#Nomor 1
#PACKAGE#
library(stats)
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
library(lmtest)
## Warning: package 'lmtest' was built under R version 4.5.2
## 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(zoo)
#MEMANGGIL DATA
data=read.table(file.choose(),header=TRUE)
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
summary(data)
## Petak Y X1 X2
## Min. : 1.00 Min. :34.20 Min. :100.0 Min. :140.0
## 1st Qu.: 3.75 1st Qu.:38.92 1st Qu.:127.5 1st Qu.:177.5
## Median : 6.50 Median :41.60 Median :155.0 Median :200.0
## Mean : 6.50 Mean :42.02 Mean :155.0 Mean :200.0
## 3rd Qu.: 9.25 3rd Qu.:44.90 3rd Qu.:182.5 3rd Qu.:222.5
## Max. :12.00 Max. :49.70 Max. :210.0 Max. :260.0
#SCATTER PLOT
plot(data$X1, data$Y, xlab="Dosis Pupuk (kg/ha)",ylab="Hasil Panen Padi (kuintal/ha)",
main="Scatter Plot Dosis Pupuk dan Hasil Panen Padi")
abline(lm(data$Y~data$X1),col="lightpink",lwd=3)
plot(data$X2, data$Y, xlab="Curah Hujan (mm/bulan)",ylab="Hasil Panen Padi (kuintal/ha)",
main="Scatter Plot Curah Hujan dan Hasil Panen Padi")
abline(lm(data$Y~data$X2),col="lightpink",lwd=3)
#RLB
reg=lm(formula=Y~X1+X2, data=data)
summary(reg)
##
## 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
#<10
vif(reg)
## X1 X2
## 2.983051 2.983051
#PENGUJIAN ASUMSI
bptest(reg,varformula=~fitted.values(reg), studentize=F)
##
## Breusch-Pagan test
##
## data: reg
## BP = 0.2226, df = 1, p-value = 0.6371
dwtest(reg, alternative='two.sided')
##
## Durbin-Watson test
##
## data: reg
## DW = 2.0988, p-value = 0.9478
## alternative hypothesis: true autocorrelation is not 0
shapiro.test(resid(reg))
##
## Shapiro-Wilk normality test
##
## data: resid(reg)
## W = 0.92837, p-value = 0.3631
#Nomor 2
#MEMBENTUK MATRIKS Y DAN X
Y=as.matrix(data$Y)
X=cbind(1, data$X1, data$X2)
#JUMLAH OBSERVASI (n) DAN JUMLAH VARIABEL BEBAS (k)
n=nrow(X)
k=ncol(X)-1
n
## [1] 12
k
## [1] 2
#b=(X'X)^-1 X'Y
b.topi=solve(t(X) %*% X) %*% t(X) %*% Y
b.topi
## [,1]
## [1,] 16.96175938
## [2,] 0.07860495
## [3,] 0.06439736
#TAHAPAN PERHITUNGAN KOEFISIEN DETERMINASI (R^2)
#a. Nilai dugaan Y
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
#b. Jumlah Kuadrat Total
JKT=sum((Y-mean(Y))^2)
JKT
## [1] 283.1825
#c. Jumlah Kuadrat Regresi
JKR=sum((Y.topi-mean(Y))^2)
JKR
## [1] 266.5227
#d. Jumlah Kuadrat Galat
JKG=sum((Y-Y.topi)^2)
JKG
## [1] 16.65977
#e.JKT
JKR+JKG
## [1] 283.1825
#f. Koefisien Determinasi (R^2) = JKR/JKT#
R2=JKR/JKT
R2
## [1] 0.9411695
#UJI F
#F = (R^2/k) / ((1-R^2)/(n-k-1))
F_hitung=(R2/k)/((1-R2)/(n-k-1))
F_hitung
## [1] 71.99094
#NILAI F TABEL
df1=k
df2=n-k-1
alpha=0.05
f_tabel=qf(alpha, df1, df2, lower.tail=FALSE)
f_tabel
## [1] 4.256495
#KEPUTUSAN
F_hitung > f_tabel
## [1] TRUE