Preparation UAS AED
Muhammad Firlan Maulana
2024-06-13
Read data
library(readxl)
data01 = read_xlsx("D:/firlan/Documents/College/Semester 4/Analisis Eksplorasi Data/UAS/Practice/data UAS AED tahun lalu.xlsx", sheet = "Sheet1")
data02 = read_xlsx("D:/firlan/Documents/College/Semester 4/Analisis Eksplorasi Data/UAS/Practice/data UAS AED tahun lalu.xlsx", sheet = "Sheet2")
data03 = read_xlsx("D:/firlan/Documents/College/Semester 4/Analisis Eksplorasi Data/UAS/Practice/data UAS AED tahun lalu.xlsx", sheet = "Sheet3")
data01## # A tibble: 50 × 3
## Participant Durasi Produktivitas
## <dbl> <dbl> <dbl>
## 1 1 7.5 85
## 2 2 6.2 72
## 3 3 8.1 91
## 4 4 6.8 78
## 5 5 7.9 87
## 6 6 5.6 63
## 7 7 6.9 76
## 8 8 7.2 81
## 9 9 6.5 70
## 10 10 8.3 93
## # ℹ 40 more rowsdata02## # A tibble: 50 × 9
## No. Usia IMT Konsumsi Kalori Haria…¹ `Jumlah Langkah` `Kadar Kolesterol`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 35 25 2000 8000 180
## 2 2 42 29 1800 6000 220
## 3 3 28 22 2200 9000 160
## 4 4 55 31 2500 5000 240
## 5 5 46 26 1900 7000 200
## 6 6 39 24 2100 8000 180
## 7 7 52 28 1800 4000 220
## 8 8 31 23 2300 9000 170
## 9 9 48 27 2200 6000 200
## 10 10 41 25 1900 7000 190
## # ℹ 40 more rows
## # ℹ abbreviated name: ¹`Konsumsi Kalori Harian`
## # ℹ 3 more variables: `Tekanan Darah` <dbl>, Merokok <chr>,
## # `Riwayat Penyakit Jantung` <chr>data03## # A tibble: 15 × 2
## Hari Penjualan
## <chr> <dbl>
## 1 Hari 1 20
## 2 Hari 2 25
## 3 Hari 3 18
## 4 Hari 4 22
## 5 Hari 5 30
## 6 Hari 6 35
## 7 Hari 7 28
## 8 Hari 8 19
## 9 Hari 9 24
## 10 Hari 10 29
## 11 Hari 11 32
## 12 Hari 12 26
## 13 Hari 13 21
## 14 Hari 14 27
## 15 Hari 15 23Eksplorasi lewat Visualisasi Data
Ringkasan data dan statistik 5 serangkai
str(data01)## tibble [50 × 3] (S3: tbl_df/tbl/data.frame)
## $ Participant : num [1:50] 1 2 3 4 5 6 7 8 9 10 ...
## $ Durasi : num [1:50] 7.5 6.2 8.1 6.8 7.9 5.6 6.9 7.2 6.5 8.3 ...
## $ Produktivitas: num [1:50] 85 72 91 78 87 63 76 81 70 93 ...summary(data02)## No. Usia IMT Konsumsi Kalori Harian
## Min. : 1.00 Min. :28.00 Min. :22.00 Min. :1800
## 1st Qu.:13.25 1st Qu.:36.25 1st Qu.:24.00 1st Qu.:1900
## Median :25.50 Median :42.50 Median :26.00 Median :2050
## Mean :25.50 Mean :42.52 Mean :26.00 Mean :2058
## 3rd Qu.:37.75 3rd Qu.:48.75 3rd Qu.:27.75 3rd Qu.:2200
## Max. :50.00 Max. :56.00 Max. :31.00 Max. :2500
## Jumlah Langkah Kadar Kolesterol Tekanan Darah Merokok
## Min. :4000 Min. :160.0 Min. :110 Length:50
## 1st Qu.:6000 1st Qu.:180.0 1st Qu.:120 Class :character
## Median :7000 Median :190.0 Median :120 Mode :character
## Mean :6780 Mean :194.2 Mean :124
## 3rd Qu.:8000 3rd Qu.:200.0 3rd Qu.:130
## Max. :9000 Max. :240.0 Max. :140
## Riwayat Penyakit Jantung
## Length:50
## Class :character
## Mode :character
##
##
## Memilih baris dan kolom yang diinginkan (filter dan select)
Kolom
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.3.2## Warning: package 'lubridate' was built under R version 4.3.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdata02kolom2 = data02 %>% select(2, 4) #Memilih kolom 2 dan 4
data02kolom2## # A tibble: 50 × 2
## Usia `Konsumsi Kalori Harian`
## <dbl> <dbl>
## 1 35 2000
## 2 42 1800
## 3 28 2200
## 4 55 2500
## 5 46 1900
## 6 39 2100
## 7 52 1800
## 8 31 2300
## 9 48 2200
## 10 41 1900
## # ℹ 40 more rowsMemilih kolom yang hanya berisi data numeric
library(dplyr)
data02numeric = data02 %>% select_if(is.numeric)
data02numeric## # A tibble: 50 × 7
## No. Usia IMT Konsumsi Kalori Haria…¹ `Jumlah Langkah` `Kadar Kolesterol`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 35 25 2000 8000 180
## 2 2 42 29 1800 6000 220
## 3 3 28 22 2200 9000 160
## 4 4 55 31 2500 5000 240
## 5 5 46 26 1900 7000 200
## 6 6 39 24 2100 8000 180
## 7 7 52 28 1800 4000 220
## 8 8 31 23 2300 9000 170
## 9 9 48 27 2200 6000 200
## 10 10 41 25 1900 7000 190
## # ℹ 40 more rows
## # ℹ abbreviated name: ¹`Konsumsi Kalori Harian`
## # ℹ 1 more variable: `Tekanan Darah` <dbl>Baris
data01filter = data01 %>% filter(Participant >= 5 & Participant <= 17) #Memilih baris ke 5 hingga 17
data01filter## # A tibble: 13 × 3
## Participant Durasi Produktivitas
## <dbl> <dbl> <dbl>
## 1 5 7.9 87
## 2 6 5.6 63
## 3 7 6.9 76
## 4 8 7.2 81
## 5 9 6.5 70
## 6 10 8.3 93
## 7 11 7.7 84
## 8 12 6.1 67
## 9 13 7.8 89
## 10 14 6.4 74
## 11 15 8.2 92
## 12 16 7.3 80
## 13 17 6.6 68data02filter = data02 %>% filter(Merokok == 'Ya') #Memilih data yang merokok
data02filter## # A tibble: 18 × 9
## No. Usia IMT Konsumsi Kalori Haria…¹ `Jumlah Langkah` `Kadar Kolesterol`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 42 29 1800 6000 220
## 2 5 46 26 1900 7000 200
## 3 7 52 28 1800 4000 220
## 4 8 31 23 2300 9000 170
## 5 11 37 28 2100 5000 180
## 6 14 32 26 1800 6000 170
## 7 17 56 30 2400 5000 220
## 8 18 47 25 2100 6000 180
## 9 20 34 24 2000 8000 170
## 10 21 51 27 1800 4000 200
## 11 25 36 26 2100 8000 190
## 12 28 33 27 2200 6000 170
## 13 32 37 28 1800 6000 180
## 14 34 35 25 1900 8000 170
## 15 36 31 23 2300 9000 180
## 16 39 38 26 2100 8000 190
## 17 42 32 27 2200 6000 170
## 18 46 36 26 1800 6000 180
## # ℹ abbreviated name: ¹`Konsumsi Kalori Harian`
## # ℹ 3 more variables: `Tekanan Darah` <dbl>, Merokok <chr>,
## # `Riwayat Penyakit Jantung` <chr>Mengakses baris tertentu
data02filterusia = data02[c(22), 2]
data02filterusia## # A tibble: 1 × 1
## Usia
## <dbl>
## 1 30Membuat data ke bentuk data frame
a <- as.data.frame(data01)
colnames(data01) <- c("Participant", "Durasi", "Produktivitas")
a## Participant Durasi Produktivitas
## 1 1 7.5 85
## 2 2 6.2 72
## 3 3 8.1 91
## 4 4 6.8 78
## 5 5 7.9 87
## 6 6 5.6 63
## 7 7 6.9 76
## 8 8 7.2 81
## 9 9 6.5 70
## 10 10 8.3 93
## 11 11 7.7 84
## 12 12 6.1 67
## 13 13 7.8 89
## 14 14 6.4 74
## 15 15 8.2 92
## 16 16 7.3 80
## 17 17 6.6 68
## 18 18 7.4 83
## 19 19 5.9 62
## 20 20 7.1 79
## 21 21 6.7 75
## 22 22 7.6 88
## 23 23 6.3 71
## 24 24 8.4 94
## 25 25 7.0 77
## 26 26 6.0 66
## 27 27 8.0 90
## 28 28 7.2 82
## 29 29 6.5 69
## 30 30 7.9 86
## 31 31 6.8 73
## 32 32 8.1 91
## 33 33 7.3 81
## 34 34 6.6 68
## 35 35 8.2 93
## 36 36 7.6 85
## 37 37 6.1 67
## 38 38 7.7 88
## 39 39 6.4 74
## 40 40 8.3 95
## 41 41 7.1 78
## 42 42 6.5 70
## 43 43 8.0 90
## 44 44 7.2 82
## 45 45 6.7 73
## 46 46 7.9 87
## 47 47 6.3 72
## 48 48 8.4 94
## 49 49 7.0 77
## 50 50 6.0 68Boxplot
boxplot(data02$`Jumlah Langkah`, horizontal = T, main = "Boxplot sebaran jumlah langkah", col = "pink")
Boxplot lebih dari 1 dengan X kategorik
boxplot(`Konsumsi Kalori Harian` ~ `Riwayat Penyakit Jantung`, data = data02, col = "skyblue", main = "Sebaran konsumsi kalori harian
per kategori riwayat penyakit jantung")
Boxplot lebih dari 1 dengan X kategorik diurutkan berdasarkan median
boxplot(`Konsumsi Kalori Harian` ~ reorder(data02$`Riwayat Penyakit Jantung`, data02$`Konsumsi Kalori Harian`, FUN = median), data = data02, col = "skyblue", main = "Sebaran konsumsi kalori harian
per kategori riwayat penyakit jantung")
Histogram
Variabel dengan frekuensinya
hist(data01$Durasi) 
Histogram per Kategori
library(ggplot2)
ggplot(data = data02, aes(x=`Tekanan Darah`)) +
geom_histogram(aes(fill=Merokok)) +
scale_fill_brewer(palette="Set2") +
facet_wrap( ~ Merokok, ncol=1) +
xlab("Tekanan Darah") +
ylab("Frekuensi") +
theme_bw() +
ggtitle("Angka Tekanan Darah per Kategori Merokok")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scatter plot
Scatter Plot Hubungan durasi tidur dengan produktivitas
ggplot(data01) +
geom_point(aes(x = Durasi,y = Produktivitas),color="orange",size=3) +
ggtitle("Scatter Plot Durasi Tidur dengan Produktivitas") +
ylab("Produktivitas") +
xlab("Durasi Tidur") +
theme_classic() +
theme(plot.title = element_text(hjust = 0.5))
Scatter Plot Hubungan Usia dengan Kadar Kolesterol dan dibedakan berdasarkan merokok atau tidak
ggplot(data02) +
geom_point(aes(x = Usia, y = `Kadar Kolesterol`, color = Merokok), size=3) +
ggtitle("Scatter Plot Usia dengan Kadar Kolesterol dan dibedakan berdasarkan merokok atau tidak") +
ylab("Kadar Kolesterol") +
xlab("Usia") +
theme_classic() +
theme(plot.title = element_text(hjust = 0.5))
Correlogram, Corrplot, Heatmap, dan Pair Plot untuk melihat besaran korelasi
Correlogram
library(GGally)## Warning: package 'GGally' was built under R version 4.3.2## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggcorr(data02, method = c("everything","pearson"),geom = "tile") ## Warning in ggcorr(data02, method = c("everything", "pearson"), geom = "tile"):
## data in column(s) 'Merokok', 'Riwayat Penyakit Jantung' are not numeric and
## were ignored
Corrplot
library(corrplot)## corrplot 0.92 loaded#Menghitung nilai korelasi
corr02 = cor(data02numeric)
corr02## No. Usia IMT
## No. 1.000000000 0.07971784 -0.02455513
## Usia 0.079717843 1.00000000 0.60724087
## IMT -0.024555126 0.60724087 1.00000000
## Konsumsi Kalori Harian -0.043682751 0.10400083 0.12349421
## Jumlah Langkah -0.076415334 -0.44921765 -0.63870192
## Kadar Kolesterol -0.011089970 0.73619766 0.57121412
## Tekanan Darah -0.007072482 0.42952994 0.30455480
## Konsumsi Kalori Harian Jumlah Langkah Kadar Kolesterol
## No. -0.04368275 -0.07641533 -0.01108997
## Usia 0.10400083 -0.44921765 0.73619766
## IMT 0.12349421 -0.63870192 0.57121412
## Konsumsi Kalori Harian 1.00000000 0.22045524 0.06910793
## Jumlah Langkah 0.22045524 1.00000000 -0.40353442
## Kadar Kolesterol 0.06910793 -0.40353442 1.00000000
## Tekanan Darah -0.24437588 -0.51170847 0.62631678
## Tekanan Darah
## No. -0.007072482
## Usia 0.429529945
## IMT 0.304554795
## Konsumsi Kalori Harian -0.244375883
## Jumlah Langkah -0.511708474
## Kadar Kolesterol 0.626316780
## Tekanan Darah 1.000000000#Membuat corrplot
corrplot(corr02, method = "number")
Corrplot bentuk lain
corrplot.mixed(corr02, upper = 'ellipse', lower = 'number', order = "original",
tl.col="black", tl.pos = "lt",diag = 'l',
number.digits=2, number.cex=0.55)
Heatmap
library(heatmaply)## Warning: package 'heatmaply' was built under R version 4.3.3## Loading required package: plotly## Warning: package 'plotly' was built under R version 4.3.2##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layout## Loading required package: viridis## Warning: package 'viridis' was built under R version 4.3.3## Loading required package: viridisLite##
## ======================
## Welcome to heatmaply version 1.5.0
##
## Type citation('heatmaply') for how to cite the package.
## Type ?heatmaply for the main documentation.
##
## The github page is: https://github.com/talgalili/heatmaply/
## Please submit your suggestions and bug-reports at: https://github.com/talgalili/heatmaply/issues
## You may ask questions at stackoverflow, use the r and heatmaply tags:
## https://stackoverflow.com/questions/tagged/heatmaply
## ======================#corr02 = cor(data02numeric)
heatmaply(corr02)Pair plot
ggpairs(data02, upper = list(continuous = wrap('cor', size = 2)))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Goodness Fits of Test
Kolmogorov-Smirnov Test
Hanya untuk data yang isinya tidak ada yang berulang H0: data menyebar normal H1: data tidak menyebar normal
Terima H0 berarti data menyebar normal
ks.test(data02$IMT, "pnorm", 0, 1) #Mengecek apakah data menyebar normal dengan rata-rata 0 dan ragam 1## Warning in ks.test.default(data02$IMT, "pnorm", 0, 1): ties should not be
## present for the Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: data02$IMT
## D = 1, p-value < 2.2e-16
## alternative hypothesis: two-sidedks.test(data02$Usia, "punif") #Mengecek apakah data menyebar uniform## Warning in ks.test.default(data02$Usia, "punif"): ties should not be present
## for the Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: data02$Usia
## D = 1, p-value < 2.2e-16
## alternative hypothesis: two-sidedD-tabel (apabila data lebih dari 35)
#Untuk alpha = 0,05
#Misal untuk data sebanyak 52
n = 52
Dtabel = 1.358/sqrt(n)
Dtabel## [1] 0.1883207Saphiro-Wilk Test
Harus input sebagai vector, bukan string
H0: data menyebar normal H1: data tidak menyebar normal
Terima H0 berarti data menyebar normal
data02usia = data02 %>% select(`Usia`)
data02usia## # A tibble: 50 × 1
## Usia
## <dbl>
## 1 35
## 2 42
## 3 28
## 4 55
## 5 46
## 6 39
## 7 52
## 8 31
## 9 48
## 10 41
## # ℹ 40 more rowsis.numeric(data02usia$Usia) #Input dalam bentuk vector## [1] TRUEshapiro.test(data02usia$Usia)##
## Shapiro-Wilk normality test
##
## data: data02usia$Usia
## W = 0.96617, p-value = 0.161Chi-Square
country <- c("US","Germany","France","Norway","Spain","China")
exp.percent <- c(0.25,0.12,0.18,0.14,0.11,0.20)
medals <- c(33,6,18,15,12,36)
medal.data <- data.frame(country, exp.percent, medals)
medal.data## country exp.percent medals
## 1 US 0.25 33
## 2 Germany 0.12 6
## 3 France 0.18 18
## 4 Norway 0.14 15
## 5 Spain 0.11 12
## 6 China 0.20 36chisq.test(medal.data$medals, p=exp.percent)##
## Chi-squared test for given probabilities
##
## data: medal.data$medals
## X-squared = 12.102, df = 5, p-value = 0.03342Deteksi Outlier
Contoh data yang digunakan
datacar <- ggplot2::mpg
head(datacar)## # A tibble: 6 × 11
## manufacturer model displ year cyl trans drv cty hwy fl class
## <chr> <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
## 1 audi a4 1.8 1999 4 auto(l5) f 18 29 p compa…
## 2 audi a4 1.8 1999 4 manual(m5) f 21 29 p compa…
## 3 audi a4 2 2008 4 manual(m6) f 20 31 p compa…
## 4 audi a4 2 2008 4 auto(av) f 21 30 p compa…
## 5 audi a4 2.8 1999 6 auto(l5) f 16 26 p compa…
## 6 audi a4 2.8 1999 6 manual(m5) f 18 26 p compa…Melalui histogram, boxplot, dan adjusted boxplot
Histog
ggplot(datacar) +
aes(x = hwy) +
geom_histogram(bins = 20, fill = "coral") +
theme_minimal()
Dari gambar di atas terlihat mungkin terdapat outlier.
ggplot(datacar) +
aes(x = "", y = hwy) +
geom_boxplot(fill = "orange") +
theme_minimal() 
Dari gambar di atas terlihat mungkin terdapat outlier.
Adjusted Boxplot
library(robustbase)## Warning: package 'robustbase' was built under R version 4.3.2adj_box = adjbox(datacar$hwy, plot = FALSE)## The default of 'doScale' is FALSE now for stability;
## set options(mc_doScale_quiet=TRUE) to suppress this (once per session) messageadjbox(datacar$hwy, main = "Adjusted Boxplot")
text(1, adj_box$out, labels = adj_box$out, pos = 4, cex = 0.8, col = "blue")
Melalui Interquartile Range (IQR)
Mencari nilai Q1, Q3, dan InterQuartile
summary(datacar$hwy)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 12.00 18.00 24.00 23.44 27.00 44.00IQRhwy = IQR(datacar$hwy)
IQRhwy## [1] 9lower_bound <- 18 - 1.5 * IQRhwy
upper_bound <- 27 + 1.5 * IQRhwy
outlier_iqr <- which(datacar$hwy < lower_bound | datacar$hwy > upper_bound)
outlier_iqr## [1] 213 222 223Angka yang muncul bukan merupakan nilai outlier, melainkan indeks dari outlier. Sehingga perlu untuk akses data.
outlierhwy = datacar[c(213,222,223), 9]
outlierhwy## # A tibble: 3 × 1
## hwy
## <int>
## 1 44
## 2 44
## 3 41Analisis Regresi
Membuat dataframe dengan nama variabel baru
data02no = data02 %>% select(-1, -8, -9)
dataframe02 = as.data.frame(data02no)
colnames(dataframe02) <- c("Y","X1","X2","X3","X4","X5")
dataframe02## Y X1 X2 X3 X4 X5
## 1 35 25 2000 8000 180 120
## 2 42 29 1800 6000 220 130
## 3 28 22 2200 9000 160 110
## 4 55 31 2500 5000 240 140
## 5 46 26 1900 7000 200 120
## 6 39 24 2100 8000 180 130
## 7 52 28 1800 4000 220 140
## 8 31 23 2300 9000 170 110
## 9 48 27 2200 6000 200 120
## 10 41 25 1900 7000 190 130
## 11 37 28 2100 5000 180 120
## 12 50 29 2300 8000 200 130
## 13 45 24 2000 9000 190 120
## 14 32 26 1800 6000 170 110
## 15 38 27 2200 7000 200 130
## 16 43 23 1900 8000 210 140
## 17 56 30 2400 5000 220 120
## 18 47 25 2100 6000 180 110
## 19 40 26 1900 7000 190 130
## 20 34 24 2000 8000 170 120
## 21 51 27 1800 4000 200 140
## 22 30 23 2300 9000 180 110
## 23 49 28 2200 6000 210 120
## 24 42 25 1900 7000 200 130
## 25 36 26 2100 8000 190 120
## 26 53 29 1800 5000 230 140
## 27 44 24 2000 9000 180 110
## 28 33 27 2200 6000 170 120
## 29 39 23 1900 7000 200 130
## 30 54 25 2400 8000 220 120
## 31 47 26 2100 5000 190 130
## 32 37 28 1800 6000 180 110
## 33 44 24 2000 7000 190 120
## 34 35 25 1900 8000 170 130
## 35 52 27 2200 4000 200 140
## 36 31 23 2300 9000 180 110
## 37 46 28 2200 6000 210 120
## 38 41 25 1900 7000 200 130
## 39 38 26 2100 8000 190 120
## 40 55 30 1800 5000 230 140
## 41 45 24 2000 9000 180 110
## 42 32 27 2200 6000 170 120
## 43 39 23 1900 7000 200 130
## 44 50 29 2400 8000 220 120
## 45 47 26 2100 5000 190 130
## 46 36 26 1800 6000 180 110
## 47 53 27 2000 7000 190 120
## 48 44 25 2200 8000 210 130
## 49 33 24 1900 5000 200 140
## 50 51 28 2100 6000 180 120Membentuk model awal
model2 = lm(Y ~ X1+X2+X3+X4+X5, data = dataframe02)
anova(model2)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 1073.95 1073.95 40.6709 9.399e-08 ***
## X2 1 2.49 2.49 0.0943 0.7603
## X3 1 28.64 28.64 1.0845 0.3034
## X4 1 640.29 640.29 24.2478 1.238e-05 ***
## X5 1 5.26 5.26 0.1991 0.6576
## Residuals 44 1161.86 26.41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.685 -3.394 -0.617 3.618 10.942
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.897e+01 2.109e+01 -0.900 0.373278
## X1 6.815e-01 5.409e-01 1.260 0.214386
## X2 1.994e-03 4.320e-03 0.462 0.646652
## X3 -6.421e-04 7.699e-04 -0.834 0.408780
## X4 2.586e-01 6.273e-02 4.123 0.000163 ***
## X5 -4.999e-02 1.120e-01 -0.446 0.657614
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.139 on 44 degrees of freedom
## Multiple R-squared: 0.6011, Adjusted R-squared: 0.5557
## F-statistic: 13.26 on 5 and 44 DF, p-value: 6.801e-08Karena R-square rendah, dilakukan pengecekan pencilan dan amatan berpengaruh
Cek Multikolinearitas
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somecar::vif(model2)## X1 X2 X3 X4 X5
## 2.548581 1.258993 2.392554 2.446731 2.280875Pendeteksian Outlier
olsrr::ols_plot_resid_lev(model2)
influence.measures(model2)## Influence measures of
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02) :
##
## dfb.1_ dfb.X1 dfb.X2 dfb.X3 dfb.X4 dfb.X5 dffit cov.r
## 1 1.70e-02 -0.041486 0.032782 -0.064452 0.04855 -0.026814 -0.11217 1.169
## 2 1.25e-01 -0.365971 0.587024 -0.276658 -0.28471 0.142844 -0.82747 0.817
## 3 -5.48e-02 0.065845 -0.069511 0.003321 0.05863 0.004225 -0.19972 1.270
## 4 3.43e-01 -0.104715 -0.334789 0.001956 -0.08508 -0.134829 -0.56344 1.413
## 5 4.39e-02 -0.004239 -0.079013 0.008512 0.06412 -0.067766 0.11858 1.195
## 6 -7.48e-02 0.012091 0.048724 0.069090 -0.10576 0.141005 0.18000 1.242
## 7 1.55e-02 -0.013024 -0.027551 -0.032034 0.02409 -0.000223 0.07830 1.314
## 8 -2.83e-02 0.059896 -0.107908 -0.009213 0.03123 0.022692 -0.21748 1.229
## 9 3.27e-02 -0.026988 0.045805 -0.061832 0.03743 -0.057776 0.11307 1.182
## 10 -4.21e-03 0.001923 -0.016616 0.012990 -0.01375 0.023760 0.04582 1.203
## 11 -6.31e-02 -0.093005 -0.066717 0.142799 0.17584 0.017357 -0.33741 1.138
## 12 -5.30e-01 0.461400 0.119331 0.437013 -0.27822 0.350469 0.59538 1.331
## 13 -5.25e-02 0.017770 -0.133535 0.248859 0.06205 0.009080 0.38062 0.997
## 14 -3.09e-01 -0.035246 0.236545 0.139767 0.05446 0.245490 -0.45604 1.172
## 15 2.55e-01 -0.140375 -0.142407 -0.146357 0.12017 -0.213748 -0.33773 0.961
## 16 -5.87e-03 -0.012862 -0.005083 0.009275 0.00902 0.014383 0.03428 1.409
## 17 -6.64e-04 0.002162 0.096496 -0.085210 0.08512 -0.101922 0.21875 1.390
## 18 5.33e-01 -0.334070 0.088553 -0.489390 0.15294 -0.465067 0.65416 0.939
## 19 1.22e-02 -0.015975 0.014692 -0.018275 0.01663 -0.020543 -0.03516 1.223
## 20 2.88e-05 -0.001556 0.000944 -0.003557 0.00689 -0.004086 -0.01089 1.234
## 21 9.37e-02 -0.059663 -0.087572 -0.218701 -0.10633 0.159326 0.48480 1.080
## 22 -1.13e-01 0.222644 -0.215735 0.015699 -0.10771 0.162379 -0.49648 1.004
## 23 3.53e-04 -0.000117 0.000532 -0.000865 0.00146 -0.001644 0.00273 1.245
## 24 -1.56e-03 0.005978 0.011822 -0.004576 -0.00643 -0.004765 -0.02611 1.205
## 25 8.93e-02 -0.109507 0.024068 -0.149765 0.03984 -0.026244 -0.21609 1.053
## 26 9.99e-03 -0.011903 0.030952 -0.006466 -0.02230 -0.002033 -0.05717 1.347
## 27 1.22e-01 0.015679 -0.205895 0.198114 0.09735 -0.216805 0.49762 0.924
## 28 3.62e-02 -0.136752 -0.169181 0.061596 0.31789 -0.118303 -0.40411 1.144
## 29 -7.13e-02 0.126319 0.025438 0.046399 -0.07655 0.010200 -0.16380 1.260
## 30 2.01e-02 -0.313437 0.262437 -0.080535 0.45504 -0.240008 0.61739 1.201
## 31 8.12e-02 -0.114766 0.141177 -0.211930 -0.08348 0.062755 0.30578 1.120
## 32 -1.59e-01 -0.169780 0.255821 0.011435 0.02742 0.214735 -0.41259 1.291
## 33 1.43e-01 -0.146641 -0.016976 -0.093268 0.08847 -0.093532 0.19991 1.118
## 34 -3.84e-02 0.044430 -0.016502 0.051887 -0.06738 0.064890 0.08798 1.428
## 35 -2.35e-02 -0.180481 0.400974 -0.378446 -0.19632 0.287147 0.67043 1.133
## 36 -9.54e-02 0.187553 -0.181734 0.013225 -0.09073 0.136786 -0.41823 1.081
## 37 -2.22e-02 0.007377 -0.033525 0.054550 -0.09230 0.103643 -0.17235 1.185
## 38 -4.25e-03 0.016259 0.032155 -0.012446 -0.01748 -0.012960 -0.07101 1.191
## 39 5.27e-02 -0.064652 0.014210 -0.088419 0.02352 -0.015494 -0.12757 1.148
## 40 -2.11e-02 0.029036 -0.036484 0.017368 0.01550 0.006956 0.06592 1.393
## 41 1.39e-01 0.017952 -0.235749 0.226839 0.11147 -0.248240 0.56977 0.840
## 42 4.37e-02 -0.165424 -0.204653 0.074511 0.38454 -0.143108 -0.48884 1.070
## 43 -7.13e-02 0.126319 0.025438 0.046399 -0.07655 0.010200 -0.16380 1.260
## 44 8.07e-02 -0.059536 -0.032044 -0.066711 -0.04215 0.017907 -0.13986 1.406
## 45 8.12e-02 -0.114766 0.141177 -0.211930 -0.08348 0.062755 0.30578 1.120
## 46 -2.48e-01 0.024011 0.183820 0.119999 -0.06085 0.237227 -0.32834 1.267
## 47 -6.48e-02 0.320632 -0.215571 0.207085 -0.11204 -0.050481 0.50229 0.606
## 48 2.95e-02 0.017113 -0.022196 -0.023022 -0.02546 -0.018692 -0.07018 1.249
## 49 -3.44e-01 0.677299 -0.118340 0.573058 -0.07512 -0.254952 -1.00247 0.751
## 50 -9.82e-02 0.417668 0.058359 0.019976 -0.45427 0.096203 0.67136 0.695
## cook.d hat inf
## 1 2.13e-03 0.0501
## 2 1.07e-01 0.1531
## 3 6.76e-03 0.1292
## 4 5.31e-02 0.2761 *
## 5 2.39e-03 0.0660
## 6 5.49e-03 0.1092
## 7 1.04e-03 0.1316
## 8 8.00e-03 0.1128
## 9 2.17e-03 0.0571
## 10 3.58e-04 0.0507
## 11 1.90e-02 0.1108
## 12 5.90e-02 0.2533
## 13 2.38e-02 0.0810
## 14 3.46e-02 0.1585
## 15 1.87e-02 0.0610
## 16 2.00e-04 0.1859
## 17 8.12e-03 0.1964
## 18 6.88e-02 0.1411
## 19 2.11e-04 0.0638
## 20 2.02e-05 0.0697
## 21 3.87e-02 0.1351
## 22 4.03e-02 0.1159
## 23 1.27e-06 0.0777
## 24 1.16e-04 0.0491
## 25 7.79e-03 0.0461
## 26 5.57e-04 0.1501
## 27 4.01e-02 0.0959
## 28 2.72e-02 0.1333
## 29 4.55e-03 0.1148
## 30 6.29e-02 0.2127
## 31 1.56e-02 0.0943
## 32 2.86e-02 0.1937
## 33 6.72e-03 0.0593
## 34 1.32e-03 0.1998 *
## 35 7.36e-02 0.2035
## 36 2.89e-02 0.1159
## 37 5.02e-03 0.0777
## 38 8.58e-04 0.0491
## 39 2.75e-03 0.0461
## 40 7.41e-04 0.1782
## 41 5.17e-02 0.0959
## 42 3.93e-02 0.1333
## 43 4.55e-03 0.1148
## 44 3.33e-03 0.1928
## 45 1.56e-02 0.0943
## 46 1.81e-02 0.1618
## 47 3.84e-02 0.0462
## 48 8.39e-04 0.0875
## 49 1.55e-01 0.1769
## 50 6.96e-02 0.0910Kombinasi model tanpa dan dengan amatan yang termasuk laverage dan pencilan
model2_tanpa47 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-47,])
model2_tanpa50 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-50,])
model2_tanpa49 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-49,])
model2_tanpa12 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-12,])
model2_tanpa4 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-4,])
model2_tanpa4750 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-c(47,50),])
model2_tanpa4749 = lm(Y~X1+X2+X3+X4+X5, data=dataframe02[-c(47,49),])
summary(model2_tanpa47)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-47,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.0432 -3.0228 -0.2936 2.6243 10.5265
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.767e+01 2.016e+01 -0.876 0.386
## X1 5.158e-01 5.219e-01 0.988 0.329
## X2 2.883e-03 4.145e-03 0.696 0.490
## X3 -7.944e-04 7.386e-04 -1.076 0.288
## X4 2.653e-01 6.000e-02 4.422 6.55e-05 ***
## X5 -4.458e-02 1.070e-01 -0.417 0.679
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.909 on 43 degrees of freedom
## Multiple R-squared: 0.6299, Adjusted R-squared: 0.5869
## F-statistic: 14.64 on 5 and 43 DF, p-value: 2.216e-08summary(model2_tanpa50)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-50,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.9578 -3.0717 -0.6841 2.7800 11.4422
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.698e+01 2.032e+01 -0.836 0.408
## X1 4.640e-01 5.306e-01 0.875 0.387
## X2 1.751e-03 4.159e-03 0.421 0.676
## X3 -6.569e-04 7.410e-04 -0.887 0.380
## X4 2.860e-01 6.174e-02 4.633 3.34e-05 ***
## X5 -6.036e-02 1.079e-01 -0.559 0.579
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.946 on 43 degrees of freedom
## Multiple R-squared: 0.6296, Adjusted R-squared: 0.5865
## F-statistic: 14.62 on 5 and 43 DF, p-value: 2.264e-08summary(model2_tanpa49)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-49,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.5880 -3.5247 -0.8706 3.2973 11.3088
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.200e+01 2.052e+01 -0.585 0.562
## X1 3.295e-01 5.445e-01 0.605 0.548
## X2 2.485e-03 4.156e-03 0.598 0.553
## X3 -1.066e-03 7.652e-04 -1.393 0.171
## X4 2.631e-01 6.030e-02 4.364 7.87e-05 ***
## X5 -2.255e-02 1.084e-01 -0.208 0.836
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.937 on 43 degrees of freedom
## Multiple R-squared: 0.6284, Adjusted R-squared: 0.5852
## F-statistic: 14.54 on 5 and 43 DF, p-value: 2.413e-08summary(model2_tanpa12)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-12,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.2160 -3.1696 -0.4858 3.0525 11.2731
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.7901917 23.7510911 -0.328 0.744509
## X1 0.4319961 0.5931766 0.728 0.470392
## X2 0.0014786 0.0043466 0.340 0.735377
## X3 -0.0009784 0.0008369 -1.169 0.248810
## X4 0.2760616 0.0649803 4.248 0.000113 ***
## X5 -0.0892241 0.1183572 -0.754 0.455045
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.136 on 43 degrees of freedom
## Multiple R-squared: 0.6028, Adjusted R-squared: 0.5566
## F-statistic: 13.05 on 5 and 43 DF, p-value: 9.566e-08summary(model2_tanpa4)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-4,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.7290 -3.0205 -0.5285 3.7852 10.9419
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.622e+01 2.258e+01 -1.161 0.25185
## X1 7.382e-01 5.455e-01 1.353 0.18306
## X2 3.443e-03 4.610e-03 0.747 0.45925
## X3 -6.436e-04 7.714e-04 -0.834 0.40868
## X4 2.640e-01 6.312e-02 4.182 0.00014 ***
## X5 -3.485e-02 1.134e-01 -0.307 0.76016
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.148 on 43 degrees of freedom
## Multiple R-squared: 0.5861, Adjusted R-squared: 0.5379
## F-statistic: 12.18 on 5 and 43 DF, p-value: 2.229e-07summary(model2_tanpa4750)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-c(47,
## 50), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.3479 -2.9873 -0.5536 2.7732 8.8884
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.550e+01 1.918e+01 -0.808 0.424
## X1 2.784e-01 5.059e-01 0.550 0.585
## X2 2.671e-03 3.940e-03 0.678 0.502
## X3 -8.174e-04 7.019e-04 -1.164 0.251
## X4 2.946e-01 5.834e-02 5.049 9.07e-06 ***
## X5 -5.526e-02 1.018e-01 -0.543 0.590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.665 on 42 degrees of freedom
## Multiple R-squared: 0.6643, Adjusted R-squared: 0.6244
## F-statistic: 16.62 on 5 and 42 DF, p-value: 4.9e-09summary(model2_tanpa4749)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataframe02[-c(47,
## 49), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.9216 -3.1845 -0.5937 2.8180 10.8472
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.039e+01 1.940e+01 -0.535 0.5952
## X1 1.446e-01 5.198e-01 0.278 0.7823
## X2 3.424e-03 3.945e-03 0.868 0.3903
## X3 -1.240e-03 7.263e-04 -1.707 0.0952 .
## X4 2.703e-01 5.704e-02 4.738 2.48e-05 ***
## X5 -1.591e-02 1.024e-01 -0.155 0.8773
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.664 on 42 degrees of freedom
## Multiple R-squared: 0.6631, Adjusted R-squared: 0.623
## F-statistic: 16.53 on 5 and 42 DF, p-value: 5.271e-09Sejauh ini didapati model dengan R-squared tertinggi yaitu model tanpa amatan ke 47 dan 50.
Uji Asumsi
1. Nilai Harapan Galat = 0 (T-test)
t.test(model2_tanpa4750$residuals, mu=0, conf.level = 0.95)##
## One Sample t-test
##
## data: model2_tanpa4750$residuals
## t = 4.5504e-17, df = 47, p-value = 1
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -1.28059 1.28059
## sample estimates:
## mean of x
## 2.896627e-17plot(model2_tanpa4750, 1)
P-value > alpha (0,05) –> Terima H0 (Nilai Harapan Galat = 0)
2. Ragam Galat Homogen (Breusch-Pagan)
library(lmtest)## Warning: package 'lmtest' was built under R version 4.3.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.3.2##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericbptest(model2_tanpa4750)##
## studentized Breusch-Pagan test
##
## data: model2_tanpa4750
## BP = 2.2868, df = 5, p-value = 0.8082P-value > alpha (0,05) –> Terima H0 (Ragam Galat Homogen)
3. Galat Saling Bebas (Durbin-Watson)
tanpa4750 = dataframe02[-c(47,50),]
plot(x = 1:dim(tanpa4750)[1],
y = model2_tanpa4750$residuals,
type = 'b',
ylab = "Residuals",
xlab = "Obeservation")
dwtest(model2_tanpa4750)##
## Durbin-Watson test
##
## data: model2_tanpa4750
## DW = 1.8807, p-value = 0.4112
## alternative hypothesis: true autocorrelation is greater than 0P-value > alpha (0,05) –> Terima H0 (Galat Saling Bebas)
4. Galat Menyebar Normal (Saphiro-Wilk)
plot(model2_tanpa4750, 2)
shapiro.test(model2_tanpa4750$residuals)##
## Shapiro-Wilk normality test
##
## data: model2_tanpa4750$residuals
## W = 0.98142, p-value = 0.6387P-value > alpha (0,05) –> Terima H0 (Galat Menyebar Normal)
library(olsrr)## Warning: package 'olsrr' was built under R version 4.3.2##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_step_best_subset(model2_tanpa4750)## Best Subsets Regression
## -----------------------------
## Model Index Predictors
## -----------------------------
## 1 X4
## 2 X1 X4
## 3 X2 X3 X4
## 4 X1 X2 X3 X4
## 5 X1 X2 X3 X4 X5
## -----------------------------
##
## Subsets Regression Summary
## -----------------------------------------------------------------------------------------------------------------------------------
## Adj. Pred
## Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
## -----------------------------------------------------------------------------------------------------------------------------------
## 1 0.6281 0.6200 0.6022 2.5358 288.5865 152.4923 294.2001 1056.9484 22.9364 0.4893 0.4043
## 2 0.6519 0.6364 0.6121 1.5563 287.4105 151.7837 294.8953 1011.7606 22.3838 0.4788 0.3945
## 3 0.6576 0.6343 0.5932 2.8404 288.6150 153.3313 297.9710 1018.2723 22.9577 0.4928 0.4047
## 4 0.6620 0.6305 0.5677 4.2945 289.9994 155.0939 301.2266 1029.2339 23.6383 0.5097 0.4166
## 5 0.6643 0.6244 0.5455 6.0000 291.6640 157.1194 304.7624 1046.9947 24.4861 0.5309 0.4316
## -----------------------------------------------------------------------------------------------------------------------------------
## AIC: Akaike Information Criteria
## SBIC: Sawa's Bayesian Information Criteria
## SBC: Schwarz Bayesian Criteria
## MSEP: Estimated error of prediction, assuming multivariate normality
## FPE: Final Prediction Error
## HSP: Hocking's Sp
## APC: Amemiya Prediction Criteriamodelfinal = lm(Y ~ X1+X4, data=dataframe02[-c(47,50),])
summary(modelfinal)##
## Call:
## lm(formula = Y ~ X1 + X4, data = dataframe02[-c(47, 50), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.329 -2.658 -1.124 3.767 9.553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.29859 8.45268 -3.466 0.00117 **
## X1 0.67103 0.38246 1.754 0.08616 .
## X4 0.27761 0.04507 6.160 1.81e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.59 on 45 degrees of freedom
## Multiple R-squared: 0.6519, Adjusted R-squared: 0.6364
## F-statistic: 42.13 on 2 and 45 DF, p-value: 4.886e-11ols_step_both_p(model2_tanpa4750, details = TRUE)## Stepwise Selection Method
## -------------------------
##
## Candidate Terms:
##
## 1. X1
## 2. X2
## 3. X3
## 4. X4
## 5. X5
##
##
## Step => 0
## Model => Y ~ 1
## R2 => 0
##
## Initiating stepwise selection...
##
## Step => 1
## Selected => X4
## Model => Y ~ X4
## R2 => 0.628
##
## Step => 2
## Selected => X1
## Model => Y ~ X4 + X1
## R2 => 0.652
##
##
## No more variables to be added or removed.##
##
## Stepwise Summary
## -------------------------------------------------------------------------
## Step Variable AIC SBC SBIC R2 Adj. R2
## -------------------------------------------------------------------------
## 0 Base Model 334.060 337.803 195.850 0.00000 0.00000
## 1 X4 (+) 288.587 294.200 152.492 0.62807 0.61998
## 2 X1 (+) 287.411 294.895 151.784 0.65188 0.63641
## -------------------------------------------------------------------------
##
## Final Model Output
## ------------------
##
## Model Summary
## ---------------------------------------------------------------
## R 0.807 RMSE 4.444
## R-Squared 0.652 MSE 21.067
## Adj. R-Squared 0.636 Coef. Var 10.896
## Pred R-Squared 0.612 AIC 287.411
## MAE 3.648 SBC 294.895
## ---------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
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## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------
## Regression 1775.229 2 887.615 42.133 0.0000
## Residual 948.021 45 21.067
## Total 2723.250 47
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##
## Parameter Estimates
## -------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------
## (Intercept) -29.299 8.453 -3.466 0.001 -46.323 -12.274
## X4 0.278 0.045 0.677 6.160 0.000 0.187 0.368
## X1 0.671 0.382 0.193 1.754 0.086 -0.099 1.441
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