TmKomstat

#Soal 1
#PACKAGE
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
data=read.table(file.choose(), header=T)
data

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

#SCATTER PLOT Y DAN X1
ggplot(data, aes(x = X1, y = Y)) +
  geom_point(color = "hotpink", size = 2) +
  geom_smooth(method = "lm", se = FALSE,
              color = "springgreen4", linewidth = 1.2) +
  ggtitle("Scatter Plot Antara X1 dan Y") +
  ylab("Y") +
  xlab("X1") +
  theme(plot.title = element_text(hjust = 0.5))

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

#SCATTER PLOT Y DAN X2
ggplot(data, aes(x = X2, y = Y)) +
  geom_point(color = "hotpink", size = 2) +
  geom_smooth(method = "lm", se = FALSE,
              color = "springgreen4", linewidth = 1.2) +
  ggtitle("Scatter Plot Antara X2 dan Y") +
  ylab("Y") +
  xlab("X2") +
  theme(plot.title = element_text(hjust = 0.5))

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

#REGRESI LINIER BERGANDA
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

#PENDETEKSIAN MULTIKOLINIERITAS
#VIF < 10
vif(model)

##       X1       X2 
## 2.983051 2.983051

#PENGUJIAN ASUMSI
bptest(model,varformula=~fitted.values(model), studentize=FALSE)

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

dwtest(model,alternative='two.sided')

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

shapiro.test(resid(model))

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

n<-nrow(data)
X<-cbind(1,data$X1,data$X2)
Y<-as.matrix(data$Y)
k<-ncol(X)
b.topi<-solve(t(X)%*%X)%*%t(X)%*%Y
#Koefisien determinasi
Y.topi<-X %*% b.topi
Y.topi

##           [,1]
##  [1,] 33.83789
##  [2,] 37.19983
##  [3,] 36.05396
##  [4,] 40.05988
##  [5,] 38.91400
##  [6,] 42.91992
##  [7,] 41.77405
##  [8,] 45.77997
##  [9,] 43.99012
## [10,] 46.70809
## [11,] 49.42606
## [12,] 47.63622

JKT<-sum((Y-mean(Y))^2)
JKT

## [1] 283.1825

JKR<-sum((Y.topi-mean(Y))^2)
JKR

## [1] 266.5227

R2<-JKR/JKT
R2

## [1] 0.9411695

#Uji F dengan matriks
F_hitung<-(R2/(k-1))/((1-R2)/(n-k))
F_hitung

## [1] 71.99094

#Nilai f tabel
df1<-k-1
df2<-n-k
f_tabel<-qf(0.05,df1,df2,lower.tail = F)
f_tabel

## [1] 4.256495