library(ggplot2)
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(car)
## Loading required package: carData
library(zoo)
library(nortest)
# Input Data
data <- read.table(file.choose(), header = TRUE)
data
## Y X1 X2 X3
## 1 57.5 78 2.75 29.5
## 2 52.8 69 2.15 26.3
## 3 61.3 77 4.41 32.2
## 4 67.0 88 5.52 36.5
## 5 53.5 67 3.21 27.2
## 6 62.7 80 4.32 27.7
## 7 56.2 74 2.31 28.3
## 8 68.5 94 4.30 30.3
## 9 69.2 102 3.71 28.7
# Visualisasi hubungan antara X1 dan Y
ggplot(data = data, mapping = aes(X1, Y)) +
geom_point(size = 3, colour = "green") +
geom_smooth(
method = "lm",
se = FALSE,
colour = "red",
linetype = "dashed"
) +
ggtitle("Hubungan antara X1 dan Y") +
xlab("Variabel X1") +
ylab("Variabel Y") +
scale_x_continuous(breaks = seq(65, 105, by = 5)) +
scale_y_continuous(breaks = seq(52, 70, by = 2)) +
theme_classic()
## `geom_smooth()` using formula = 'y ~ x'
# Visualisasi hubungan antara X2 dan Y
ggplot(data = data, aes(x = X2, y = Y)) +
geom_point(colour = "green", size = 3) +
geom_smooth(
method = "lm",
se = FALSE,
colour = "red",
linetype = "dashed"
) +
ggtitle("Hubungan antara X2 dan Y") +
xlab("Variabel X2") +
ylab("Variabel Y") +
scale_x_continuous(breaks = seq(2, 6, by = 0.5)) +
scale_y_continuous(breaks = seq(52, 70, by = 2)) +
theme_classic()
## `geom_smooth()` using formula = 'y ~ x'
# Visualisasi hubungan antara X3 dan Y
ggplot(data = data, aes(x = X3, y = Y)) +
geom_point(colour = "green", size = 3) +
geom_smooth(
method = "lm",
se = FALSE,
colour = "red",
linetype = "dashed"
) +
ggtitle("Hubungan antara X3 dan Y") +
xlab("Variabel X3") +
ylab("Variabel Y") +
scale_x_continuous(breaks = seq(26, 37, by = 1)) +
scale_y_continuous(breaks = seq(52, 70, by = 2)) +
theme_classic()
## `geom_smooth()` using formula = 'y ~ x'
# REGRESI LINIER SEDERHANA (RLS)
# --- Model Regresi Y terhadap X1 ---
model_rls1 <- lm(formula = Y ~ X1, data = data)
# Menampilkan hasil regresi
summary(model_rls1)
##
## Call:
## lm(formula = Y ~ X1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6440 -1.9128 -0.2151 2.2513 2.4075
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.01108 5.42272 3.506 0.009915 **
## X1 0.51797 0.06635 7.807 0.000106 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.174 on 7 degrees of freedom
## Multiple R-squared: 0.897, Adjusted R-squared: 0.8823
## F-statistic: 60.95 on 1 and 7 DF, p-value: 0.0001065
# --- UJI ASUMSI KLASIK ---
# Uji Heteroskedastisitas Breusch-Pagan
bptest(model_rls1)
##
## studentized Breusch-Pagan test
##
## data: model_rls1
## BP = 1.715, df = 1, p-value = 0.1903
# Uji Heteroskedastisitas Metode Glejser
residual1 <- residuals(model_rls1)
abs_residual1 <- abs(residual1)
# Menampilkan nilai absolut residual
abs_residual1
## 1 2 3 4 5 6 7 8
## 1.9127561 1.9510242 2.4052142 2.4075419 0.2150838 2.2513035 1.1408752 0.7997207
## 9
## 2.6440410
model_glejser1 <- lm(abs_residual1 ~ X1, data = data)
summary(model_glejser1)
##
## Call:
## lm(formula = abs_residual1 ~ X1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3200 -0.4062 0.2952 0.5324 0.7722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.57193 2.04979 -0.279 0.788
## X1 0.02864 0.02508 1.142 0.291
##
## Residual standard error: 0.8219 on 7 degrees of freedom
## Multiple R-squared: 0.157, Adjusted R-squared: 0.03657
## F-statistic: 1.304 on 1 and 7 DF, p-value: 0.2911
# Uji Autokorelasi Durbin-Watson
dwtest(model_rls1)
##
## Durbin-Watson test
##
## data: model_rls1
## DW = 1.785, p-value = 0.2872
## alternative hypothesis: true autocorrelation is greater than 0
# Uji Autokorelasi Breusch-Godfrey
bgtest(model_rls1)
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model_rls1
## LM test = 0.033549, df = 1, p-value = 0.8547
# Uji Normalitas Residual Shapiro-Wilk
shapiro.test(residuals(model_rls1))
##
## Shapiro-Wilk normality test
##
## data: residuals(model_rls1)
## W = 0.87986, p-value = 0.1565
# REGRESI LINIER SEDERHANA: Y terhadap X2
# Membentuk model regresi
model_rls2 <- lm(formula = Y ~ X2, data = data)
# Menampilkan ringkasan hasil regresi
summary(model_rls2)
##
## Call:
## lm(formula = Y ~ X2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.6496 -2.1172 -1.2392 0.9339 7.8929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.298 5.254 8.621 5.64e-05 ***
## X2 4.315 1.390 3.105 0.0172 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.394 on 7 degrees of freedom
## Multiple R-squared: 0.5793, Adjusted R-squared: 0.5192
## F-statistic: 9.64 on 1 and 7 DF, p-value: 0.0172
# --- UJI ASUMSI KLASIK ---
# Uji Heteroskedastisitas Breusch-Pagan
bptest(model_rls2)
##
## studentized Breusch-Pagan test
##
## data: model_rls2
## BP = 0.072359, df = 1, p-value = 0.7879
# Uji Heteroskedastisitas Metode Glejser
residual2 <- residuals(model_rls2)
abs_residual2 <- abs(residual2)
# Menampilkan nilai absolut residual
abs_residual2
## 1 2 3 4 5 6 7 8
## 0.3353100 1.7757020 3.0275565 2.1171842 5.6495807 1.2392084 0.9339012 4.6470912
## 9
## 7.8929294
model_glejser2 <- lm(abs_residual2 ~ X2, data = data)
summary(model_glejser2)
##
## Call:
## lm(formula = abs_residual2 ~ X2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3452 -1.7837 -0.6405 1.2837 4.7895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.4690 3.1460 0.467 0.655
## X2 0.4406 0.8321 0.529 0.613
##
## Residual standard error: 2.631 on 7 degrees of freedom
## Multiple R-squared: 0.03851, Adjusted R-squared: -0.09885
## F-statistic: 0.2804 on 1 and 7 DF, p-value: 0.6128
# Uji Autokorelasi Durbin-Watson
dwtest(model_rls2)
##
## Durbin-Watson test
##
## data: model_rls2
## DW = 0.50193, p-value = 0.002713
## alternative hypothesis: true autocorrelation is greater than 0
# Uji Autokorelasi Breusch-Godfrey
bgtest(model_rls2)
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model_rls2
## LM test = 5.4817, df = 1, p-value = 0.01922
# Uji Normalitas Residual Shapiro-Wilk
shapiro.test(residuals(model_rls2))
##
## Shapiro-Wilk normality test
##
## data: residuals(model_rls2)
## W = 0.93927, p-value = 0.5742
# REGRESI LINIER SEDERHANA: Y terhadap X3
# Membentuk model regresi linier sederhana
model_rls3 <- lm(formula = Y ~ X3, data = data)
# Menampilkan hasil ringkasan model
summary(model_rls3)
##
## Call:
## lm(formula = Y ~ X3, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.693 -3.315 -2.592 3.937 9.297
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.1873 18.9650 1.434 0.195
## X3 1.1399 0.6369 1.790 0.117
##
## Residual standard error: 5.611 on 7 degrees of freedom
## Multiple R-squared: 0.314, Adjusted R-squared: 0.216
## F-statistic: 3.204 on 1 and 7 DF, p-value: 0.1166
# --- UJI ASUMSI KLASIK ---
# Uji Heteroskedastisitas Breusch-Pagan
bptest(model_rls3)
##
## studentized Breusch-Pagan test
##
## data: model_rls3
## BP = 0.62733, df = 1, p-value = 0.4283
# Uji Heteroskedastisitas dengan Metode Glejser
residual3 <- residuals(model_rls3)
abs_residual3 <- abs(residual3)
# Menampilkan nilai absolut residual
abs_residual3
## 1 2 3 4 5 6 7 8
## 3.314678 4.366959 2.592442 1.794065 4.692880 3.937164 3.246783 6.773392
## 9
## 9.297252
model_glejser3 <- lm(abs_residual3 ~ X3, data = data)
summary(model_glejser3)
##
## Call:
## lm(formula = abs_residual3 ~ X3, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6039 -1.0955 -1.0751 -0.4915 4.5679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.4360 7.5924 1.77 0.120
## X3 -0.3034 0.2550 -1.19 0.273
##
## Residual standard error: 2.246 on 7 degrees of freedom
## Multiple R-squared: 0.1682, Adjusted R-squared: 0.0494
## F-statistic: 1.416 on 1 and 7 DF, p-value: 0.2729
# Uji Autokorelasi Durbin-Watson
dwtest(model_rls3)
##
## Durbin-Watson test
##
## data: model_rls3
## DW = 1.117, p-value = 0.08255
## alternative hypothesis: true autocorrelation is greater than 0
# Uji Autokorelasi Breusch-Godfrey
bgtest(model_rls3)
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model_rls3
## LM test = 0.80317, df = 1, p-value = 0.3701
# Uji Normalitas Residual Shapiro-Wilk
shapiro.test(residuals(model_rls3))
##
## Shapiro-Wilk normality test
##
## data: residuals(model_rls3)
## W = 0.81761, p-value = 0.03238
# 3. REGRESI LINIER BERGANDA (RLB)
# Estimasi Parameter & Uji Hipotesis RLB
Reg <- lm(Y ~ X1 + X2 + X3, data = data)
summary(Reg)
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3, data = data)
##
## Residuals:
## 1 2 3 4 5 6 7 8 9
## -0.2981 -0.2142 0.4714 -0.4746 -0.9524 0.4761 0.9274 0.7466 -0.6823
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.87353 4.07389 5.369 0.00302 **
## X1 0.41277 0.03067 13.460 4.05e-05 ***
## X2 2.20267 0.47199 4.667 0.00550 **
## X3 -0.07895 0.15551 -0.508 0.63330
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8484 on 5 degrees of freedom
## Multiple R-squared: 0.9888, Adjusted R-squared: 0.9821
## F-statistic: 147.1 on 3 and 5 DF, p-value: 2.696e-05
# Deteksi Multikolinearitas
vif(Reg)
## X1 X2 X3
## 1.403219 3.093549 2.607991
# Uji Asumsi Klasik RLB
# Uji Heteroskedastisitas
bptest(Reg)
##
## studentized Breusch-Pagan test
##
## data: Reg
## BP = 0.52402, df = 3, p-value = 0.9136
# Uji Autokorelasi
dwtest(Reg)
##
## Durbin-Watson test
##
## data: Reg
## DW = 1.6446, p-value = 0.1165
## alternative hypothesis: true autocorrelation is greater than 0
# Uji Autokorelasi
bgtest(Reg)
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: Reg
## LM test = 0.51249, df = 1, p-value = 0.4741
# Uji Normalitas Residual
shapiro.test(resid(Reg))
##
## Shapiro-Wilk normality test
##
## data: resid(Reg)
## W = 0.93208, p-value = 0.5014