_normality(Model_ARKU)## OK: residuals appear as normally distributed (p = 0.051).# Uji Heteroskedastisitas
check_heteroscedasticity(Model_ARKU)## OK: Error variance appears to be homoscedastic (p = 0.402).# Uji Multikolinieritas
multicollinearity(Model_ARKU)## Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULL# Uji Autokorelasi
check_autocorrelation(Model_ARKU)## OK: Residuals appear to be independent and not autocorrelated (p = 0.066).# Cek Performa/Kinerja Model
model_performance(Model_ARKU,metrics = "all")## # Indices of model performance
##
## AIC | AICc | BIC | R2 | R2 (adj.) | RMSE | Sigma
## -------------------------------------------------------------------
## 536.442 | 537.299 | 540.839 | 0.931 | 0.929 | 962.190 | 993.746# Hasil Prediksi Model (y_dugaARLB)
y_dugaARKU <- predict(Model_ARKU)
y_dugaARKU## 1 2 3 4 5 6 7 8
## 24695.58 27769.67 28033.22 28435.47 28844.20 28854.80 27330.41 27745.72
## 9 10 11 12 13 14 15 16
## 29334.87 29446.59 29029.97 29583.29 31667.93 31630.44 30889.32 30306.07
## 17 18 19 20 21 22 23 24
## 31654.30 31695.56 32065.26 32262.37 32721.70 33382.46 36078.74 34441.15
## 25 26 27 28 29 30 31 32
## 35001.92 34466.13 36818.18 38192.51 36411.66 36110.72 37676.03 38069.56# Korelasi Antara Pertumbuhan Ekonomi dan Y Duga
cor.test (y, y_dugaARKU)##
## Pearson's product-moment correlation
##
## data: y and y_dugaARKU
## t = 20.104, df = 30, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9285209 0.9828608
## sample estimates:
## cor
## 0.9648317