Load & Preparation

# Read Dataset
df_mentah <- read_csv("StudentsPerformance.csv")
print(colnames(df_mentah))
## [1] "gender"                      "race/ethnicity"             
## [3] "parental level of education" "lunch"                      
## [5] "test preparation course"     "math score"                 
## [7] "reading score"               "writing score"
# Data Cleaning

# 1. perbaiki nama kolom
colnames(df_mentah) <- c(
  "gender",
  "race_ethnicity",
  "parental_level_of_education",
  "lunch",
  "test_preparation_course",
  "math_score",
  "reading_score",
  "writing_score"
)

df <- df_mentah

# 2. ubah variabel kategori menjadi faktor
df <- df_mentah %>% mutate(across(where(is.character), as.factor))

# 3. cek missing value
missing_table <- colSums(is.na(df)) %>% as.data.frame() %>% rename(Jumlah_NA = ".")

# 4. tabel missing value
missing_table %>% kable(caption = "Tabel 1: Pengecekan Missing Value per Kolom") %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F, position = "left")
Tabel 1: Pengecekan Missing Value per Kolom
Jumlah_NA
gender 0
race_ethnicity 0
parental_level_of_education 0
lunch 0
test_preparation_course 0
math_score 0
reading_score 0
writing_score 0 
# 5. cek data duplikasi
sum(duplicated(df)) %>% tibble(Keterangan = "total data duplikat", Jumlah = .) %>% kable() %>% kable_styling(full_width = F)
Keterangan Jumlah
total data duplikat 0 
# 6. cek outlier
df %>%
  dplyr::select(math_score, reading_score, writing_score) %>%
  pivot_longer(cols = everything()) %>%
  ggplot(aes(x=name, y=value, fill=name)) +
  geom_boxplot() +
  theme_minimal() +
  labs(title = "Cek Outlier pada Skor Ujian")

# 7. penanganan outlier

# cari batas bawah
Q1 <- apply(df[, 6:8], 2, quantile, probs = 0.25)
IQR_val <- apply(df[, 6:8], 2, IQR)

# batas bawah masing masing skor
low_math <- Q1[1] - 1.5 * IQR_val[1]
low_reading <- Q1[2] - 1.5 * IQR_val[2]
low_writing <- Q1[3] - 1.5 * IQR_val[3]

# ambil yang di atas batas bawah
df_final <- df %>% filter(math_score >= low_math, reading_score >= low_reading, writing_score >= low_writing)

# cek data yang terbuang
tibble(Keterangan = c("data awal", "data akhir", "data terbuang"), Jumlah = c(nrow(df_mentah), nrow(df_final), nrow(df_mentah) - nrow(df_final))) %>% kable(caption = "ringkasan pembersihan data") %>% kable_styling(full_width = F, position = "left")
ringkasan pembersihan data
Keterangan Jumlah
data awal 1000
data akhir 988
data terbuang 12 
# Summary
describe(df_final)[, c("n", "mean", "sd", "min", "max")] %>% kable(caption = "statistik deskriptif data final", digits = 2) %>% kable_styling(full_width = F)
statistik deskriptif data final
n mean sd min max
gender* 988 1.48 0.50 1 2
race_ethnicity* 988 3.18 1.16 1 5
parental_level_of_education* 988 3.47 1.83 1 6
lunch* 988 1.65 0.48 1 2
test_preparation_course* 988 1.64 0.48 1 2
math_score 988 66.63 14.41 27 100
reading_score 988 69.64 14.02 29 100
writing_score 988 68.57 14.53 27 100

Menampilkan Dataset

Dataset Student Performace
gender race_ethnicity parental_level_of_education lunch test_preparation_course math_score reading_score writing_score
female group B bachelor’s degree standard none 72 72 74
female group C some college standard completed 69 90 88
female group B master’s degree standard none 90 95 93
male group A associate’s degree free/reduced none 47 57 44
male group C some college standard none 76 78 75
female group B associate’s degree standard none 71 83 78
female group B some college standard completed 88 95 92
male group B some college free/reduced none 40 43 39
male group D high school free/reduced completed 64 64 67
female group B high school free/reduced none 38 60 50
male group C associate’s degree standard none 58 54 52
male group D associate’s degree standard none 40 52 43
female group B high school standard none 65 81 73
male group A some college standard completed 78 72 70
female group A master’s degree standard none 50 53 58
female group C some high school standard none 69 75 78
male group C high school standard none 88 89 86
male group C master’s degree free/reduced completed 46 42 46
female group C associate’s degree free/reduced none 54 58 61
male group D high school standard none 66 69 63
female group B some college free/reduced completed 65 75 70
male group D some college standard none 44 54 53
female group C some high school standard none 69 73 73
male group D bachelor’s degree free/reduced completed 74 71 80
male group A master’s degree free/reduced none 73 74 72
male group B some college standard none 69 54 55
female group C bachelor’s degree standard none 67 69 75
male group C high school standard none 70 70 65
female group D master’s degree standard none 62 70 75
female group D some college standard none 69 74 74
female group B some college standard none 63 65 61
female group E master’s degree free/reduced none 56 72 65
male group D some college standard none 40 42 38
male group E some college standard none 97 87 82
male group E associate’s degree standard completed 81 81 79
female group D associate’s degree standard none 74 81 83
female group D some high school free/reduced none 50 64 59
female group D associate’s degree free/reduced completed 75 90 88
male group B associate’s degree free/reduced none 57 56 57
male group C associate’s degree free/reduced none 55 61 54
female group C associate’s degree standard none 58 73 68
female group B associate’s degree standard none 53 58 65
male group B some college free/reduced completed 59 65 66
female group E associate’s degree free/reduced none 50 56 54
male group B associate’s degree standard none 65 54 57
female group A associate’s degree standard completed 55 65 62
female group C high school standard none 66 71 76
female group D associate’s degree free/reduced completed 57 74 76
male group C high school standard completed 82 84 82
male group E some college standard none 53 55 48
male group E associate’s degree free/reduced completed 77 69 68
male group C some college standard none 53 44 42
male group D high school standard none 88 78 75
female group C some high school free/reduced completed 71 84 87
female group C high school free/reduced none 33 41 43
female group E associate’s degree standard completed 82 85 86
male group D associate’s degree standard none 52 55 49
male group D some college standard completed 58 59 58
male group E bachelor’s degree free/reduced completed 79 74 72
male group A some high school free/reduced none 39 39 34
male group A associate’s degree free/reduced none 62 61 55
female group C associate’s degree standard none 69 80 71
female group D some high school standard none 59 58 59
male group B some high school standard none 67 64 61
male group D some high school free/reduced none 45 37 37
female group C some college standard none 60 72 74
male group B associate’s degree free/reduced none 61 58 56
female group C associate’s degree standard none 39 64 57
female group D some college free/reduced completed 58 63 73
male group D some college standard completed 63 55 63
female group A associate’s degree free/reduced none 41 51 48
male group C some high school free/reduced none 61 57 56
male group C some high school standard none 49 49 41
male group B associate’s degree free/reduced none 44 41 38
male group A bachelor’s degree standard completed 80 78 81
female group D some high school standard completed 61 74 72
female group E master’s degree standard none 62 68 68
female group B associate’s degree standard none 47 49 50
male group B high school free/reduced none 49 45 45
male group A some college free/reduced completed 50 47 54
male group E associate’s degree standard none 72 64 63
male group D high school free/reduced none 42 39 34
female group C some college standard none 73 80 82
female group C some college free/reduced none 76 83 88
female group D associate’s degree standard none 71 71 74
female group A some college standard none 58 70 67
female group D some high school standard none 73 86 82
female group C bachelor’s degree standard none 65 72 74
male group C high school free/reduced none 27 34 36
male group C high school standard none 71 79 71
male group C associate’s degree free/reduced completed 43 45 50
female group B some college standard none 79 86 92
male group C associate’s degree free/reduced completed 78 81 82
male group B some high school standard completed 65 66 62
female group E some college standard completed 63 72 70
female group D some college free/reduced none 58 67 62
female group D bachelor’s degree standard none 65 67 62
male group B some college standard none 79 67 67
male group D bachelor’s degree standard completed 68 74 74
female group D associate’s degree standard none 85 91 89
male group B high school standard completed 60 44 47
male group C some college standard completed 98 86 90
female group C some college standard none 58 67 72
female group D master’s degree standard none 87 100 100
male group E associate’s degree standard completed 66 63 64
female group B associate’s degree free/reduced none 52 76 70
female group B some high school standard none 70 64 72
female group D associate’s degree free/reduced completed 77 89 98
male group C high school standard none 62 55 49
male group A associate’s degree standard none 54 53 47
female group D some college standard none 51 58 54
female group E bachelor’s degree standard completed 99 100 100
male group C high school standard none 84 77 74
female group B bachelor’s degree free/reduced none 75 85 82
female group D bachelor’s degree standard none 78 82 79
female group D some high school standard none 51 63 61
female group C some college standard none 55 69 65
female group C bachelor’s degree standard completed 79 92 89
male group B associate’s degree standard completed 91 89 92
female group C some college standard completed 88 93 93
male group D high school free/reduced none 63 57 56
male group E some college standard none 83 80 73
female group B high school standard none 87 95 86
male group B some high school standard none 72 68 67
male group D some college standard completed 65 77 74
male group D master’s degree standard none 82 82 74
female group A bachelor’s degree standard none 51 49 51
male group D master’s degree standard none 89 84 82
male group C some high school free/reduced completed 53 37 40
male group E some college free/reduced completed 87 74 70
female group C some college standard completed 75 81 84
male group D bachelor’s degree free/reduced completed 74 79 75
male group C bachelor’s degree standard none 58 55 48
male group B some high school standard completed 51 54 41
male group E high school standard none 70 55 56
female group C associate’s degree standard none 59 66 67
male group D some college standard completed 71 61 69
female group D some high school standard none 76 72 71
female group C some college free/reduced none 59 62 64
female group E some college free/reduced completed 42 55 54
male group A high school standard none 57 43 47
male group D some college standard none 88 73 78
male group B some high school standard none 88 84 75
male group C associate’s degree free/reduced none 73 68 66
female group D bachelor’s degree standard completed 68 75 81
male group E associate’s degree free/reduced completed 100 100 93
male group A some high school standard completed 62 67 69
male group A bachelor’s degree standard none 77 67 68
female group B associate’s degree standard completed 59 70 66
male group D bachelor’s degree standard none 54 49 47
male group D some high school standard none 62 67 61
female group C some college standard completed 70 89 88
female group E high school free/reduced completed 66 74 78
male group B some college free/reduced none 60 60 60
female group B associate’s degree standard completed 61 86 87
male group D associate’s degree free/reduced none 66 62 64
male group B associate’s degree free/reduced completed 82 78 74
female group E some college free/reduced completed 75 88 85
male group B master’s degree free/reduced none 49 53 52
male group C high school standard none 52 53 49
female group E master’s degree standard none 81 92 91
female group C bachelor’s degree standard completed 96 100 100
male group C high school free/reduced completed 53 51 51
female group B master’s degree free/reduced completed 58 76 78
female group B high school standard completed 68 83 78
female group C some college free/reduced completed 67 75 70
male group A high school standard completed 72 73 74
male group E some high school standard none 94 88 78
female group D some college standard none 79 86 81
female group C associate’s degree standard none 63 67 70
female group C bachelor’s degree free/reduced completed 43 51 54
female group C master’s degree standard completed 81 91 87
female group B high school free/reduced completed 46 54 58
female group C associate’s degree standard completed 71 77 77
female group B master’s degree free/reduced completed 52 70 62
female group D some high school standard completed 97 100 100
male group C master’s degree free/reduced completed 62 68 75
female group C some college free/reduced none 46 64 66
female group E high school standard none 50 50 47
female group D associate’s degree standard none 65 69 70
male group C some high school free/reduced completed 45 52 49
male group C associate’s degree free/reduced completed 65 67 65
male group E high school standard none 80 76 65
male group D some high school standard completed 62 66 68
male group B some high school free/reduced none 48 52 45
female group C bachelor’s degree standard none 77 88 87
female group E associate’s degree standard none 66 65 69
male group D some college standard completed 76 83 79
female group B some high school standard none 62 64 66
male group D some college standard completed 77 62 62
female group C master’s degree standard completed 69 84 85
male group D associate’s degree standard none 61 55 52
male group C some high school free/reduced completed 59 69 65
male group E high school free/reduced none 55 56 51
female group B some college free/reduced none 45 53 55
female group B bachelor’s degree free/reduced none 78 79 76
female group C associate’s degree standard completed 67 84 86
female group D some college free/reduced none 65 81 77
male group C associate’s degree standard none 69 77 69
female group B associate’s degree standard none 57 69 68
male group C some college standard none 59 41 42
male group D some high school standard completed 74 71 78
male group E bachelor’s degree standard none 82 62 62
male group E high school standard completed 81 80 76
female group B some college free/reduced none 74 81 76
female group B some college free/reduced none 58 61 66
male group D some high school free/reduced completed 80 79 79
female group C high school free/reduced none 42 62 60
male group C associate’s degree free/reduced completed 60 51 56
male group E high school standard completed 87 91 81
male group B some high school standard completed 84 83 75
female group E associate’s degree free/reduced completed 83 86 88
female group C high school free/reduced none 34 42 39
male group B high school free/reduced none 66 77 70
male group B some high school standard completed 61 56 56
female group D high school standard completed 56 68 74
male group B associate’s degree standard none 87 85 73
female group C some high school free/reduced none 55 65 62
male group D some high school standard none 86 80 75
female group B associate’s degree standard completed 52 66 73
female group E master’s degree free/reduced none 45 56 54
female group C some college standard none 72 72 71
male group D high school standard none 57 50 54
male group A some high school free/reduced none 68 72 64
female group C some college standard completed 88 95 94
male group D some college standard none 76 64 66
male group C associate’s degree standard none 46 43 42
female group B bachelor’s degree standard none 67 86 83
male group E some high school standard none 92 87 78
male group C bachelor’s degree standard completed 83 82 84
male group D associate’s degree standard none 80 75 77
male group D bachelor’s degree free/reduced none 63 66 67
female group D some high school standard completed 64 60 74
male group B some college standard none 54 52 51
male group C associate’s degree standard none 84 80 80
male group D high school free/reduced completed 73 68 66
female group E bachelor’s degree standard none 80 83 83
female group D high school standard none 56 52 55
male group E some college standard none 59 51 43
male group D some high school standard none 75 74 69
male group C associate’s degree standard none 85 76 71
male group E associate’s degree standard none 89 76 74
female group B high school standard completed 58 70 68
female group B high school standard none 65 64 62
male group C high school standard none 68 60 53
male group A some high school standard completed 47 49 49
female group D some college free/reduced none 71 83 83
female group B some high school standard completed 60 70 70
male group D master’s degree standard none 80 80 72
male group D high school standard none 54 52 52
female group E some college standard none 62 73 70
female group C associate’s degree free/reduced none 64 73 68
male group C associate’s degree standard completed 78 77 77
female group B some college standard none 70 75 78
female group C master’s degree free/reduced completed 65 81 81
female group C some high school free/reduced completed 64 79 77
male group C some college standard completed 79 79 78
female group C some high school free/reduced none 44 50 51
female group E high school standard none 99 93 90
male group D high school standard none 76 73 68
male group D some high school free/reduced none 59 42 41
female group C bachelor’s degree standard none 63 75 81
female group D high school standard none 69 72 77
female group D associate’s degree standard completed 88 92 95
female group E some college free/reduced none 71 76 70
male group C bachelor’s degree standard none 69 63 61
male group C some college standard none 58 49 42
female group D associate’s degree free/reduced none 47 53 58
female group D some college standard none 65 70 71
male group B some college standard completed 88 85 76
male group C bachelor’s degree standard none 83 78 73
female group C some high school standard completed 85 92 93
female group E high school standard completed 59 63 75
female group C some high school free/reduced none 65 86 80
male group B bachelor’s degree free/reduced none 73 56 57
male group D high school standard none 53 52 42
male group D high school standard none 45 48 46
female group D bachelor’s degree free/reduced none 73 79 84
female group D some college free/reduced completed 70 78 78
female group B some high school standard none 37 46 46
male group B associate’s degree standard completed 81 82 82
male group E associate’s degree standard completed 97 82 88
female group B some high school standard none 67 89 82
male group B bachelor’s degree free/reduced none 88 75 76
male group E some high school standard completed 77 76 77
male group C associate’s degree standard none 76 70 68
male group D some high school standard none 86 73 70
male group C some high school standard completed 63 60 57
female group E bachelor’s degree standard none 65 73 75
male group D high school free/reduced completed 78 77 80
male group B associate’s degree free/reduced none 67 62 60
male group A some high school standard completed 46 41 43
male group E associate’s degree standard completed 71 74 68
male group C high school free/reduced completed 40 46 50
male group D associate’s degree free/reduced none 90 87 75
male group A some college free/reduced completed 81 78 81
male group D some high school free/reduced none 56 54 52
female group C associate’s degree standard completed 67 84 81
male group B associate’s degree standard none 80 76 64
female group C associate’s degree standard completed 74 75 83
male group A some college standard none 69 67 69
male group E some college standard completed 99 87 81
male group C some high school standard none 51 52 44
female group B associate’s degree free/reduced none 53 71 67
female group D high school free/reduced none 49 57 52
female group B associate’s degree standard none 73 76 80
male group B bachelor’s degree standard none 66 60 57
male group D bachelor’s degree standard completed 67 61 68
female group C associate’s degree free/reduced completed 68 67 69
female group C bachelor’s degree standard completed 59 64 75
male group C high school standard none 71 66 65
female group D master’s degree standard completed 77 82 91
male group C associate’s degree standard none 83 72 78
male group B bachelor’s degree standard none 63 71 69
female group D associate’s degree free/reduced none 56 65 63
female group C high school free/reduced completed 67 79 84
female group E high school standard none 75 86 79
female group C some college standard none 71 81 80
female group C some high school free/reduced none 43 53 53
female group C high school free/reduced none 41 46 43
female group C some college standard none 82 90 94
male group C some college standard none 61 61 62
male group C associate’s degree standard completed 82 75 77
female group B some high school standard none 41 55 51
male group C high school standard none 71 60 61
male group C associate’s degree standard none 47 37 35
male group E associate’s degree standard completed 62 56 53
male group B associate’s degree standard none 90 78 81
female group C bachelor’s degree standard none 83 93 95
female group B some college free/reduced none 61 68 66
male group D some high school standard completed 76 70 69
male group C associate’s degree standard none 49 51 43
female group D some high school free/reduced completed 35 55 60
male group C high school free/reduced none 58 61 52
female group C high school standard none 61 73 63
female group B high school standard completed 69 76 74
male group D associate’s degree standard completed 67 72 67
male group D some college standard none 79 73 67
female group C high school standard none 72 80 75
male group B some college standard none 62 61 57
female group C bachelor’s degree standard completed 77 94 95
male group D high school free/reduced none 75 74 66
male group E associate’s degree standard none 87 74 76
female group B bachelor’s degree standard none 52 65 69
male group E some college standard none 66 57 52
female group C some college standard completed 63 78 80
female group C associate’s degree standard none 46 58 57
female group C some college standard none 59 71 70
female group B bachelor’s degree standard none 61 72 70
male group A associate’s degree standard none 63 61 61
female group C some college free/reduced completed 42 66 69
male group D some college free/reduced none 59 62 61
female group D some college standard none 80 90 89
female group B high school standard none 58 62 59
male group B some high school standard completed 85 84 78
female group C some college standard none 52 58 58
female group D some high school free/reduced none 27 34 32
male group C some college standard none 59 60 58
male group A bachelor’s degree free/reduced completed 49 58 60
male group C high school standard completed 69 58 53
male group C bachelor’s degree free/reduced none 61 66 61
female group A some high school free/reduced none 44 64 58
female group D some high school standard none 73 84 85
male group E some college standard none 84 77 71
female group C some college free/reduced completed 45 73 70
male group D some high school standard none 74 74 72
female group D some college standard completed 82 97 96
female group D bachelor’s degree standard none 59 70 73
male group E associate’s degree free/reduced none 46 43 41
female group D some high school standard none 80 90 82
female group D master’s degree free/reduced completed 85 95 100
female group A some high school standard none 71 83 77
male group A bachelor’s degree standard none 66 64 62
female group B associate’s degree standard none 80 86 83
male group C associate’s degree standard completed 87 100 95
male group C master’s degree free/reduced none 79 81 71
female group E some high school free/reduced none 38 49 45
female group A some high school free/reduced none 38 43 43
female group E some college standard none 67 76 75
female group E bachelor’s degree standard none 64 73 70
female group C associate’s degree free/reduced none 57 78 67
female group D high school standard none 62 64 64
male group D master’s degree standard none 73 70 75
male group E some high school free/reduced completed 73 67 59
female group D some college standard none 77 68 77
male group E some college standard none 76 67 67
male group C associate’s degree standard completed 57 54 56
female group C some high school standard completed 65 74 77
male group A high school free/reduced none 48 45 41
female group B high school free/reduced none 50 67 63
female group C associate’s degree standard none 85 89 95
male group B some high school standard none 74 63 57
male group D some high school standard none 60 59 54
female group C some high school standard completed 59 54 67
male group A some college standard none 53 43 43
female group A some college free/reduced none 49 65 55
female group D high school standard completed 88 99 100
female group C high school standard none 54 59 62
female group C some high school standard none 63 73 68
male group B associate’s degree standard completed 65 65 63
female group B associate’s degree standard none 82 80 77
female group D high school free/reduced completed 52 57 56
male group D associate’s degree standard completed 87 84 85
female group D master’s degree standard completed 70 71 74
male group E some college standard completed 84 83 78
male group D associate’s degree standard none 71 66 60
male group B some high school standard completed 63 67 67
female group C bachelor’s degree free/reduced completed 51 72 79
male group E high school standard none 84 73 69
male group C bachelor’s degree standard completed 71 74 68
male group C associate’s degree standard none 74 73 67
male group D some college standard none 68 59 62
male group E high school free/reduced completed 57 56 54
female group C associate’s degree free/reduced completed 82 93 93
female group D high school standard completed 57 58 64
female group D master’s degree free/reduced completed 47 58 67
female group A some high school standard completed 59 85 80
male group B some college free/reduced none 41 39 34
female group C some college free/reduced none 62 67 62
male group C bachelor’s degree standard none 86 83 86
male group C some high school free/reduced none 69 71 65
male group A some high school free/reduced none 65 59 53
male group C some high school free/reduced none 68 63 54
male group C associate’s degree free/reduced none 64 66 59
female group C high school standard none 61 72 70
male group C high school standard none 61 56 55
female group A some high school free/reduced none 47 59 50
male group C some high school standard none 73 66 66
male group C some college free/reduced completed 50 48 53
male group D associate’s degree standard none 75 68 64
male group D associate’s degree free/reduced none 75 66 73
male group C high school standard none 70 56 51
male group D some high school standard completed 89 88 82
female group C some college standard completed 67 81 79
female group D high school standard none 78 81 80
female group A some high school free/reduced none 59 73 69
female group B associate’s degree standard none 73 83 76
male group A some high school free/reduced none 79 82 73
female group C some high school standard completed 67 74 77
male group D some college free/reduced none 69 66 60
male group C high school standard completed 86 81 80
male group B high school standard none 47 46 42
male group B associate’s degree standard none 81 73 72
female group C some college free/reduced completed 64 85 85
female group E some college standard none 100 92 97
female group C associate’s degree free/reduced none 65 77 74
male group C some college free/reduced none 65 58 49
female group C associate’s degree free/reduced none 53 61 62
male group C bachelor’s degree free/reduced none 37 56 47
female group D bachelor’s degree standard none 79 89 89
male group D associate’s degree free/reduced none 53 54 48
female group E bachelor’s degree standard none 100 100 100
male group B high school standard completed 72 65 68
male group C bachelor’s degree free/reduced none 53 58 55
male group B some college free/reduced none 54 54 45
female group E some college standard none 71 70 76
female group C some college free/reduced none 77 90 91
male group A bachelor’s degree standard completed 75 58 62
female group C some college standard none 84 87 91
male group A high school free/reduced completed 72 67 65
female group A high school free/reduced completed 77 88 85
male group C some college standard none 91 74 76
female group C associate’s degree standard completed 83 85 90
female group C high school standard none 63 69 74
female group C associate’s degree standard completed 68 86 84
female group D some high school standard none 59 67 61
female group B associate’s degree standard completed 90 90 91
female group D bachelor’s degree standard completed 71 76 83
male group E bachelor’s degree standard completed 76 62 66
male group D associate’s degree standard none 80 68 72
female group D master’s degree standard none 55 64 70
male group E associate’s degree standard none 76 71 67
male group B high school standard completed 73 71 68
female group D associate’s degree free/reduced none 52 59 56
male group C some college free/reduced none 68 68 61
male group A high school standard none 59 52 46
female group B associate’s degree standard none 49 52 54
male group C high school standard none 70 74 71
male group D some college free/reduced none 61 47 56
female group C associate’s degree free/reduced none 60 75 74
male group B some high school standard completed 64 53 57
male group A associate’s degree free/reduced completed 79 82 82
female group A associate’s degree free/reduced none 65 85 76
female group C associate’s degree standard none 64 64 70
female group C some college standard none 83 83 90
female group C bachelor’s degree standard none 81 88 90
female group B high school standard none 54 64 68
male group D high school standard completed 68 64 66
female group C some college standard none 54 48 52
female group D some college free/reduced completed 59 78 76
female group B some high school standard none 66 69 68
male group E some college standard none 76 71 72
female group D master’s degree standard none 74 79 82
female group B associate’s degree standard completed 94 87 92
male group C some college free/reduced none 63 61 54
female group E associate’s degree standard completed 95 89 92
female group D master’s degree free/reduced none 40 59 54
female group B some high school standard none 82 82 80
male group A high school standard none 68 70 66
male group B bachelor’s degree free/reduced none 55 59 54
male group C master’s degree standard none 79 78 77
female group C bachelor’s degree standard none 86 92 87
male group D some college standard none 76 71 73
male group A some high school standard none 64 50 43
male group D some high school free/reduced none 62 49 52
female group B some high school standard completed 54 61 62
female group B master’s degree free/reduced completed 77 97 94
female group C some high school standard completed 76 87 85
female group D some college standard none 74 89 84
female group E some college standard completed 66 74 73
female group D some high school standard completed 66 78 78
female group B high school free/reduced completed 67 78 79
male group D some college standard none 71 49 52
female group C associate’s degree standard none 91 86 84
male group D bachelor’s degree standard none 69 58 57
male group C master’s degree free/reduced none 54 59 50
male group C high school standard completed 53 52 49
male group E some college standard none 68 60 59
male group C some high school free/reduced completed 56 61 60
female group C high school free/reduced none 36 53 43
female group D bachelor’s degree free/reduced none 29 41 47
female group C associate’s degree standard none 62 74 70
female group C associate’s degree standard completed 68 67 73
female group C some high school standard none 47 54 53
male group E associate’s degree standard completed 62 61 58
female group E associate’s degree standard completed 79 88 94
male group B high school standard completed 73 69 68
female group C bachelor’s degree free/reduced completed 66 83 83
male group C associate’s degree standard completed 51 60 58
female group D high school standard none 51 66 62
male group E bachelor’s degree standard completed 85 66 71
male group A associate’s degree standard completed 97 92 86
male group C high school standard completed 75 69 68
male group D associate’s degree free/reduced completed 79 82 80
female group C associate’s degree standard none 81 77 79
female group D associate’s degree standard none 82 95 89
female group D master’s degree standard none 64 63 66
male group E some high school free/reduced completed 78 83 80
female group A some high school standard completed 92 100 97
male group C high school standard completed 72 67 64
female group C high school free/reduced none 62 67 64
male group C master’s degree standard none 79 72 69
male group C some high school free/reduced none 79 76 65
male group B bachelor’s degree free/reduced completed 87 90 88
female group B associate’s degree standard none 40 48 50
male group D some college free/reduced none 77 62 64
male group E associate’s degree standard none 53 45 40
female group C some college free/reduced none 32 39 33
female group C associate’s degree standard completed 55 72 79
male group C master’s degree free/reduced none 61 67 66
female group B associate’s degree free/reduced none 53 70 70
male group D some high school standard none 73 66 62
female group D some college standard completed 74 75 79
female group C some college standard none 63 74 74
male group C bachelor’s degree standard completed 96 90 92
female group D some college free/reduced completed 63 80 80
male group B bachelor’s degree free/reduced none 48 51 46
male group B associate’s degree standard none 48 43 45
female group E bachelor’s degree free/reduced completed 92 100 100
female group D master’s degree free/reduced completed 61 71 78
male group B high school free/reduced none 63 48 47
male group D bachelor’s degree free/reduced none 68 68 67
male group B some college standard completed 71 75 70
male group A bachelor’s degree standard none 91 96 92
female group C some college standard none 53 62 56
female group C high school free/reduced completed 50 66 64
female group E high school standard none 74 81 71
male group A associate’s degree free/reduced completed 40 55 53
male group A some college standard completed 61 51 52
female group B high school standard none 81 91 89
female group B some college free/reduced completed 48 56 58
female group D master’s degree standard none 53 61 68
female group D some high school standard none 81 97 96
female group E some high school standard none 77 79 80
female group D bachelor’s degree free/reduced none 63 73 78
female group D associate’s degree standard completed 73 75 80
female group D some college standard none 69 77 77
female group C associate’s degree standard none 65 76 76
female group A high school standard none 55 73 73
female group C bachelor’s degree free/reduced none 44 63 62
female group C some college standard none 54 64 65
female group A some high school standard none 48 66 65
male group C some college free/reduced none 58 57 54
male group A some high school standard none 71 62 50
male group E bachelor’s degree standard none 68 68 64
female group E high school standard none 74 76 73
female group C bachelor’s degree standard completed 92 100 99
female group C bachelor’s degree standard completed 56 79 72
male group A some high school standard none 53 54 48
female group D high school standard none 69 77 73
female group D some high school standard none 65 82 81
female group D master’s degree standard none 54 60 63
female group C high school standard none 29 29 30
female group E some college standard none 76 78 80
male group D high school free/reduced none 60 57 51
male group D master’s degree free/reduced completed 84 89 90
male group C some high school standard none 75 72 62
female group C associate’s degree standard none 85 84 82
female group C master’s degree free/reduced none 40 58 54
female group E some college standard none 61 64 62
female group B associate’s degree standard none 58 63 65
male group D some college free/reduced completed 69 60 63
female group C some college standard none 58 59 66
male group C bachelor’s degree standard completed 94 90 91
female group C associate’s degree standard none 65 77 74
female group A associate’s degree standard none 82 93 93
female group C high school standard none 60 68 72
female group E bachelor’s degree standard none 37 45 38
male group D bachelor’s degree standard none 88 78 83
male group D master’s degree standard none 95 81 84
male group C associate’s degree free/reduced completed 65 73 68
female group C high school free/reduced none 35 61 54
male group B bachelor’s degree free/reduced none 62 63 56
male group C high school free/reduced completed 58 51 52
male group A some college standard completed 100 96 86
female group E bachelor’s degree free/reduced none 61 58 62
male group D some college standard completed 100 97 99
male group B associate’s degree free/reduced completed 69 70 63
male group D associate’s degree standard none 61 48 46
male group D some college free/reduced none 49 57 46
female group C some high school standard completed 44 51 55
male group D some college standard none 67 64 70
male group B high school standard none 79 60 65
female group B bachelor’s degree standard completed 66 74 81
female group C high school standard none 75 88 85
male group D some high school standard none 84 84 80
male group A high school standard none 71 74 64
female group B high school free/reduced completed 67 80 81
female group D some high school standard completed 80 92 88
male group E some college standard none 86 76 74
female group D associate’s degree standard none 76 74 73
male group D high school standard none 41 52 51
female group D associate’s degree free/reduced completed 74 88 90
female group B some high school free/reduced none 72 81 79
female group E high school standard completed 74 79 80
male group B high school standard none 70 65 60
female group B bachelor’s degree standard completed 65 81 81
female group D associate’s degree standard none 59 70 65
female group E high school free/reduced none 64 62 68
female group B high school standard none 50 53 55
female group D some college standard completed 69 79 81
male group C some high school free/reduced completed 51 56 53
female group A high school standard completed 68 80 76
female group D some college standard completed 85 86 98
female group A associate’s degree standard completed 65 70 74
female group B some high school standard none 73 79 79
female group B some college standard none 62 67 67
male group C associate’s degree free/reduced none 77 67 64
male group D some high school standard none 69 66 61
female group D associate’s degree free/reduced none 43 60 58
male group D associate’s degree standard none 90 87 85
male group C some college free/reduced none 74 77 73
male group C some high school standard none 73 66 63
female group D some college free/reduced none 55 71 69
female group C high school standard none 65 69 67
male group D associate’s degree standard none 80 63 63
female group C some high school free/reduced completed 50 60 60
female group C some college free/reduced completed 63 73 71
female group B bachelor’s degree free/reduced none 77 85 87
male group C some college standard none 73 74 61
male group D associate’s degree standard completed 81 72 77
female group C high school free/reduced none 66 76 68
male group D associate’s degree free/reduced none 52 57 50
female group C some college standard none 69 78 76
female group C associate’s degree standard completed 65 84 84
female group D high school standard completed 69 77 78
female group B some college standard completed 50 64 66
female group E some college standard completed 73 78 76
female group C some high school standard completed 70 82 76
male group D associate’s degree free/reduced none 81 75 78
male group D some college free/reduced none 63 61 60
female group D high school standard none 67 72 74
male group B high school standard none 60 68 60
male group B high school standard none 62 55 54
female group C some high school free/reduced completed 29 40 44
male group B some college standard completed 62 66 68
female group E master’s degree standard completed 94 99 100
male group E some college standard completed 85 75 68
male group D associate’s degree free/reduced none 77 78 73
male group A high school free/reduced none 53 58 44
male group E some college free/reduced none 93 90 83
female group C associate’s degree standard none 49 53 53
female group E associate’s degree free/reduced none 73 76 78
female group C bachelor’s degree free/reduced completed 66 74 81
female group D associate’s degree standard none 77 77 73
female group C some high school standard none 49 63 56
female group D some college free/reduced none 79 89 86
female group C associate’s degree standard completed 75 82 90
female group A bachelor’s degree standard none 59 72 70
female group D associate’s degree standard completed 57 78 79
male group C high school free/reduced none 66 66 59
female group E bachelor’s degree standard completed 79 81 82
female group B some high school standard none 57 67 72
male group A bachelor’s degree standard completed 87 84 87
female group D some college standard none 63 64 67
female group B some high school free/reduced completed 59 63 64
male group A bachelor’s degree free/reduced none 62 72 65
male group D high school standard none 46 34 36
male group C some college standard none 66 59 52
male group D high school standard none 89 87 79
female group D associate’s degree free/reduced completed 42 61 58
male group C some college standard completed 93 84 90
female group E some high school standard completed 80 85 85
female group D some college standard none 98 100 99
male group D master’s degree standard none 81 81 84
female group B some high school standard completed 60 70 74
female group B associate’s degree free/reduced completed 76 94 87
male group C associate’s degree standard completed 73 78 72
female group C associate’s degree standard completed 96 96 99
female group C high school standard none 76 76 74
male group E associate’s degree free/reduced completed 91 73 80
female group C some college free/reduced none 62 72 70
male group D some high school free/reduced completed 55 59 59
female group B some high school free/reduced completed 74 90 88
male group C high school standard none 50 48 42
male group B some college standard none 47 43 41
male group E some college standard completed 81 74 71
female group E associate’s degree standard completed 65 75 77
male group E some high school standard completed 68 51 57
female group D high school free/reduced none 73 92 84
male group C some college standard none 53 39 37
female group B associate’s degree free/reduced completed 68 77 80
male group A some high school free/reduced none 55 46 43
female group C some college standard completed 87 89 94
male group D some high school standard none 55 47 44
female group E some college free/reduced none 53 58 57
male group C master’s degree standard none 67 57 59
male group C associate’s degree standard none 92 79 84
female group B some college free/reduced completed 53 66 73
male group D associate’s degree standard none 81 71 73
male group C high school free/reduced none 61 60 55
male group D bachelor’s degree standard none 80 73 72
female group A associate’s degree free/reduced none 37 57 56
female group C high school standard none 81 84 82
female group C associate’s degree standard completed 59 73 72
male group B some college free/reduced none 55 55 47
male group D associate’s degree standard none 72 79 74
male group D high school standard none 69 75 71
male group C some college standard none 69 64 68
female group C bachelor’s degree free/reduced none 50 60 59
male group B some college standard completed 87 84 86
male group D some high school standard completed 71 69 68
male group E some college standard none 68 72 65
male group C master’s degree free/reduced completed 79 77 75
female group C some high school standard completed 77 90 85
male group C associate’s degree free/reduced none 58 55 53
female group E associate’s degree standard none 84 95 92
male group D some college standard none 55 58 52
male group E bachelor’s degree free/reduced completed 70 68 72
female group D some college free/reduced completed 52 59 65
male group B some college standard completed 69 77 77
female group C high school free/reduced none 53 72 64
female group D some high school standard none 48 58 54
male group D some high school standard completed 78 81 86
female group B high school standard none 62 62 63
male group D some college standard none 60 63 59
female group B high school standard none 74 72 72
female group C high school standard completed 58 75 77
male group B high school standard completed 76 62 60
female group D some high school standard none 68 71 75
male group A some college free/reduced none 58 60 57
male group B high school standard none 52 48 49
male group D bachelor’s degree standard none 75 73 74
female group B some high school free/reduced completed 52 67 72
female group C bachelor’s degree free/reduced none 62 78 79
male group B some college standard none 66 65 60
female group B some high school free/reduced none 49 58 55
female group B high school standard none 66 72 70
female group C some college free/reduced none 35 44 43
female group A some college standard completed 72 79 82
male group E associate’s degree standard completed 94 85 82
female group D associate’s degree free/reduced none 46 56 57
female group B master’s degree standard none 77 90 84
female group B high school free/reduced completed 76 85 82
female group C associate’s degree standard completed 52 59 62
male group C bachelor’s degree standard completed 91 81 79
female group B some high school standard completed 32 51 44
female group E some high school free/reduced none 72 79 77
male group C associate’s degree free/reduced none 68 65 61
female group C master’s degree free/reduced none 52 65 61
female group B high school standard none 48 62 60
female group D some college free/reduced none 60 66 70
male group D high school free/reduced none 66 74 69
male group E some high school standard completed 89 84 77
female group B high school standard none 42 52 51
female group E associate’s degree free/reduced completed 57 68 73
male group D high school standard none 70 70 70
female group E associate’s degree free/reduced none 70 84 81
male group E some college standard none 69 60 54
female group C associate’s degree standard none 52 55 57
male group C some high school standard completed 67 73 68
male group C some high school standard completed 76 80 73
female group E associate’s degree standard none 87 94 95
female group B some college standard none 82 85 87
female group C some college standard none 73 76 78
male group A some college free/reduced none 75 81 74
female group D some college free/reduced none 64 74 75
female group E high school free/reduced none 41 45 40
male group C high school standard none 90 75 69
male group B bachelor’s degree standard none 59 54 51
male group A some high school standard none 51 31 36
male group A high school free/reduced none 45 47 49
female group C master’s degree standard completed 54 64 67
male group E some high school standard completed 87 84 76
female group C high school standard none 72 80 83
male group B some high school standard completed 94 86 87
female group A bachelor’s degree standard none 45 59 64
male group D bachelor’s degree free/reduced completed 61 70 76
female group B high school free/reduced none 60 72 68
female group C some high school standard none 77 91 88
female group A some high school standard completed 85 90 92
female group D bachelor’s degree free/reduced none 78 90 93
male group E some college free/reduced completed 49 52 51
female group B high school free/reduced none 71 87 82
female group C some high school free/reduced none 48 58 52
male group C high school standard none 62 67 58
female group C associate’s degree free/reduced completed 56 68 70
female group C some high school standard none 65 69 76
female group D some high school free/reduced completed 69 86 81
male group B some high school standard none 68 54 53
female group A some college free/reduced none 61 60 57
female group C bachelor’s degree free/reduced completed 74 86 89
male group A bachelor’s degree standard none 64 60 58
female group B high school standard completed 77 82 89
male group B some college standard none 58 50 45
female group C high school standard completed 60 64 74
male group E high school standard none 73 64 57
female group A high school standard completed 75 82 79
male group B associate’s degree free/reduced completed 58 57 53
female group C associate’s degree standard none 66 77 73
female group D high school free/reduced none 39 52 46
male group C some high school standard none 64 58 51
male group B some college free/reduced completed 74 77 76
female group D some high school free/reduced completed 40 65 64
male group E master’s degree standard none 90 85 84
male group C master’s degree standard completed 91 85 85
male group D high school standard none 64 54 50
female group C high school standard none 59 72 68
male group D associate’s degree standard none 80 75 69
male group C master’s degree standard none 71 67 67
female group A high school standard none 61 68 63
female group E some college standard none 87 85 93
male group E some high school standard none 82 67 61
male group C some high school standard none 62 64 55
female group B bachelor’s degree standard none 97 97 96
male group B some college free/reduced none 75 68 65
female group C bachelor’s degree standard none 65 79 81
male group B high school standard completed 52 49 46
male group C associate’s degree free/reduced none 87 73 72
female group C associate’s degree standard none 53 62 53
female group E master’s degree free/reduced none 81 86 87
male group D bachelor’s degree free/reduced completed 39 42 38
female group C some college standard completed 71 71 80
male group C associate’s degree standard none 97 93 91
male group D some college standard completed 82 82 88
male group C high school free/reduced none 59 53 52
male group B associate’s degree standard none 61 42 41
male group E associate’s degree free/reduced completed 78 74 72
male group C associate’s degree free/reduced none 49 51 51
male group B high school standard none 59 58 47
female group C some college standard completed 70 72 76
male group B associate’s degree standard completed 82 84 78
male group E associate’s degree free/reduced none 90 90 82
female group C bachelor’s degree free/reduced none 43 62 61
male group C some college free/reduced none 80 64 66
male group D some college standard none 81 82 84
male group C some high school standard none 57 61 54
female group D some high school standard none 59 72 80
female group D associate’s degree standard none 64 76 74
male group C bachelor’s degree standard completed 63 64 66
female group E bachelor’s degree standard completed 71 70 70
female group B high school free/reduced none 64 73 71
male group D bachelor’s degree free/reduced none 55 46 44
female group E associate’s degree standard none 51 51 54
female group C associate’s degree standard completed 62 76 80
female group E associate’s degree standard completed 93 100 95
male group C high school free/reduced none 54 72 59
female group D some college free/reduced none 69 65 74
male group D high school free/reduced none 44 51 48
female group E some college standard completed 86 85 91
female group E associate’s degree standard none 85 92 85
female group A master’s degree free/reduced none 50 67 73
male group D some high school standard completed 88 74 75
female group E associate’s degree standard none 59 62 69
female group E some high school free/reduced none 32 34 38
male group B high school free/reduced none 36 29 27
female group B some high school free/reduced completed 63 78 79
male group D associate’s degree standard completed 67 54 63
female group D some high school standard completed 65 78 82
male group D master’s degree standard none 85 84 89
female group C master’s degree standard none 73 78 74
female group A high school free/reduced completed 34 48 41
female group D bachelor’s degree free/reduced completed 93 100 100
female group D some high school free/reduced none 67 84 84
male group D some college standard none 88 77 77
male group B high school standard none 57 48 51
female group D some college standard completed 79 84 91
female group C bachelor’s degree free/reduced none 67 75 72
male group E bachelor’s degree standard completed 70 64 70
male group D bachelor’s degree free/reduced none 50 42 48
female group A some college standard none 69 84 82
female group C bachelor’s degree standard completed 52 61 66
female group C bachelor’s degree free/reduced completed 47 62 66
female group B associate’s degree free/reduced none 46 61 55
female group E some college standard none 68 70 66
male group E bachelor’s degree standard completed 100 100 100
female group C high school standard none 44 61 52
female group C associate’s degree standard completed 57 77 80
male group B some college standard completed 91 96 91
male group D high school free/reduced none 69 70 67
female group C high school free/reduced none 35 53 46
male group D high school standard none 72 66 66
female group B associate’s degree free/reduced none 54 65 65
male group D high school free/reduced none 74 70 69
male group E some high school standard completed 74 64 60
male group E associate’s degree free/reduced none 64 56 52
female group D high school free/reduced completed 65 61 71
male group E associate’s degree free/reduced completed 46 43 44
female group C some high school free/reduced none 48 56 51
male group C some college free/reduced completed 67 74 70
male group D some college free/reduced none 62 57 62
male group D associate’s degree free/reduced completed 61 71 73
male group C bachelor’s degree free/reduced completed 70 75 74
male group C associate’s degree standard completed 98 87 90
male group D some college free/reduced none 70 63 58
male group A associate’s degree standard none 67 57 53
female group E high school free/reduced none 57 58 57
male group D some college standard completed 85 81 85
male group D some high school standard completed 77 68 69
male group C master’s degree free/reduced completed 72 66 72
female group D master’s degree standard none 78 91 96
male group C high school standard none 81 66 64
male group A some high school free/reduced completed 61 62 61
female group B high school standard none 58 68 61
female group C associate’s degree standard none 54 61 58
male group B high school standard none 82 82 80
female group D some college free/reduced none 49 58 60
male group B some high school free/reduced completed 49 50 52
female group E high school free/reduced completed 57 75 73
male group E high school standard none 94 73 71
female group D some college standard completed 75 77 83
female group E some high school free/reduced none 74 74 72
male group C high school standard completed 58 52 54
female group C some college standard none 62 69 69
male group E associate’s degree standard none 72 57 62
male group C some college standard none 84 87 81
female group D master’s degree standard none 92 100 100
female group D high school standard none 45 63 59
male group C high school standard none 75 81 71
female group A some college standard none 56 58 64
female group D some high school free/reduced none 48 54 53
female group E associate’s degree standard none 100 100 100
female group C some high school free/reduced completed 65 76 75
male group D some college standard none 72 57 58
female group D some college standard none 62 70 72
male group A some high school standard completed 66 68 64
male group C some college standard none 63 63 60
female group E associate’s degree standard none 68 76 67
female group B bachelor’s degree standard none 75 84 80
female group D bachelor’s degree standard none 89 100 100
male group C some high school standard completed 78 72 69
female group A high school free/reduced completed 53 50 60
female group D some college free/reduced none 49 65 61
female group A some college standard none 54 63 67
female group C some college standard completed 64 82 77
male group B some college free/reduced completed 60 62 60
male group C associate’s degree standard none 62 65 58
male group D high school standard completed 55 41 48
female group C associate’s degree standard none 91 95 94
male group D some high school standard none 81 78 78
male group B some high school standard completed 79 85 86
female group A some college standard completed 78 87 91
female group C some high school standard none 74 75 82
male group A high school standard none 57 51 54
female group C associate’s degree standard none 40 59 51
male group E some high school standard completed 81 75 76
female group A some high school free/reduced none 44 45 45
female group D some college free/reduced completed 67 86 83
male group E high school free/reduced completed 86 81 75
female group B some high school standard completed 65 82 78
female group D associate’s degree free/reduced none 55 76 76
female group D bachelor’s degree free/reduced none 62 72 74
male group A high school standard none 63 63 62
female group E master’s degree standard completed 88 99 95
male group C high school free/reduced none 62 55 55
female group C high school free/reduced completed 59 71 65
female group D some college standard completed 68 78 77
female group D some college free/reduced none 77 86 86

MANOVA

Uji Asumsi MANOVA

Y_final <- cbind(df_final$math_score, df_final$reading_score, df_final$writing_score)

# 1. Uji Homogenitas varians-kovarians (Box's M)
vars <- df_final[, c("gender", "test_preparation_course", "lunch", "race_ethnicity", "parental_level_of_education")]

boxm_results <- sapply(vars, function(x) boxM(Y_final, x)$p.value)

tibble(Variabel = names(boxm_results),P_Value = boxm_results) %>% kable(caption = "Uji Homogenitas Varians-Kovarians (Box's M)", digits = 4) %>% kable_styling(full_width = FALSE)
Uji Homogenitas Varians-Kovarians (Box’s M)
Variabel P_Value
gender 0.5074
test_preparation_course 0.1207
lunch 0.9889
race_ethnicity 0.6959
parental_level_of_education 0.6031 
# 2. Normalitas Multivariat
hasil_mvn <- mvn(df_final[,6:8])

hasil_mvn$multivariate_normality %>% kable(caption = "Uji Normalitas Multivariat", digits = 4) %>% kable_styling(full_width = FALSE)
Uji Normalitas Multivariat
Test Statistic p.value Method MVN
Henze-Zirkler 1.309 0.002 asymptotic ✗ Not normal 
# QQ Plot
par(mfrow=c(1,3))
invisible(mapply(qqPlot, df_final[, 6:8], main = names(df_final)[6:8], id=FALSE))

# 3. Multikolinearitas
cor(df_final[, 6:8]) %>% kable(caption = "Matriks Korelasi Variabel Dependen", digits = 3) %>% kable_styling(full_width = FALSE)
Matriks Korelasi Variabel Dependen
math_score reading_score writing_score
math_score 1.000 0.801 0.783
reading_score 0.801 1.000 0.951
writing_score 0.783 0.951 1.000 
# 4. Linearitas
pairs(df_final[, 6:8], pch = 19, col = "steelblue", main = "Scatterplot Matriks Skor Ujian", lower.panel = NULL)

# 5. Uji Homogenitas Varians (Levene Test)
lev <- leveneTest(math_score ~ gender, data=df_final)

as.data.frame(lev) %>% kable(caption = "Uji Homogenitas Varians (Levene Test)", digits = 4) %>% kable_styling(full_width = FALSE)
Uji Homogenitas Varians (Levene Test)
Df F value Pr(>F)
group 1 2e-04 0.9897
986 NA NA

Model MANOVA

# menggabungkan ketiga skor menjadi 1 variabel dependen
Y_final <- cbind(df_final$math_score, df_final$reading_score, df_final$writing_score)

# menjalankan model MANOVA 
fit_manova <- manova(Y_final ~ gender + race_ethnicity + parental_level_of_education + lunch + test_preparation_course, data = df_final)

# menampilkan
broom::tidy(fit_manova, test = "Pillai") %>% kable(caption = "Hasil Uji MANOVA (Pillai's Trace)", digits = 4) %>% kable_styling(full_width = FALSE, bootstrap_options = "striped")
Hasil Uji MANOVA (Pillai’s Trace)
term df pillai statistic num.df den.df p.value
gender 1 0.6378 571.0370 3 973 0
race_ethnicity 4 0.1536 13.1536 12 2925 0
parental_level_of_education 5 0.1209 8.1891 15 2925 0
lunch 1 0.1513 57.8181 3 973 0
test_preparation_course 1 0.2497 107.9477 3 973 0
Residuals 975 NA NA NA NA NA

MANCOVA

# gabungkan variabel dependen
Y_mancova <- cbind(df_final$reading_score, df_final$writing_score)

Uji Asumsi MANCOVA

# Homogenitas Kemiringan Regresi
fit_lm_slope <- lm(Y_mancova ~ math_score * (gender + race_ethnicity + lunch + test_preparation_course + parental_level_of_education), data = df_final)

# summary multivariat
res_slope_summary <- summary(manova(fit_lm_slope), test = "Pillai")

# ambil Pillai
tabel_slope <- as.data.frame(res_slope_summary$stats)

# menampilkan
tabel_slope %>% tibble::rownames_to_column("Variabel") %>% kable(caption = "Uji Homogenitas Kemiringan Regresi (MANCOVA)", digits = 4) %>% kable_styling(full_width = FALSE)
Uji Homogenitas Kemiringan Regresi (MANCOVA)
Variabel Df Pillai approx F num Df den Df Pr(>F)
math_score 1 0.8372 2471.6700 2 961 0.0000
gender 1 0.6322 826.0012 2 961 0.0000
race_ethnicity 4 0.0920 11.6009 8 1924 0.0000
lunch 1 0.0407 20.3949 2 961 0.0000
test_preparation_course 1 0.2226 137.5782 2 961 0.0000
parental_level_of_education 5 0.0878 8.8300 10 1924 0.0000
math_score:gender 1 0.0003 0.1375 2 961 0.8715
math_score:race_ethnicity 4 0.0096 1.1654 8 1924 0.3164
math_score:lunch 1 0.0001 0.0291 2 961 0.9714
math_score:test_preparation_course 1 0.0116 5.6562 2 961 0.0036
math_score:parental_level_of_education 5 0.0166 1.6145 10 1924 0.0965
Residuals 962 NA NA NA NA NA

Model MANCOVA

fit_mancova <- manova(Y_mancova ~ math_score + gender + race_ethnicity + parental_level_of_education + lunch + test_preparation_course, data = df_final)

# 1. Hasil Multivariate
broom::tidy(fit_mancova, test = "Pillai") %>% kable(caption = "Hasil Multivariate MANCOVA", digits = 4) %>% kable_styling(full_width = FALSE, bootstrap_options = "striped")
Hasil Multivariate MANCOVA
term df pillai statistic num.df den.df p.value
math_score 1 0.8355 2470.3371 2 973 0
gender 1 0.6292 825.5128 2 973 0
race_ethnicity 4 0.0906 11.5549 8 1948 0
parental_level_of_education 5 0.0849 8.6325 10 1948 0
lunch 1 0.0361 18.2059 2 973 0
test_preparation_course 1 0.2235 140.0621 2 973 0
Residuals 974 NA NA NA NA NA 
# 2.Hasil Univariate 
univ_res <- summary.aov(fit_mancova)

as.data.frame(univ_res[[1]]) %>% kable(caption = "Univariate: Reading Score", digits = 4) %>% kable_styling(full_width = FALSE)
Univariate: Reading Score
Df Sum Sq Mean Sq F value Pr(>F)
math_score 1 124542.3170 124542.3170 3563.9269 0.0000
gender 1 31099.9199 31099.9199 889.9613 0.0000
race_ethnicity 4 1070.5766 267.6441 7.6590 0.0000
parental_level_of_education 5 511.1453 102.2291 2.9254 0.0125
lunch 1 1269.2208 1269.2208 36.3203 0.0000
test_preparation_course 1 1385.5913 1385.5913 39.6503 0.0000
Residuals 974 34036.6734 34.9452 NA NA 
as.data.frame(univ_res[[2]]) %>% kable(caption = "Univariate: Writing Score", digits = 4) %>% kable_styling(full_width = FALSE)
Univariate: Writing Score
Df Sum Sq Mean Sq F value Pr(>F)
math_score 1 127783.7876 127783.7876 4786.0308 0
gender 1 44122.7860 44122.7860 1652.5806 0
race_ethnicity 4 1892.8996 473.2249 17.7242 0
parental_level_of_education 5 1761.8115 352.3623 13.1974 0
lunch 1 590.1837 590.1837 22.1048 0
test_preparation_course 1 6083.9809 6083.9809 227.8702 0
Residuals 974 26005.1417 26.6993 NA NA