library(moments)
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.4.3
## corrplot 0.95 loaded
library(GGally)
## Warning: package 'GGally' was built under R version 4.4.3
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.4.2
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
library(ggplot2)
library(tidyr)
## Warning: package 'tidyr' was built under R version 4.4.2
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.4.2
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(car)
## Warning: package 'car' was built under R version 4.4.3
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.4.3
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
library(readxl)
## Warning: package 'readxl' was built under R version 4.4.2
data <- read_excel("C:/Users/Raiqa/Downloads/Data Miskin Kak Bintang.xlsx")
# Lihat Data
head(data)
## # A tibble: 6 × 11
## `Nama Wilayah` P0 RLS PPK IPM UHH SNTS AIR TPT TPAK PDRB
## <chr> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 DKI JAKARTA NA <NA> NA NA NA NA NA NA NA NA
## 2 Kepulauan Seribu 15.1 8.81 12587 72.1 69.0 83.8 94.2 8.58 65.5 3.65e6
## 3 Kota Jakarta Se… 3.56 11.64 23888 84.9 74.2 96.5 100. 7.33 61.4 4.29e8
## 4 Kota Jakarta Ti… 4.28 11.67 17733 83.0 74.5 96.7 99.6 8.23 60.9 3.14e8
## 5 Kota Jakarta Pu… 4.94 11.39 17365 81.6 74.2 89.6 100 7.75 63.2 4.60e8
## 6 Kota Jakarta Ba… 4.31 10.78 20801 81.8 73.7 97.7 100 9.06 63.2 3.28e8
str(data)
## tibble [17 × 11] (S3: tbl_df/tbl/data.frame)
## $ Nama Wilayah: chr [1:17] "DKI JAKARTA" "Kepulauan Seribu" "Kota Jakarta Selatan" "Kota Jakarta Timur" ...
## $ P0 : num [1:17] NA 15.06 3.56 4.28 4.94 ...
## $ RLS : chr [1:17] NA "8.81" "11.64" "11.67" ...
## $ PPK : num [1:17] NA 12587 23888 17733 17365 ...
## $ IPM : num [1:17] NA 72.1 84.9 83 81.6 ...
## $ UHH : num [1:17] NA 69 74.2 74.5 74.2 ...
## $ SNTS : num [1:17] NA 83.8 96.5 96.7 89.6 ...
## $ AIR : num [1:17] NA 94.2 100 99.6 100 ...
## $ TPT : num [1:17] NA 8.58 7.33 8.23 7.75 ...
## $ TPAK : num [1:17] NA 65.5 61.4 60.9 63.2 ...
## $ PDRB : num [1:17] NA 3.65e+06 4.29e+08 3.14e+08 4.60e+08 ...
summary(data)
## Nama Wilayah P0 RLS PPK
## Length:17 Min. : 2.570 Length:17 Min. :10410
## Class :character 1st Qu.: 4.287 Class :character 1st Qu.:12352
## Mode :character Median : 5.075 Mode :character Median :15586
## Mean : 5.922 Mean :15609
## 3rd Qu.: 7.210 3rd Qu.:17641
## Max. :15.060 Max. :23888
## NA's :3 NA's :3
## IPM UHH SNTS AIR
## Min. :70.60 Min. :68.99 Min. :63.91 Min. : 91.83
## 1st Qu.:74.98 1st Qu.:71.82 1st Qu.:84.29 1st Qu.: 97.98
## Median :80.94 Median :73.75 Median :92.78 Median : 99.37
## Mean :78.65 Mean :72.98 Mean :89.25 Mean : 98.10
## 3rd Qu.:81.72 3rd Qu.:74.20 3rd Qu.:96.98 3rd Qu.: 99.99
## Max. :84.90 Max. :75.19 Max. :98.84 Max. :100.00
## NA's :3 NA's :3 NA's :3 NA's :3
## TPT TPAK PDRB
## Min. : 7.332 Min. :60.85 Min. : 3649179
## 1st Qu.: 8.587 1st Qu.:62.56 1st Qu.: 64222352
## Median : 9.065 Median :63.19 Median :133143936
## Mean : 9.447 Mean :63.46 Mean :192635338
## 3rd Qu.:10.029 3rd Qu.:64.70 3rd Qu.:324177110
## Max. :12.224 Max. :65.87 Max. :460081046
## NA's :3 NA's :3 NA's :3
data_sederhana <- data[-c(1, 2, 8, 14), -c(1, 3, 4, 5, 6, 7, 8, 10, 11)]
colnames(data_sederhana) <- c("y", "x")
print(data_sederhana)
## # A tibble: 13 × 2
## y x
## <dbl> <dbl>
## 1 3.56 7.33
## 2 4.28 8.23
## 3 4.94 7.75
## 4 4.31 9.06
## 5 7.24 9.84
## 6 8.13 12.2
## 7 5.21 10.1
## 8 7.24 11.8
## 9 4.74 10.9
## 10 2.58 9.76
## 11 7.12 9.06
## 12 5.93 9.07
## 13 2.57 8.60
head(data_sederhana)
## # A tibble: 6 × 2
## y x
## <dbl> <dbl>
## 1 3.56 7.33
## 2 4.28 8.23
## 3 4.94 7.75
## 4 4.31 9.06
## 5 7.24 9.84
## 6 8.13 12.2
str(data_sederhana)
## tibble [13 × 2] (S3: tbl_df/tbl/data.frame)
## $ y: num [1:13] 3.56 4.28 4.94 4.31 7.24 8.13 5.21 7.24 4.74 2.58 ...
## $ x: num [1:13] 7.33 8.23 7.75 9.06 9.84 ...
summary(data_sederhana)
## y x
## Min. :2.570 Min. : 7.332
## 1st Qu.:4.280 1st Qu.: 8.601
## Median :4.940 Median : 9.069
## Mean :5.219 Mean : 9.514
## 3rd Qu.:7.120 3rd Qu.:10.092
## Max. :8.130 Max. :12.224
PEMODELAN
data_sederhana$y <- as.numeric(as.character(data_sederhana$y))
data_sederhana$x <- as.numeric(as.character(data_sederhana$x))
# Definisikan x dan y secara eksplisit
x <- data_sederhana$x
y <- data_sederhana$y
n <- length(y) # atau length(x), sama aja
MANUAL
Koefisien Regresi
b1 <- (sum(x*y)-sum(x)*sum(y)/n)/ (sum(x^2)-sum(x^2/n))
b0 <- mean(y)-b1*mean(x)
cat("Koefisien B1:", b1, "\n")
## Koefisien B1: 0.01692941
cat("Koefisien B0:", b0, "\n")
## Koefisien B0: 5.058171
Standar Error Parameter Regresi
galat <- y-(b0+b1*x)
ragam_galat <- sum(galat^2)/(n-2)
se_b1 <- sqrt(ragam_galat/sum((x-mean(x))^2))
se_b0 <- sqrt(ragam_galat*(1/n+mean(x)^2/sum((x-mean(x))^2)))
cat("Standar Error B1:", se_b1, "\n")
## Standar Error B1: 0.3699017
cat("Standar Error B0:", se_b0, "\n")
## Standar Error B0: 3.557518
Signifikansi Parameter (nilai-t)
t_b1 <- b1/se_b1
t_b0 <- b0/se_b0
p_b1 <- 2*pt(-abs(t_b1 ),df<-n-2)
p_b0 <- 2*pt(-abs(t_b0 ),df<-n-2)
cat("Nilai t pada b0 adalah", t_b0, "dengan nilai p sebesar", p_b0, "\n")
## Nilai t pada b0 adalah 1.421826 dengan nilai p sebesar 0.1828053
cat("Nilai t pada b1 adalah", t_b1, "dengan nilai p sebesar", p_b1, "\n")
## Nilai t pada b1 adalah 0.04576731 dengan nilai p sebesar 0.964316
Koefisien Determinasi dan Penyesuaiannya
r <- (sum(x*y)-sum(x)*sum(y)/n)/
sqrt((sum(x^2)-(sum(x)^2/n))*(sum(y^2)-(sum(y)^2/n)))
koef_det <- r^2
koef_det
## [1] 0.3459232
adj_r2 <- 1-((1-koef_det))*(n-1)/(n-1-1)
adj_r2
## [1] 0.2864617
Signifikansi F
JKG <- sum((y - (b0+b1*x))^2)
JKReg <- sum(((b0+b1*x)- mean(y))^2)
JKT <- sum((y - mean(y))^2)
JKT <- JKReg+JKG
dbReg <- 1
dbg <- n-2
dbt <- n-1
Fhit <- (JKReg/dbReg)/(JKG/dbg)
p_Fhit <- 1-pf(Fhit, dbReg, dbg, lower.tail <- F)
cat("JKG:", JKG, "\n")
## JKG: 38.88246
cat("JKReg:", JKReg, "\n")
## JKReg: 0.007404094
cat("JKT:", JKT, "\n")
## JKT: 38.88987
cat("F Hitung:", Fhit, "\n")
## F Hitung: 0.002094647
cat("P Hitung:", p_Fhit, "\n")
## P Hitung: 0.964316
FUNGSI LM
head(data_sederhana)
## # A tibble: 6 × 2
## y x
## <dbl> <dbl>
## 1 3.56 7.33
## 2 4.28 8.23
## 3 4.94 7.75
## 4 4.31 9.06
## 5 7.24 9.84
## 6 8.13 12.2
str(data_sederhana)
## tibble [13 × 2] (S3: tbl_df/tbl/data.frame)
## $ y: num [1:13] 3.56 4.28 4.94 4.31 7.24 8.13 5.21 7.24 4.74 2.58 ...
## $ x: num [1:13] 7.33 8.23 7.75 9.06 9.84 ...
summary(data_sederhana)
## y x
## Min. :2.570 Min. : 7.332
## 1st Qu.:4.280 1st Qu.: 8.601
## Median :4.940 Median : 9.069
## Mean :5.219 Mean : 9.514
## 3rd Qu.:7.120 3rd Qu.:10.092
## Max. :8.130 Max. :12.224
modelRLS <- lm(y~x, data = data_sederhana)
summary(modelRLS)
##
## Call:
## lm(formula = y ~ x, data = data_sederhana)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.81858 -0.57991 -0.00445 1.00171 2.23418
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7007 2.9003 -0.586 0.5695
## x 0.7274 0.3016 2.412 0.0345 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.533 on 11 degrees of freedom
## Multiple R-squared: 0.3459, Adjusted R-squared: 0.2865
## F-statistic: 5.818 on 1 and 11 DF, p-value: 0.03449
anova(modelRLS)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 1 13.668 13.6679 5.8176 0.03449 *
## Residuals 11 25.843 2.3494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
PENGURAIAN KERAGAMAN
y.bar <- mean(y)
plot(x,y)
abline(modelRLS, col="firebrick3")
text(30, 220, "Y_duga", adj = c(-0.1, 1.5), col = "firebrick3", cex = 0.8)
abline(h=y.bar, col="steelblue")
text(31, 185, "Y_bar", adj = c(-0.1, 1.5), col = "steelblue", cex = 0.8)
anova.model <- anova(modelRLS)
print(anova.model)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 1 13.668 13.6679 5.8176 0.03449 *
## Residuals 11 25.843 2.3494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(KTG <- anova.model$`Mean Sq`[2])
## [1] 2.349402
(galat.baku <- sqrt(KTG))
## [1] 1.532776
KERAGAMAN DUGA PARAMETER
Dugaan Parameter B0
(b0 <- modelRLS$coefficients[[1]])
## [1] -1.700687
(b1 <- modelRLS$coefficients[[2]])
## [1] 0.7273714
(se_b0 <- sqrt(KTG*(1/n+mean(x)^2/sum((x-mean(x))^2))))
## [1] 2.900316
(t_b0 <- b0/se_b0)
## [1] -0.58638
Dugaan Parameter B1
(se_b1 <- sqrt(KTG/sum((x-mean(x))^2)))
## [1] 0.3015674
(t_b1 <- b1/se_b1)
## [1] 2.411969
Selang Kepercayaan Parameter
#Batas Bawah beta0
(bb.b0 <- b0 - abs(qt(0.025, df=n-2))*se_b0)
## [1] -8.084239
#Batas Bawah beta1
(bb.b1 <- b1 - abs(qt(0.025, df=n-2))*se_b1)
## [1] 0.06362598
#Batas Atas beta_0
(ba.b0 <- b0 + abs(qt(0.025, df=n-2))*se_b0)
## [1] 4.682865
#Batas Atas beta_1
(ba.b1 <- b1 + abs(qt(0.025, df=n-2))*se_b1)
## [1] 1.391117
Selang Kepercayaan
Bagi Nilai Rataan / Nilai Harapan Amatan
amatan.diduga <- data.frame(x=17)
predict(modelRLS, amatan.diduga, interval = "confidence")
## fit lwr upr
## 1 10.66463 5.608234 15.72102
Bagi Individu Amatan
predict(modelRLS, amatan.diduga, interval = "prediction")
## fit lwr upr
## 1 10.66463 4.586108 16.74315