#Soal1
#PACKAGE
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(ggplot2)
library(car)
## Loading required package: carData
#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 49.7 200 269
## 12 12 48.7 210 220
#SCATTER PLOT Y (Hasil Panen Padi) DAN X1 (Dosis Pupuk)
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 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'
#SCATTER PLOT Y (Hasil Panen Padi) DAN X2 (Curah Hujan)
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 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'
#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
## -1.92924 -0.97284 -0.00117 1.03601 1.70057
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.39287 2.21841 7.840 2.6e-05 ***
## X1 0.07918 0.01942 4.077 0.00277 **
## X2 0.06157 0.01862 3.307 0.00913 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.356 on 9 degrees of freedom
## Multiple R-squared: 0.9415, Adjusted R-squared: 0.9285
## F-statistic: 72.45 on 2 and 9 DF, p-value: 2.828e-06
#PENDETEKSIAN MULTIKOLINIERITAS
#VIF < 10
vif(model)
## X1 X2
## 2.930714 2.930714
#PENGUJIAN ASUMSI
#Uji Heteroskedastisitas
bptest(model,varformula=~fitted.values(model),studentize=FALSE)
##
## Breusch-Pagan test
##
## data: model
## BP = 0.32528, df = 1, p-value = 0.5685
dwtest(model,alternative='two.sided')
##
## Durbin-Watson test
##
## data: model
## DW = 2.283, p-value = 0.6963
## alternative hypothesis: true autocorrelation is not 0
shapiro.test(resid(model))
##
## Shapiro-Wilk normality test
##
## data: resid(model)
## W = 0.9462, p-value = 0.5822
#Soal2
#Mengubah data menjadi matriks
n<-nrow(data)
n
## [1] 12
k<-ncol(data)
k
## [1] 4
#Membuat matriks
x0<-as.matrix(rep(1,n))
x1<-as.matrix(data$X1)
x2<-as.matrix(data$X2)
X<-as.matrix(cbind(x0,x1,x2))
X
## [,1] [,2] [,3]
## [1,] 1 100 140
## [2,] 1 110 180
## [3,] 1 120 150
## [4,] 1 130 200
## [5,] 1 140 170
## [6,] 1 150 220
## [7,] 1 160 190
## [8,] 1 170 240
## [9,] 1 180 200
## [10,] 1 190 230
## [11,] 1 200 269
## [12,] 1 210 220
Y<-as.matrix(data$Y)
Y
## [,1]
## [1,] 34.4
## [2,] 38.7
## [3,] 34.2
## [4,] 41.7
## [5,] 39.0
## [6,] 41.5
## [7,] 40.9
## [8,] 44.0
## [9,] 43.9
## [10,] 47.6
## [11,] 49.7
## [12,] 48.7
#Penaksiran parameter dengan matriks
x.trans<-t(X)
a<-x.trans %*% X
a
## [,1] [,2] [,3]
## [1,] 12 1860 2409
## [2,] 1860 302600 385500
## [3,] 2409 385500 499161
a.inv<-solve(a)
a.inv
## [,1] [,2] [,3]
## [1,] 2.6746125391 0.0002525866 -0.0131030144
## [2,] 0.0002525866 0.0002049450 -0.0001594972
## [3,] -0.0131030144 -0.0001594972 0.0001884188
b<-x.trans %*% Y
b
## [,1]
## [1,] 504.3
## [2,] 80044.0
## [3,] 103154.3
b.topi<-a.inv %*% b
b.topi
## [,1]
## [1,] 17.39287316
## [2,] 0.07917565
## [3,] 0.06156862
#Membuat nama koefisien
var_names<-c("intercept","Beta_1","Beta_2")
#Membuat tabel hasil
hasil<-data.frame(
Estimate=as.numeric(b.topi),
row.names = var_names
)
print(hasil)
## Estimate
## intercept 17.39287316
## Beta_1 0.07917565
## Beta_2 0.06156862
#Membuat model regresi
model=lm(Y~X1+X2,data=data)
summary(model)
##
## Call:
## lm(formula = Y ~ X1 + X2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.92924 -0.97284 -0.00117 1.03601 1.70057
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.39287 2.21841 7.840 2.6e-05 ***
## X1 0.07918 0.01942 4.077 0.00277 **
## X2 0.06157 0.01862 3.307 0.00913 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.356 on 9 degrees of freedom
## Multiple R-squared: 0.9415, Adjusted R-squared: 0.9285
## F-statistic: 72.45 on 2 and 9 DF, p-value: 2.828e-06
#MEMBENTUK MATRIKS
Y <- as.matrix(data$Y)
X <- as.matrix(cbind(data$X1,data$X2))
X <- cbind(1,X)
n <- nrow(X)
k <- ncol(X)-1
#KOEFISIEN DETERMINASI
Y.topi <- X %*% b.topi
Y.topi
## [,1]
## [1,] 33.93005
## [2,] 37.18455
## [3,] 36.12924
## [4,] 39.99943
## [5,] 38.94413
## [6,] 42.81432
## [7,] 41.75902
## [8,] 45.62920
## [9,] 43.95821
## [10,] 46.59703
## [11,] 49.78996
## [12,] 47.56486
JKT <- sum((Y-mean(Y))^2)
JKT
## [1] 283.1825
JKR <- sum((Y.topi-mean(Y))^2)
JKR
## [1] 266.6224
R2 <- JKR/JKT
R2
## [1] 0.9415214
#UJI F DENGAN MATRIKS
F_hitung <- (R2/k)/((1-R2)/(n-k-1))
F_hitung
## [1] 72.45123
#NILAI F TABEL
df1 <- k
df2 <- n-k-1
f_tabel <- qf(0.05,df1,df2,lower.tail = FALSE)
f_tabel
## [1] 4.256495