KOMPUTASI STATISTIKA
~ Ujian Tengah Semester ~
| Kontak | : \(\downarrow\) |
| jirene113@gmail.com | |
| https://www.instagram.com/irenegani/ | |
| RPubs | https://rpubs.com/irenegani/ |
Data Set
Kumpulan data akan anda gunakan dalam ujian tengah semester ini adalah data konsumen yang melakukan pinjaman di suatu Bank. Dataset ini memiliki 613 observasi, 13 atribut sebagai berikut:
Tugas 1
Lakukan proses persiapan data dengan R dan Python, dengan beberapa langkah berikut:
- Import Data
- Penanganan Data Hilang
## Loan_ID Gender Married Dependents Education Self_Employed
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## [613,] FALSE FALSE FALSE FALSE FALSE FALSE
## [614,] FALSE FALSE FALSE FALSE FALSE FALSE
## ApplicantIncome CoapplicantIncome LoanAmount Loan_Amount_Term
## [1,] FALSE FALSE TRUE FALSE
## [2,] FALSE FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE FALSE
## [4,] FALSE FALSE FALSE FALSE
## [5,] FALSE FALSE FALSE FALSE
## [6,] FALSE FALSE FALSE FALSE
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## [128,] FALSE FALSE TRUE FALSE
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## [436,] FALSE FALSE TRUE FALSE
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## [480,] FALSE FALSE TRUE FALSE
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## [525,] FALSE FALSE TRUE FALSE
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## [546,] FALSE FALSE FALSE FALSE
## [547,] FALSE FALSE FALSE FALSE
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## [549,] FALSE FALSE FALSE FALSE
## [550,] FALSE FALSE FALSE FALSE
## [551,] FALSE FALSE TRUE FALSE
## [552,] FALSE FALSE TRUE FALSE
## [553,] FALSE FALSE FALSE FALSE
## [554,] FALSE FALSE FALSE FALSE
## [555,] FALSE FALSE FALSE FALSE
## [556,] FALSE FALSE FALSE FALSE
## [557,] FALSE FALSE FALSE FALSE
## [558,] FALSE FALSE FALSE FALSE
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## [564,] FALSE FALSE FALSE FALSE
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## [567,] FALSE FALSE FALSE FALSE
## [568,] FALSE FALSE FALSE FALSE
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## [570,] FALSE FALSE FALSE FALSE
## [571,] FALSE FALSE FALSE FALSE
## [572,] FALSE FALSE FALSE FALSE
## [573,] FALSE FALSE FALSE FALSE
## [574,] FALSE FALSE FALSE FALSE
## [575,] FALSE FALSE FALSE FALSE
## [576,] FALSE FALSE FALSE FALSE
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## [578,] FALSE FALSE FALSE FALSE
## [579,] FALSE FALSE FALSE FALSE
## [580,] FALSE FALSE FALSE FALSE
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## [586,] FALSE FALSE FALSE FALSE
## [587,] FALSE FALSE FALSE FALSE
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## [594,] FALSE FALSE FALSE FALSE
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## [600,] FALSE FALSE FALSE FALSE
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## [602,] FALSE FALSE FALSE FALSE
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## [604,] FALSE FALSE FALSE FALSE
## [605,] FALSE FALSE FALSE FALSE
## [606,] FALSE FALSE TRUE FALSE
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## [608,] FALSE FALSE FALSE FALSE
## [609,] FALSE FALSE FALSE FALSE
## [610,] FALSE FALSE FALSE FALSE
## [611,] FALSE FALSE FALSE FALSE
## [612,] FALSE FALSE FALSE FALSE
## [613,] FALSE FALSE FALSE FALSE
## [614,] FALSE FALSE FALSE FALSE
## Credit_History Property_Area Loan_Status
## [1,] FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE
## [3,] FALSE FALSE FALSE
## [4,] FALSE FALSE FALSE
## [5,] FALSE FALSE FALSE
## [6,] FALSE FALSE FALSE
## [7,] FALSE FALSE FALSE
## [8,] FALSE FALSE FALSE
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## [10,] FALSE FALSE FALSE
## [11,] FALSE FALSE FALSE
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## [18,] FALSE FALSE FALSE
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## [25,] TRUE FALSE FALSE
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## [30,] FALSE FALSE FALSE
## [31,] TRUE FALSE FALSE
## [32,] FALSE FALSE FALSE
## [33,] FALSE FALSE FALSE
## [34,] FALSE FALSE FALSE
## [35,] FALSE FALSE FALSE
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## [66,] FALSE FALSE FALSE
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## [68,] FALSE FALSE FALSE
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## [70,] FALSE FALSE FALSE
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## [78,] FALSE FALSE FALSE
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## [80,] TRUE FALSE FALSE
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## [84,] TRUE FALSE FALSE
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## [88,] FALSE FALSE FALSE
## [89,] FALSE FALSE FALSE
## [90,] FALSE FALSE FALSE
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## [94,] FALSE FALSE FALSE
## [95,] FALSE FALSE FALSE
## [96,] TRUE FALSE FALSE
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## [98,] FALSE FALSE FALSE
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## [100,] FALSE FALSE FALSE
## [101,] FALSE FALSE FALSE
## [102,] FALSE FALSE FALSE
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## [104,] FALSE FALSE FALSE
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## [109,] FALSE FALSE FALSE
## [110,] FALSE FALSE FALSE
## [111,] FALSE FALSE FALSE
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## [113,] FALSE FALSE FALSE
## [114,] FALSE FALSE FALSE
## [115,] FALSE FALSE FALSE
## [116,] FALSE FALSE FALSE
## [117,] FALSE FALSE FALSE
## [118,] TRUE FALSE FALSE
## [119,] FALSE FALSE FALSE
## [120,] FALSE FALSE FALSE
## [121,] FALSE FALSE FALSE
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## [123,] FALSE FALSE FALSE
## [124,] FALSE FALSE FALSE
## [125,] FALSE FALSE FALSE
## [126,] TRUE FALSE FALSE
## [127,] FALSE FALSE FALSE
## [128,] FALSE FALSE FALSE
## [129,] FALSE FALSE FALSE
## [130,] TRUE FALSE FALSE
## [131,] TRUE FALSE FALSE
## [132,] FALSE FALSE FALSE
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## [1] FALSE- Pemisahan Data Kategori dan Numerik
## Warning: package 'tidyverse' was built under R version 4.0.5## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.1 v dplyr 1.0.6
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.1## Warning: package 'ggplot2' was built under R version 4.0.5## Warning: package 'tibble' was built under R version 4.0.5## Warning: package 'tidyr' was built under R version 4.0.5## Warning: package 'dplyr' was built under R version 4.0.5## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()- Penanganan Data Numerik
normalisasi <- function(x){(x- min(x))/(max(x)-min(x))}
normalisasidata <- as.data.frame(lapply(dataloanNum,normalisasi))
normalisasidata- Penganann Data Pencilan
## Warning: package 'leaps' was built under R version 4.0.5outliers <- function(x) {
Q1 <- quantile(x, probs = .25)
Q3 <- quantile(x, probs = .75)
iqr <- IQR(x)
upper_limit <- Q3 + (1.5*iqr)
lower_limit <- Q1 - (1.5*iqr)
}- Penanganan Data Kategorikal
Tugas 2
Lakukan Proses Visualisasi Data dengan menggunakan R dan Python dengan beberapa langkah berikut:
- Visualisasi Univariabel ** Kategorik
ggplot(loantrain, aes(x = Gender)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Gender",
y = "Frequency",
title = "Loan by Gender")
ggplot(loantrain, aes(x = Married)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Married",
y = "Frequency",
title = "Loan by Married")
ggplot(loantrain, aes(x = Dependents)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Dependents",
y = "Frequency",
title = "Loan by Dependents")
ggplot(loantrain, aes(x = Education)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Education",
y = "Frequency",
title = "Loan by Education")
ggplot(loantrain, aes(x = Self_Employed)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Self_Employed",
y = "Frequency",
title = "Loan by Self Employed")
ggplot(loantrain, aes(x = Property_Area)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Property_Area",
y = "Frequency",
title = "Loan by Property Area")
ggplot(loantrain, aes(x = Loan_Status)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Loan_Status",
y = "Frequency",
title = "Loan by Loan Status")
ggplot(loantrain, aes(x = Credit_History)) +
geom_bar(fill = "cornflowerblue",
color= "azure4") +
theme_minimal()+
labs(x = "Credit_History",
y = "Frequency",
title = "Loan by Credit History")## Warning: Removed 50 rows containing non-finite values (stat_count).
** Numerik
##
## Attaching package: 'scales'## The following object is masked from 'package:purrr':
##
## discard## The following object is masked from 'package:readr':
##
## col_factorggplot(loantrain,
aes(x = LoanAmount,
y = ..count.. / sum(..count..))) +
geom_histogram(fill = "cornflowerblue",
color = "white",
binwidth = 5) +
theme_minimal() +
labs(title="Loan Amount",
y = "Percent",
x = "LoanAmount") +
scale_y_continuous(labels = percent)## Warning: Removed 22 rows containing non-finite values (stat_bin).
library(ggplot2)
library(scales)
ggplot(loantrain,
aes(x = Loan_Amount_Term,
y = ..count.. / sum(..count..))) +
geom_histogram(fill = "cornflowerblue",
color = "white",
binwidth = 5) +
theme_minimal() +
labs(title="Loan Amount Term",
y = "Percent",
x = "Loan_Amount_Term") +
scale_y_continuous(labels = percent)## Warning: Removed 14 rows containing non-finite values (stat_bin).
library(ggplot2)
library(scales)
ggplot(loantrain,
aes(x = ApplicantIncome,
y = ..count.. / sum(..count..))) +
geom_histogram(fill = "cornflowerblue",
color = "white",
binwidth = 5) +
theme_minimal() +
labs(title="Applicant Income",
y = "Percent",
x = "Applicant Income") +
scale_y_continuous(labels = percent)
library(ggplot2)
library(scales)
ggplot(loantrain,
aes(x = CoapplicantIncome,
y = ..count.. / sum(..count..))) +
geom_histogram(fill = "cornflowerblue",
color = "white",
binwidth = 5) +
theme_minimal() +
labs(title="Coapplicant Income",
y = "Percent",
x = "Coapplicant Income") +
scale_y_continuous(labels = percent)
library(ggplot2)
library(scales)
ggplot(loantrain,
aes(x = Credit_History,
y = ..count.. / sum(..count..))) +
geom_histogram(fill = "cornflowerblue",
color = "white",
binwidth = 5) +
theme_minimal() +
labs(title="Credit History",
y = "Percent",
x = "Credit_History") +
scale_y_continuous(labels = percent)## Warning: Removed 50 rows containing non-finite values (stat_bin).
- Visualisasi Bivariabel ** Categorical vs Categorical
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Education)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Self_Employed)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Property_Area)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Loan_Status)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Married,
fill = Education)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Married,
fill = Self_Employed)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Married,
fill = Loan_Status)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Education,
fill = Property_Area)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Education,
fill = Gender)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Education)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
library(ggplot2)
ggplot(loantrain,
aes(x = Gender,
fill = Married)) +
theme_minimal() +
geom_bar(position = position_dodge(preserve = "single"))
** Continuous VS Continuous
## Warning in data(loantrain, package = "carData"): data set 'loantrain' not foundggplot(loantrain,
aes(x = LoanAmount,
y = ApplicantIncome)) +
geom_point(color = "cornflowerblue",
size = 2,
alpha=.8) +
scale_y_continuous(label = scales::dollar,
limits= c(0, 10000)) +
scale_x_continuous(breaks = seq(0, 60, 10),
limits = c(0, 60)) +
theme_minimal() +
labs(x = "LoanAmount",
y = "ApplicantIncome",
title = "",
subtitle = "")## Warning: Removed 579 rows containing missing values (geom_point).
## Warning in data(loantrain, package = "carData"): data set 'loantrain' not foundggplot(loantrain,
aes(x = LoanAmount,
y = CoapplicantIncome)) +
geom_point(color = "cornflowerblue",
size = 2,
alpha=.8) +
scale_y_continuous(label = scales::dollar,
limits= c(0, 10000)) +
scale_x_continuous(breaks = seq(0, 60, 10),
limits = c(0, 60)) +
theme_minimal() +
labs(x = "LoanAmount",
y = "CopplicantIncome",
title = "",
subtitle = "")## Warning: Removed 577 rows containing missing values (geom_point).
## Warning in data(loantrain, package = "carData"): data set 'loantrain' not foundggplot(loantrain,
aes(x = ApplicantIncome,
y = CoapplicantIncome)) +
geom_point(color = "cornflowerblue",
size = 2,
alpha=.8) +
scale_y_continuous(label = scales::dollar,
limits= c(0, 10000)) +
scale_x_continuous(breaks = seq(0, 60, 10),
limits = c(0, 60)) +
theme_minimal() +
labs(x = "ApplicantIncome",
y = "CopplicantIncome",
title = "",
subtitle = "")## Warning: Removed 614 rows containing missing values (geom_point).
## Warning in data(loantrain, package = "carData"): data set 'loantrain' not foundggplot(loantrain,
aes(x = LoanAmount,
y = Loan_Amount_Term)) +
geom_point(color = "cornflowerblue",
size = 2,
alpha=.8) +
scale_y_continuous(label = scales::dollar,
limits= c(0, 10000)) +
scale_x_continuous(breaks = seq(0, 60, 10),
limits = c(0, 60)) +
theme_minimal() +
labs(x = "LoanAmount",
y = "Loan_Amount_Term",
title = "",
subtitle = "")## Warning: Removed 577 rows containing missing values (geom_point).
- Visualisasi Multivariabel
library(ggplot2)
ggplot(loantrain,
aes(x = LoanAmount,
y = ApplicantIncome,
color = Education,
shape = Gender)) +
geom_point(size = 3,
alpha= .6) +
theme_minimal() +
labs(title = "")## Warning: Removed 22 rows containing missing values (geom_point).
Tugas 3
Lakukan proses analisa data secara deskriptif menggunakan R dan Python dengan beberapa langkah berikut:
- Kualitatif
- Kategori Univariat
## $Loan_ID
## integer(0)
##
## $Gender
## integer(0)
##
## $Married
## integer(0)
##
## $Dependents
## integer(0)
##
## $Education
## integer(0)
##
## $Self_Employed
## integer(0)
##
## $ApplicantIncome
## integer(0)
##
## $CoapplicantIncome
## integer(0)
##
## $LoanAmount
## [1] 1 36 64 82 96 103 104 114 128 203 285 306 323 339 388 436 438 480 525
## [20] 551 552 606
##
## $Loan_Amount_Term
## [1] 20 37 45 46 74 113 166 198 224 233 336 368 422 424
##
## $Credit_History
## [1] 17 25 31 43 80 84 87 96 118 126 130 131 157 182 188 199 220 237 238
## [20] 260 261 280 310 314 318 319 324 349 364 378 393 396 412 445 450 452 461 474
## [39] 491 492 498 504 507 531 534 545 557 566 584 601
##
## $Property_Area
## integer(0)
##
## $Loan_Status
## integer(0)##
## Female Male
## 12 95 422##
## Female Male
## 0.02268431 0.17958412 0.79773157- Kategori Bivariat
##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
##
## set_names## The following object is masked from 'package:tidyr':
##
## extract## Education
## Gender Graduate Not Graduate
## 11 1
## Female 80 15
## Male 330 92- Kategori Multivariat
## Loan_Status N Y
## Gender Education
## Graduate 4 7
## Not Graduate 1 0
## Female Graduate 30 50
## Not Graduate 4 11
## Male Graduate 88 242
## Not Graduate 36 56- Kuantitatif
- Univariat numerik
## [1] "ApplicantIncome" "CoapplicantIncome" "LoanAmount"
## [4] "Loan_Amount_Term" "Credit_History"## [1] 145.8526## 0% 25% 50% 75% 100%
## 9 100 128 167 700## [1] 128## [1] "numeric"## ApplicantIncome CoapplicantIncome LoanAmount Loan_Amount_Term
## Min. : 150 Min. : 0 Min. : 9.0 Min. : 36.0
## 1st Qu.: 2900 1st Qu.: 0 1st Qu.:100.0 1st Qu.:360.0
## Median : 3816 Median : 1086 Median :128.0 Median :360.0
## Mean : 5508 Mean : 1542 Mean :145.9 Mean :342.4
## 3rd Qu.: 5815 3rd Qu.: 2232 3rd Qu.:167.0 3rd Qu.:360.0
## Max. :81000 Max. :33837 Max. :700.0 Max. :480.0
## Credit_History
## Min. :0.0000
## 1st Qu.:1.0000
## Median :1.0000
## Mean :0.8507
## 3rd Qu.:1.0000
## Max. :1.0000## [1] 7074.224## [1] 67## [1] 0## [1] 0.3567591## Warning: package 'e1071' was built under R version 4.0.5## [1] 2.593174## [1] 9.936842- Bivariat numerik
## [1] 126.7792## [1] 0.02323917- Multivariat numerik
## ApplicantIncome CoapplicantIncome LoanAmount
## ApplicantIncome 4.101291e+07 -1.982437e+06 3.074072e+05
## CoapplicantIncome -1.982437e+06 6.372069e+06 3.379027e+04
## LoanAmount 3.074072e+05 3.379027e+04 7.074224e+03
## Loan_Amount_Term -2.611139e+04 -4.740321e+01 1.267792e+02
## Credit_History -5.432772e+01 -9.768561e+00 -5.447886e-01
## Loan_Amount_Term Credit_History
## ApplicantIncome -2.611139e+04 -54.3277231
## CoapplicantIncome -4.740321e+01 -9.7685610
## LoanAmount 1.267792e+02 -0.5447886
## Loan_Amount_Term 4.207035e+03 0.2003351
## Credit_History 2.003351e-01 0.1272770## ApplicantIncome CoapplicantIncome LoanAmount
## ApplicantIncome 1.00000000 -0.1226305807 0.57070849
## CoapplicantIncome -0.12263058 1.0000000000 0.15915197
## LoanAmount 0.57070849 0.1591519703 1.00000000
## Loan_Amount_Term -0.06286105 -0.0002895206 0.02323917
## Credit_History -0.02377860 -0.0108471425 -0.01815573
## Loan_Amount_Term Credit_History
## ApplicantIncome -0.0628610527 -0.02377860
## CoapplicantIncome -0.0002895206 -0.01084714
## LoanAmount 0.0232391675 -0.01815573
## Loan_Amount_Term 1.0000000000 0.00865753
## Credit_History 0.0086575296 1.00000000- EDA dengan cara Malas
Tugas 4
Lakukan pemeriksaan distribusi densitas menggunakan R dan Python pada setiap variabel kuantitatif dengan beberapa bagian sebagai berikut:
- Univariat numerik
## Warning: Removed 22 rows containing non-finite values (stat_density).
- Bivariat numerik
## Warning: package 'plotly' was built under R version 4.0.5##
## 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':
##
## layoutbivariat <- ggplot(dataloan,
aes(x = ApplicantIncome,
y = LoanAmount)) +
geom_point(alpha = .5) +
geom_density_2d()
ggplotly(bivariat)## Warning: Removed 22 rows containing non-finite values (stat_density2d).bivariat2 <- ggplot(dataloan, aes(x = ApplicantIncome, y = CoapplicantIncome)) +
geom_point(alpha = .5) +
geom_density_2d()
ggplotly(bivariat2)- Multivariat numerik
## Warning: package 'GGally' was built under R version 4.0.5## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 22 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 14 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 50 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 22 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 14 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 50 rows containing missing values## Warning: Removed 22 rows containing missing values (geom_point).
## Warning: Removed 22 rows containing missing values (geom_point).## Warning: Removed 22 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 36 rows containing missing values## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 71 rows containing missing values## Warning: Removed 14 rows containing missing values (geom_point).
## Warning: Removed 14 rows containing missing values (geom_point).## Warning: Removed 36 rows containing missing values (geom_point).## Warning: Removed 14 rows containing non-finite values (stat_density).## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 64 rows containing missing values## Warning: Removed 50 rows containing missing values (geom_point).
## Warning: Removed 50 rows containing missing values (geom_point).## Warning: Removed 71 rows containing missing values (geom_point).## Warning: Removed 64 rows containing missing values (geom_point).## Warning: Removed 50 rows containing non-finite values (stat_density).
Tugas 5
Lakukan proses pengujian Hipotesis menggunakan R dan Python pada setiap variabel kuantitatif dengan beberapa bagian sebagai berikut:
- Hitunglah margin of error dan estimasi interval untuk proporsi peminjam bejenis kelamin perempuan dalam pada tingkat kepercayaan 95%.
## Warning: package 'MASS' was built under R version 4.0.5##
## Attaching package: 'MASS'## The following object is masked from 'package:plotly':
##
## select## The following object is masked from 'package:dplyr':
##
## selectk = sum(dataloan$Gender == "Female")
n = length(dataloan$Gender)
pbar = k/n
SE = sqrt(pbar*(1-pbar)/n); SE ## [1] 0.01558505## [1] 0.03054614## [1] 0.1518643 0.2129566- Jika anda berencana menggunakan perkiraan proporsi 50% data konsumen berjenis kelamin perempuan, temukan ukuran sampel yang diperlukan untuk mencapai margin kesalahan 5% untuk data obeservasi pada tingkat kepercayaan 95%.
## [1] 384.1459Lakukan pembuktian kebenaran assumsi dengan tingakat signifikansi 0.05, jika Bank mengklaim bahwa pinjaman rata-rata konsumen adalah:
- Lebih besar $ 150.
mu0 = 150
xbar = mean(dataloan$LoanAmount)
s = sd(dataloan$LoanAmount)
n = length(dataloan$LoanAmount)
t = (xbar-mu0)/(s/sqrt(n)) ; t## [1] NA## [1] -1.647343- Lebih kecil $ 150
mu0 = 150
xbar = mean(dataloan$LoanAmount)
s = sd(dataloan$LoanAmount)
n = length(dataloan$LoanAmount)
t = (xbar-mu0)/(s/sqrt(n)) ; t## [1] NA## [1] 1.647343- Sama dengan $ 150.
mu0 = 150
xbar = mean(dataloan$LoanAmount)
s = sd(dataloan$LoanAmount)
n = length(dataloan$LoanAmount)
t = (xbar-mu0)/(s/sqrt(n)) ; t## [1] NA## [1] -1.963841 1.963841- Lakukan pembuktian kebenaran assumsi dengan tingakat signifikansi 0.05, seperti diatas jika diketahui simpangan baku pinjaman adalah $ 85.
mu0 = 150
xbar = mean(dataloan$LoanAmount)
s = 85
n = sum(count(dataloan))
t = (xbar-mu0)/(s/sqrt(n));t## [1] NA## [1] 1.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