TM KOMSTAT

# PACKAGE YANG DIBUTUHKAN
library(lmtest)

## Warning: package 'lmtest' was built under R version 4.5.3

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 4.5.3

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.5.3

library(car)

## Warning: package 'car' was built under R version 4.5.3

## Loading required package: carData

## Warning: package 'carData' was built under R version 4.5.3

# MEMANGGIL DATA DARI FILE EKSTERNAL (PILIH FILE DATA ANDA)
data = read.table(file.choose(), header = TRUE)
data

##       Y  X1  X2
## 1  34.4 100 140
## 2  38.7 110 180
## 3  34.2 120 150
## 4  41.7 130 200
## 5  39.0 140 170
## 6  41.5 150 220
## 7  40.9 160 190
## 8  44.0 170 240
## 9  43.9 180 200
## 10 47.6 190 230
## 11 49.7 200 260
## 12 48.7 210 220

# 1. SCATTER PLOT ANTARA Y DENGAN X1
ggplot(data, aes(x = X1, y = Y)) +
  geom_point(color = "darkorchid", size = 2) +
  geom_smooth(method = "lm", se = FALSE, color = "navy", linewidth = 1.2) +
  ggtitle("Scatter Plot Antara Dosis Pupuk dan Hasil Panen Padi") +
  ylab("Hasil Panen Padi (kuintal/ha)") +
  xlab("Dosis Pupuk (kg/ha)") +
  theme(plot.title = element_text(hjust = 0.5))

## `geom_smooth()` using formula = 'y ~ x'

# 1. SCATTER PLOT ANTARA Y DENGAN X2
ggplot(data, aes(x = X2, y = Y)) +
  geom_point(color = "darkorchid", size = 2) +
  geom_smooth(method = "lm", se = FALSE, color = "navy", linewidth = 1.2) +
  ggtitle("Scatter Plot Antara Curah Hujan dan Hasil Panen Padi") +
  ylab("Hasil Panen Padi (kuintal/ha)") +
  xlab("Curah Hujan (mm/bulan)") +
  theme(plot.title = element_text(hjust = 0.5))

## `geom_smooth()` using formula = 'y ~ x'

# 1b. ANALISIS REGRESI LINIER BERGANDA & ESTIMASI PARAMETER
model = lm(Y ~ X1 + X2, data = data)
summary(model)

## 
## Call:
## lm(formula = Y ~ X1 + X2, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8540 -1.0105  0.1800  0.9349  1.6401 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 16.96176    2.30605   7.355  4.3e-05 ***
## X1           0.07860    0.01965   4.000  0.00311 ** 
## X2           0.06440    0.01958   3.289  0.00940 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.361 on 9 degrees of freedom
## Multiple R-squared:  0.9412, Adjusted R-squared:  0.9281 
## F-statistic: 71.99 on 2 and 9 DF,  p-value: 2.905e-06

# 1c. PENDETEKSIAN MULTIKOLINIERITAS (VIF < 10)
vif(model)

##       X1       X2 
## 2.983051 2.983051

# 1c. PENGUJIAN ASUMSI KLASIK
# Uji Heteroskedastisitas (Breusch-Pagan)
bptest(model, varformula = ~fitted.values(model), studentize = FALSE)

## 
##  Breusch-Pagan test
## 
## data:  model
## BP = 0.2226, df = 1, p-value = 0.6371

# Uji Autokorelasi (Durbin-Watson)
dwtest(model, alternative = "two.sided")

## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.0988, p-value = 0.9478
## alternative hypothesis: true autocorrelation is not 0

# Uji Normalitas Residual (Shapiro-Wilk)
shapiro.test(resid(model))

## 
##  Shapiro-Wilk normality test
## 
## data:  resid(model)
## W = 0.92837, p-value = 0.3631

# 2. UJI F MANUAL / MATRIKS SESUAI SOAL NOMOR 2
n = nrow(data)
k = length(coef(model))

# Koefisien Determinasi
JKT = sum((data$Y - mean(data$Y))^2)
JKR = sum((fitted(model) - mean(data$Y))^2)
R2 = JKR / JKT
cat("Koefisien Determinasi (R^2):", R2, "\n")

## Koefisien Determinasi (R^2): 0.9411695

# Statistik Uji F Hitung
F_hitung = (R2 / (k - 1)) / ((1 - R2) / (n - k))
cat("F Hitung:", F_hitung, "\n")

## F Hitung: 71.99094

# Nilai F Tabel pada taraf signifikansi 5% (alpha = 0.05)
df1 = k - 1
df2 = n - k
f_tabel = qf(0.05, df1, df2, lower.tail = FALSE)
cat("F Tabel:", f_tabel, "\n")

## F Tabel: 4.256495