ONE WAY & TWO WAY MANOVA
Gusti Ayu Anisa Eldina
2024-10-24
ONE WAY MANOVA
DATA
Data berisi empat ukuran hasil dari kinerja mahasiswa dalam mata kuliah pengantar sosiologi dengan dan satu nilai tambahan college board test. Kelas yang didapatkan diberi simbol 1=A, 2=B, dan 3=C
data <- read.csv("SociocourseCSV.csv") ;data## boards pretest midterm1 midterm2 final class results
## 1 410 17 43 61 129 2 B
## 2 390 20 50 47 60 2 B
## 3 510 22 47 79 119 2 B
## 4 430 13 24 40 100 3 C
## 5 600 16 47 60 79 2 B
## 6 610 28 57 59 99 3 C
## 7 610 14 42 61 92 1 A
## 8 560 10 42 79 107 2 B
## 9 700 28 69 83 156 3 C
## 10 460 30 48 67 110 2 B
## 11 590 28 59 74 116 2 B
## 12 500 15 21 40 49 3 C
## 13 410 24 52 71 107 1 A
## 14 470 15 35 40 125 2 B
## 15 210 26 35 57 64 2 B
## 16 610 16 59 58 100 2 B
## 17 510 25 68 66 138 2 B
## 18 600 3 38 58 63 3 C
## 19 470 5 45 24 82 2 B
## 20 460 16 37 48 73 2 B
## 21 800 28 54 100 132 2 B
## 22 610 13 45 83 87 1 A
## 23 490 9 31 70 89 2 B
## 24 470 13 39 48 99 2 B
## 25 610 30 67 85 119 2 B
## 26 580 10 30 14 100 1 A
## 27 410 13 19 55 84 2 B
## 28 630 8 71 100 166 1 A
## 29 790 29 80 94 111 2 B
## 30 490 17 47 45 110 3 C
## 31 400 15 46 58 93 2 B
## 32 610 16 59 90 141 2 B
## 33 610 13 48 84 99 1 A
## 34 500 30 68 81 114 1 A
## 35 430 17 43 49 96 2 B
## 36 540 17 31 54 39 3 C
## 37 610 25 64 87 149 1 A
## 38 400 10 19 36 53 2 B
## 39 390 23 43 51 39 3 C
## 40 490 18 20 59 91 1 Ahead(data)## boards pretest midterm1 midterm2 final class results
## 1 410 17 43 61 129 2 B
## 2 390 20 50 47 60 2 B
## 3 510 22 47 79 119 2 B
## 4 430 13 24 40 100 3 C
## 5 600 16 47 60 79 2 B
## 6 610 28 57 59 99 3 CHIPOTESIS ONE WAY MANOVA
H0 ; Rata-rata dari semua variabel nilai (boards, pretest, midterm1, midterm2, dan final) tersebut adalah sama untuk semua kelas (A, B, dan C)
H1 ; Setidaknya terdapat satu kelas yang menghasilkan rata-rata nilai yang berbeda
Tolak H0 jika p-value < α. Terima dalam hal lainnya.
ASUMSI KENORMALAN
Uji Normalitas Univariat dengan Uji Shapiro-Wilks dan Uji Normalitas Multivariat dengan MardiaDB Test
dengan hipotesis :
H0 : Galat data berdistribusi normal
H1 : Galat data tidak berdistribusi normal
Tolak H0 jika p-value < α. Terima dalam hal lainnya.
library(MVN)## Warning: package 'MVN' was built under R version 4.3.3data_fix <- data.frame(data[,1:5])
head(data_fix)## boards pretest midterm1 midterm2 final
## 1 410 17 43 61 129
## 2 390 20 50 47 60
## 3 510 22 47 79 119
## 4 430 13 24 40 100
## 5 600 16 47 60 79
## 6 610 28 57 59 99test = mvn(data_fix, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 43.057133116949 0.164519203713527 YES
## 2 Mardia Kurtosis 0.395692343410474 0.692332004552624 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk boards 0.9499 0.0751 YES
## 2 Shapiro-Wilk pretest 0.9450 0.0509 YES
## 3 Shapiro-Wilk midterm1 0.9742 0.4846 YES
## 4 Shapiro-Wilk midterm2 0.9795 0.6724 YES
## 5 Shapiro-Wilk final 0.9841 0.8362 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## boards 40 524.250 114.665344 505.0 210 800 452.50 610.00 0.09528188
## pretest 40 18.125 7.425485 16.5 3 30 13.00 25.00 0.10237108
## midterm1 40 46.050 15.395554 45.5 19 80 36.50 57.50 0.08435919
## midterm2 40 62.875 20.087230 59.5 14 100 48.75 79.50 -0.10360651
## final 40 99.475 30.323036 99.5 39 166 83.50 116.75 -0.03353441
## Kurtosis
## boards 0.4692111
## pretest -1.0377216
## midterm1 -0.6714114
## midterm2 -0.4943713
## final -0.3889549
Didapatkan bahwa semua variabel independen memenuhi asumsi normal secara univariat, dan memenuhi asumsi normal multivariat dengan p-value 0,16 (skewness) dan 0,69 (kurtosis) sehingga H0 diterima. Dengan taraf signifikansi 5%, data dinyatakan normal secara univariat dan multivariat
ASUMSI HOMOGENITAS
Uji Homogenitas
dengan hipotesis :
H0 : Data homogen
H1 : Data heterogen
Tolak H0 jika p-value < α. Terima dalam hal lainnya.
library(biotools)## Warning: package 'biotools' was built under R version 4.3.3## Loading required package: MASS## ---
## biotools version 4.2grup <- data$results
head(grup)## [1] "B" "B" "B" "C" "B" "C"boxM(data = data_fix, grouping = grup)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data_fix
## Chi-Sq (approx.) = 28.542, df = 30, p-value = 0.5418Didapatkan bahwa dengan taraf signifikansi 5%, p-value (0,514) > α (0,05) sehingga H0 diterima. Data dinyatakan homogen.
UJI ONE WAY MANOVA
One Way MANOVA untuk mengetahui signifikansi 1 faktor independen terhadap variabel dependen.
owm = manova(cbind(data$boards, data$pretest, data$midterm1, data$midterm2, data$final)~data$results)
summary(owm)## Df Pillai approx F num Df den Df Pr(>F)
## data$results 2 0.24714 0.95874 10 68 0.4869
## Residuals 37Didapatkan p-value (0,4869) > α (0,05) sehingga h0 diterima. Dengan taraf signifikansi 5% dapat dinyatakan bawah rata-rata dari semua variabel nilai (boards, pretest, midterm1, midterm2, dan final) tersebut adalah sama untuk semua kelas (A, B, dan C)
KESIMPULAN & INTERPRETASI
Hasil analisis One Way Manova menunjukkan p-value (0,4869) < α (0,05) sehingga H0 diterima. Dengan taraf signifikansi 5% dapat dinyatakan bahwa rata-rata dari semua variabel nilai (boards, pretest, midterm1, midterm2, dan final) tersebut adalah sama untuk semua kelas (A, B, dan C). Sehingga tidak diperlukan uji lanjut.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TWO WAY MANOVA
DATA
Data berisi informasi tingkat pelanggan untuk perusahaan telekomunikasi. Berbagai atribut yang terkait dengan layanan yang digunakan dicatat untuk setiap pelanggan.
data2 <- read.csv("telecom_churn.csv")
data2## Churn AccountWeeks ContractRenewal DataPlan DataUsage CustServCalls
## 1 0 128 1 1 2.70 1
## 2 0 107 1 1 3.70 1
## 3 0 137 1 0 0.00 0
## 4 0 84 0 0 0.00 2
## 5 0 75 0 0 0.00 3
## 6 0 118 0 0 0.00 0
## 7 0 121 1 1 2.03 3
## 8 0 147 0 0 0.00 0
## 9 0 117 1 0 0.19 1
## 10 0 141 0 1 3.02 0
## 11 1 65 1 0 0.29 4
## 12 0 74 1 0 0.34 0
## 13 0 168 1 0 0.00 1
## 14 0 95 1 0 0.44 3
## 15 0 62 1 0 0.00 4
## 16 1 161 1 0 0.00 4
## 17 0 85 1 1 3.73 1
## 18 0 93 1 0 0.00 3
## 19 0 76 1 1 2.70 1
## 20 0 73 1 0 0.00 1
## 21 0 147 1 0 0.31 0
## 22 1 77 1 0 0.00 5
## 23 0 130 1 0 0.00 0
## 24 0 111 1 0 0.39 2
## 25 0 132 1 0 0.00 0
## 26 0 174 1 0 0.00 3
## 27 0 57 1 1 2.57 0
## 28 0 54 1 0 0.00 3
## 29 0 20 1 0 0.32 0
## 30 0 49 1 0 0.21 1
## 31 0 142 1 0 0.00 2
## 32 0 75 1 0 0.00 1
## 33 0 172 1 0 0.00 3
## 34 1 12 1 0 0.00 1
## 35 0 57 1 1 2.24 0
## 36 0 72 1 1 3.97 3
## 37 0 36 1 1 3.92 0
## 38 0 78 1 0 0.00 1
## 39 0 136 0 1 2.84 3
## 40 0 149 1 0 0.00 1
## 41 0 98 1 0 0.30 3
## 42 1 135 0 1 3.94 0
## 43 0 34 1 0 0.00 2
## 44 0 160 1 0 0.38 3
## 45 0 64 1 0 0.24 1
## 46 0 59 1 1 2.30 2
## 47 0 65 1 0 0.00 3
## 48 0 142 1 0 0.35 2
## 49 1 119 1 0 0.00 5
## 50 0 97 1 1 2.97 1
## 51 0 52 1 0 0.32 3
## 52 0 60 1 0 0.00 1
## 53 0 10 1 0 0.00 2
## 54 0 96 1 0 0.21 2
## 55 1 87 1 0 0.00 5
## 56 0 81 1 0 0.11 1
## 57 0 141 1 0 0.00 1
## 58 1 121 1 1 1.57 3
## 59 0 68 1 0 0.00 3
## 60 0 125 1 0 0.00 1
## 61 0 174 1 0 0.00 1
## 62 0 116 1 1 3.13 2
## 63 0 74 1 1 3.94 2
## 64 0 149 1 1 3.40 3
## 65 0 38 1 0 0.00 2
## 66 0 40 1 1 1.67 2
## 67 0 43 0 0 0.00 0
## 68 0 113 0 0 0.00 0
## 69 0 126 1 0 0.00 1
## 70 1 150 1 0 0.00 4
## 71 0 138 1 0 0.00 3
## 72 0 162 1 1 3.27 0
## 73 0 147 1 0 0.00 3
## 74 0 90 1 0 0.00 1
## 75 0 85 1 0 0.00 0
## 76 0 50 1 0 0.00 1
## 77 1 82 1 0 0.21 0
## 78 1 144 1 0 0.21 4
## 79 0 46 1 0 0.26 2
## 80 0 70 1 0 0.30 1
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## 82 0 116 0 0 0.30 3
## 83 0 55 1 1 2.97 3
## 84 0 70 1 1 2.65 1
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## 3026 0 123 1 1 4.21 2
## 3027 0 78 1 1 2.92 6
## 3028 0 101 1 1 2.54 4
## 3029 0 129 1 0 0.00 1
## 3030 0 67 1 1 2.48 0
## 3031 0 37 1 0 0.00 3
## 3032 0 64 0 0 0.26 3
## 3033 0 173 1 0 0.00 1
## 3034 0 135 1 0 0.33 1
## 3035 0 75 1 1 3.02 1
## 3036 1 88 1 0 0.00 4
## 3037 0 112 1 0 0.00 3
## 3038 0 113 1 0 0.00 0
## 3039 0 121 1 1 1.73 2
## 3040 0 70 1 0 0.00 1
## 3041 0 90 1 0 0.22 0
## 3042 0 39 1 0 0.00 0
## 3043 0 142 1 0 0.42 0
## 3044 0 176 1 0 0.32 1
## 3045 0 105 1 0 0.30 1
## 3046 1 57 1 0 0.00 2
## 3047 0 110 1 0 0.24 1
## 3048 0 88 1 0 0.00 2
## 3049 0 95 1 0 0.00 0
## 3050 0 147 1 0 0.00 3
## 3051 1 101 1 0 0.00 4
## 3052 0 115 1 0 0.00 1
## 3053 0 103 1 0 0.00 2
## 3054 0 82 1 0 0.00 0
## 3055 0 141 1 0 0.00 0
## 3056 0 149 1 0 0.00 2
## 3057 0 131 1 0 0.00 2
## 3058 0 119 1 0 0.00 1
## 3059 0 112 1 0 0.26 3
## 3060 0 116 1 1 3.19 2
## 3061 0 94 1 0 0.00 3
## 3062 0 90 1 0 0.22 2
## 3063 0 114 1 1 3.51 0
## 3064 0 63 1 1 3.29 1
## 3065 1 130 1 0 0.33 4
## 3066 0 122 1 1 2.27 3
## 3067 0 166 1 0 0.00 3
## 3068 0 62 1 0 0.00 0
## 3069 0 78 1 1 2.57 2
## 3070 0 148 1 1 2.67 1
## 3071 1 154 1 0 0.00 3
## 3072 0 110 1 1 1.70 1
## 3073 1 75 1 0 0.00 0
## 3074 0 84 1 1 2.00 2
## 3075 0 113 1 0 0.27 1
## 3076 0 181 1 1 1.70 2
## 3077 0 51 1 0 0.00 2
## 3078 0 102 1 1 3.86 0
## 3079 0 107 1 0 0.00 1
## 3080 1 88 1 0 0.00 5
## 3081 0 82 1 0 0.21 0
## 3082 0 204 1 0 0.00 6
## 3083 0 130 1 0 0.00 3
## 3084 0 174 1 0 0.00 0
## 3085 0 129 1 0 0.00 2
## 3086 0 190 0 0 0.00 3
## 3087 0 54 0 0 0.00 3
## 3088 0 78 1 0 0.00 0
## 3089 0 100 1 1 2.40 1
## 3090 0 70 1 1 2.54 3
## 3091 0 111 1 0 0.35 1
## 3092 0 117 1 0 0.00 1
## 3093 0 68 1 0 0.00 0
## 3094 1 27 1 0 0.36 2
## 3095 0 91 1 0 0.00 1
## 3096 0 181 1 1 2.86 1
## 3097 0 118 1 1 2.65 3
## 3098 0 112 1 0 0.00 2
## 3099 0 93 1 0 0.00 0
## 3100 0 102 1 0 0.00 0
## 3101 0 93 1 0 0.00 0
## 3102 0 107 1 1 2.21 1
## 3103 0 100 1 1 3.40 3
## 3104 0 115 1 0 0.00 2
## 3105 0 63 1 1 2.78 0
## 3106 0 57 1 0 0.00 0
## 3107 0 119 1 1 3.13 1
## 3108 0 73 1 0 0.41 1
## 3109 0 98 1 1 2.97 2
## 3110 0 139 0 0 0.00 0
## 3111 0 31 1 1 2.86 1
## 3112 0 129 1 1 3.08 1
## 3113 1 115 1 0 0.00 7
## 3114 1 108 1 0 0.27 2
## 3115 0 139 1 0 0.35 0
## 3116 0 102 1 0 0.00 4
## 3117 0 149 1 0 0.00 1
## 3118 0 113 1 0 0.00 2
## 3119 0 131 1 1 1.40 1
## 3120 0 83 1 0 0.00 0
## 3121 0 96 1 1 2.92 2
## 3122 0 98 1 0 0.00 1
## 3123 0 3 1 0 0.00 3
## 3124 0 77 1 1 3.05 0
## 3125 0 75 1 1 2.54 3
## 3126 1 40 1 0 0.00 4
## 3127 0 108 1 0 0.00 0
## 3128 1 100 1 0 0.00 4
## 3129 0 16 1 0 0.33 3
## 3130 0 115 1 1 1.51 2
## 3131 0 108 1 1 2.35 3
## 3132 0 107 1 0 0.21 5
## 3133 1 161 1 0 0.00 2
## 3134 0 147 1 0 0.26 2
## 3135 0 107 1 0 0.00 3
## 3136 0 120 1 0 0.26 1
## 3137 0 107 1 1 2.78 1
## 3138 0 58 1 0 0.00 3
## 3139 0 91 1 0 0.00 2
## 3140 0 13 1 0 0.00 2
## 3141 0 104 1 0 0.27 5
## 3142 0 93 1 1 2.89 1
## 3143 0 95 1 0 0.22 2
## 3144 0 104 1 0 0.34 3
## 3145 1 35 1 0 0.00 5
## 3146 0 62 1 0 0.00 3
## 3147 0 143 1 0 0.00 1
## 3148 0 62 1 0 0.00 4
## 3149 1 60 0 0 0.00 0
## 3150 0 41 1 0 0.00 1
## 3151 0 34 1 1 2.89 2
## 3152 1 56 1 0 0.25 0
## 3153 0 183 1 0 0.28 1
## 3154 0 94 1 0 0.00 2
## 3155 0 73 1 1 1.70 2
## 3156 0 123 1 0 0.00 2
## 3157 0 64 1 0 0.29 3
## 3158 1 127 0 0 0.00 4
## 3159 0 33 1 0 0.00 3
## 3160 0 27 1 0 0.00 1
## 3161 0 123 1 0 0.00 0
## 3162 0 148 1 0 0.00 2
## 3163 0 81 1 0 0.00 0
## 3164 0 122 1 1 1.86 2
## 3165 0 52 1 0 0.00 1
## 3166 0 91 1 1 2.46 1
## 3167 1 54 1 0 0.21 2
## 3168 0 152 1 0 0.00 1
## 3169 1 201 1 0 0.00 1
## 3170 1 78 1 0 0.40 4
## 3171 0 67 1 0 0.14 0
## 3172 0 100 1 0 0.00 1
## 3173 0 41 1 0 0.00 3
## 3174 0 133 1 0 0.00 3
## 3175 0 36 1 1 2.32 2
## 3176 0 51 1 1 2.24 0
## 3177 0 122 1 0 0.00 0
## 3178 0 84 1 1 3.46 1
## 3179 0 91 1 0 0.00 0
## 3180 0 110 1 0 0.34 1
## 3181 0 91 0 0 0.00 1
## 3182 0 121 1 0 0.00 5
## 3183 0 109 1 0 0.31 3
## 3184 0 95 1 0 0.00 2
## 3185 0 72 1 0 0.28 0
## 3186 0 73 1 0 0.31 0
## 3187 0 108 1 0 0.33 3
## 3188 0 58 1 1 1.46 1
## 3189 0 148 0 0 0.00 1
## 3190 1 76 0 0 0.00 0
## 3191 1 103 1 0 0.00 6
## 3192 1 87 1 0 0.00 0
## 3193 0 35 1 1 1.35 2
## 3194 0 88 1 0 0.00 1
## 3195 0 67 1 1 3.62 0
## 3196 0 77 1 1 2.62 2
## 3197 0 124 1 0 0.00 1
## 3198 0 30 1 0 0.00 0
## 3199 0 53 1 1 3.46 2
## 3200 0 152 1 0 0.23 1
## 3201 0 100 0 0 0.00 1
## 3202 0 59 1 1 2.38 1
## 3203 0 143 1 0 0.00 3
## 3204 0 142 1 1 1.73 1
## 3205 0 105 1 0 0.23 1
## 3206 1 111 1 0 0.00 1
## 3207 0 143 1 0 0.00 1
## 3208 0 93 1 1 3.16 0
## 3209 0 79 1 0 0.00 2
## 3210 1 68 0 1 3.83 3
## 3211 0 93 0 0 0.32 1
## 3212 0 103 1 0 0.38 2
## 3213 0 144 1 1 1.00 0
## 3214 0 93 1 0 0.19 1
## 3215 0 149 0 0 0.27 3
## 3216 0 23 1 1 2.54 1
## 3217 0 221 1 1 0.65 0
## 3218 0 164 1 1 3.56 1
## 3219 0 104 1 1 3.62 2
## 3220 0 150 1 1 2.38 2
## 3221 0 184 1 1 2.75 0
## 3222 0 88 1 0 0.31 1
## 3223 0 61 0 1 3.16 3
## 3224 0 110 1 0 0.00 2
## 3225 1 115 1 0 0.00 3
## 3226 0 33 1 0 0.00 2
## 3227 1 100 1 0 0.20 2
## 3228 0 209 1 0 0.00 0
## 3229 0 27 1 0 0.00 5
## 3230 0 117 1 0 0.22 1
## 3231 0 87 1 0 0.00 1
## 3232 0 129 1 1 1.78 1
## 3233 0 142 1 0 0.00 1
## 3234 0 112 1 0 0.00 0
## 3235 0 75 1 1 0.68 1
## 3236 0 97 1 1 1.32 3
## 3237 0 121 1 1 2.03 0
## 3238 0 142 0 0 0.00 1
## 3239 1 121 1 0 0.00 3
## 3240 0 87 1 1 2.75 2
## 3241 0 34 1 0 0.00 1
## 3242 1 177 0 0 0.00 1
## 3243 0 58 1 1 2.27 0
## 3244 1 113 0 0 0.00 5
## 3245 0 101 1 0 0.00 1
## 3246 0 89 1 0 0.00 3
## 3247 1 77 0 1 3.21 0
## 3248 1 146 1 0 0.00 4
## 3249 0 93 1 0 0.00 0
## 3250 0 160 1 0 0.00 0
## 3251 0 55 1 0 0.00 0
## 3252 0 88 1 0 0.00 2
## 3253 0 63 1 0 0.00 0
## 3254 0 127 1 1 2.43 1
## 3255 0 57 1 1 3.97 1
## 3256 1 138 0 0 0.00 2
## 3257 0 115 1 0 0.23 3
## 3258 0 171 1 0 0.31 2
## 3259 0 148 1 0 0.29 2
## 3260 0 127 1 0 0.35 1
## 3261 0 61 1 0 0.20 1
## 3262 0 131 1 0 0.00 1
## 3263 0 88 1 0 0.00 1
## 3264 0 130 1 0 0.26 2
## 3265 0 89 1 1 1.59 0
## 3266 1 82 1 0 0.00 3
## 3267 0 138 1 1 2.62 3
## 3268 0 115 1 0 0.00 1
## 3269 1 84 1 0 0.00 2
## 3270 0 117 0 0 0.00 1
## 3271 0 60 1 0 0.00 2
## 3272 0 62 1 0 0.00 2
## 3273 1 133 1 0 0.00 2
## 3274 0 131 1 0 0.28 3
## 3275 0 65 1 0 0.00 1
## 3276 0 120 1 1 0.00 1
## 3277 0 142 1 1 2.38 1
## 3278 0 134 1 0 0.00 2
## 3279 0 87 1 0 0.00 2
## 3280 0 139 1 1 2.24 2
## 3281 1 76 1 0 0.00 4
## 3282 0 100 1 0 0.00 1
## 3283 0 99 1 1 2.08 3
## 3284 0 99 1 0 0.00 3
## 3285 0 48 1 1 3.56 1
## 3286 0 57 1 0 0.00 0
## 3287 0 106 1 1 3.54 0
## 3288 1 170 1 1 2.94 4
## 3289 0 78 1 0 0.17 1
## 3290 0 39 1 0 0.00 1
## 3291 0 127 1 0 0.00 0
## 3292 1 119 0 1 3.75 1
## 3293 0 114 1 0 0.12 1
## 3294 0 95 1 0 0.00 0
## 3295 0 116 1 0 0.00 1
## 3296 0 110 1 0 0.00 1
## 3297 0 74 1 0 0.00 1
## 3298 0 148 1 1 3.05 1
## 3299 0 83 1 0 0.00 1
## 3300 0 73 1 0 0.00 2
## 3301 0 111 1 1 1.92 1
## 3302 1 84 1 0 0.00 0
## 3303 0 75 0 0 0.29 1
## 3304 0 114 1 1 3.11 2
## 3305 1 71 0 0 0.00 4
## 3306 0 58 1 1 3.11 2
## 3307 0 106 1 1 2.19 1
## 3308 0 172 1 0 0.00 4
## 3309 0 45 1 0 0.00 1
## 3310 0 100 0 0 0.00 4
## 3311 0 94 1 0 0.21 2
## 3312 0 128 1 0 0.00 2
## 3313 0 181 1 0 0.26 2
## 3314 0 127 1 0 0.00 1
## 3315 0 89 1 0 0.29 1
## 3316 0 149 1 1 1.76 0
## 3317 0 103 1 1 3.32 0
## 3318 0 163 0 0 0.00 1
## 3319 0 52 1 0 0.34 2
## 3320 0 89 1 0 0.25 3
## 3321 1 122 0 0 0.30 4
## 3322 0 60 1 0 0.00 3
## 3323 1 62 1 0 0.00 4
## 3324 1 117 1 0 0.39 5
## 3325 0 159 1 0 0.00 1
## 3326 0 78 1 0 0.23 2
## 3327 0 96 1 0 0.36 1
## 3328 0 79 1 0 0.00 2
## 3329 0 192 1 1 2.67 2
## 3330 0 68 1 0 0.34 3
## 3331 0 28 1 0 0.00 2
## 3332 0 184 0 0 0.00 2
## 3333 0 74 1 1 3.70 0
## DayMins DayCalls MonthlyCharge OverageFee RoamMins
## 1 265.1 110 89.0 9.87 10.0
## 2 161.6 123 82.0 9.78 13.7
## 3 243.4 114 52.0 6.06 12.2
## 4 299.4 71 57.0 3.10 6.6
## 5 166.7 113 41.0 7.42 10.1
## 6 223.4 98 57.0 11.03 6.3
## 7 218.2 88 87.3 17.43 7.5
## 8 157.0 79 36.0 5.16 7.1
## 9 184.5 97 63.9 17.58 8.7
## 10 258.6 84 93.2 11.10 11.2
## 11 129.1 137 44.9 11.43 12.7
## 12 187.7 127 49.4 8.17 9.1
## 13 128.8 96 31.0 5.25 11.2
## 14 156.6 88 52.4 12.38 12.3
## 15 120.7 70 47.0 15.36 13.1
## 16 332.9 67 84.0 15.89 5.4
## 17 196.4 139 95.3 14.05 13.8
## 18 190.7 114 51.0 10.91 8.1
## 19 189.7 66 78.0 10.64 10.0
## 20 224.4 90 52.0 7.98 13.0
## 21 155.1 117 50.1 11.99 10.6
## 22 62.4 89 26.0 8.50 5.7
## 23 183.0 112 38.0 3.65 9.5
## 24 110.4 103 34.9 6.87 7.7
## 25 81.1 86 35.0 12.26 10.3
## 26 124.3 76 45.0 13.86 15.5
## 27 213.0 115 78.7 9.56 9.5
## 28 134.3 73 37.0 7.78 14.7
## 29 190.0 109 58.2 12.91 6.3
## 30 119.3 117 41.1 10.76 11.1
## 31 84.8 95 27.0 6.84 14.2
## 32 226.1 105 56.0 10.08 10.3
## 33 212.0 121 39.0 1.56 12.6
## 34 249.6 118 64.0 12.62 11.8
## 35 176.8 94 69.4 9.75 8.3
## 36 220.0 80 95.7 10.87 14.7
## 37 146.3 128 78.2 8.13 14.5
## 38 130.8 64 42.0 11.19 10.0
## 39 203.9 106 79.4 9.38 10.5
## 40 140.4 94 47.0 13.59 11.1
## 41 126.3 102 39.0 8.34 9.4
## 42 173.1 85 86.4 10.20 14.6
## 43 124.8 82 46.0 14.11 10.0
## 44 85.8 77 32.8 8.27 9.2
## 45 154.0 67 48.4 11.29 3.5
## 46 120.9 97 62.0 10.65 8.5
## 47 211.3 120 50.0 8.13 13.2
## 48 187.0 133 47.5 6.73 7.4
## 49 159.1 114 47.0 11.57 8.8
## 50 133.2 135 71.7 10.86 11.0
## 51 191.9 108 59.2 13.49 7.8
## 52 220.6 57 56.0 10.56 6.8
## 53 186.1 112 48.0 9.51 11.4
## 54 160.2 117 52.1 13.38 9.3
## 55 151.0 83 45.0 10.99 9.7
## 56 175.5 67 53.1 12.47 10.2
## 57 126.9 98 37.0 9.00 8.0
## 58 198.4 129 56.7 3.77 5.8
## 59 148.8 70 47.0 12.33 12.1
## 60 229.3 103 55.0 8.87 12.0
## 61 192.1 97 48.0 8.50 11.4
## 62 268.6 83 92.3 8.91 11.6
## 63 193.7 91 93.4 12.31 14.6
## 64 180.7 92 81.0 9.39 12.6
## 65 131.2 98 37.0 8.15 8.2
## 66 148.1 74 56.7 8.48 6.2
## 67 251.5 105 61.0 10.64 9.3
## 68 125.2 93 39.0 10.32 8.3
## 69 211.6 70 55.0 10.85 7.8
## 70 178.9 101 45.0 8.46 13.8
## 71 241.8 93 56.0 8.53 11.8
## 72 224.9 97 87.7 9.41 12.1
## 73 248.6 83 55.0 7.45 8.0
## 74 203.4 146 54.0 11.34 7.3
## 75 235.8 109 54.0 7.86 12.0
## 76 157.1 90 46.0 11.17 6.1
## 77 300.3 109 69.1 9.05 11.7
## 78 61.6 117 20.1 3.86 8.2
## 79 214.1 72 53.6 8.22 8.2
## 80 170.2 98 46.0 7.76 15.0
## 81 201.1 99 60.0 15.18 13.2
## 82 215.4 104 58.0 10.24 12.6
## 83 165.6 123 69.7 6.81 11.0
## 84 249.5 101 91.5 12.99 9.8
## 85 210.6 96 57.0 12.46 12.4
## 86 179.3 104 73.2 11.30 8.6
## 87 157.9 105 41.0 7.75 8.0
## 88 214.3 118 55.0 10.43 12.0
## 89 154.1 104 66.4 6.17 10.9
## 90 237.9 125 62.0 12.38 13.9
## 91 143.9 61 43.7 9.75 11.1
## 92 203.4 100 51.0 9.55 8.9
## 93 124.3 100 36.0 8.65 7.9
## 94 252.9 93 59.0 8.92 9.5
## 95 179.1 71 47.0 9.53 10.6
## 96 278.4 106 58.0 4.05 9.8
## 97 160.1 110 46.0 10.67 13.0
## 98 198.2 87 52.0 10.37 8.7
## 99 212.1 131 54.0 10.47 5.3
## 100 251.8 72 61.0 10.29 9.8
## 101 161.2 114 60.9 12.61 4.4
## 102 178.3 137 50.4 9.45 14.6
## 103 151.7 82 36.0 5.95 10.5
## 104 135.0 99 39.0 9.18 12.5
## 105 170.5 94 47.9 8.69 11.3
## 106 238.1 65 57.0 9.36 11.8
## 107 281.4 102 90.3 10.11 9.0
## 108 117.9 131 61.5 8.23 9.8
## 109 148.6 91 64.3 6.56 10.1
## 110 229.8 90 52.0 7.40 9.6
## 111 165.0 100 56.0 15.86 8.3
## 112 185.0 117 51.0 11.17 12.6
## 113 161.0 117 44.0 9.55 12.1
## 114 126.7 108 40.0 10.30 13.3
## 115 58.9 125 25.0 8.48 9.4
## 116 196.8 89 110.0 12.75 20.0
## 117 162.6 83 43.9 7.62 14.2
## 118 282.5 114 69.1 11.00 9.4
## 119 113.7 117 60.0 7.88 10.0
## 120 239.8 125 60.0 10.74 8.7
## 121 210.2 92 58.1 11.37 13.1
## 122 213.8 102 68.4 7.09 7.2
## 123 190.7 103 49.0 9.18 9.8
## 124 170.9 124 41.0 6.62 11.6
## 125 154.2 119 36.0 5.51 9.2
## 126 201.4 52 58.0 11.47 12.0
## 127 70.7 108 26.0 7.88 9.1
## 128 187.5 124 62.3 7.33 6.4
## 129 91.7 90 33.0 9.69 9.2
## 130 214.2 115 76.7 8.09 9.5
## 131 145.5 92 44.0 10.89 10.9
## 132 166.3 125 42.0 7.91 6.1
## 133 231.0 115 59.0 11.52 9.5
## 134 200.3 96 52.0 10.06 7.1
## 135 197.0 109 51.0 10.13 9.1
## 136 129.9 112 40.1 8.67 11.2
## 137 175.8 97 63.3 10.88 5.3
## 138 203.1 106 53.0 10.51 12.0
## 139 183.2 117 72.2 6.34 11.2
## 140 205.0 101 75.5 7.60 10.2
## 141 148.5 115 49.0 13.82 12.4
## 142 200.3 68 81.4 11.02 10.5
## 143 192.6 107 68.4 9.78 6.8
## 144 246.5 47 59.0 9.78 11.7
## 145 167.1 86 44.0 8.88 14.1
## 146 231.9 101 54.0 8.01 14.3
## 147 146.7 91 43.0 10.18 13.7
## 148 271.5 87 67.6 10.82 11.7
## 149 181.5 121 50.0 10.92 8.5
## 150 257.7 97 88.0 8.11 11.1
## 151 193.8 99 52.0 11.07 10.6
## 152 102.8 119 36.0 10.34 10.1
## 153 187.9 116 46.0 7.88 7.5
## 154 226.0 112 60.0 12.43 6.9
## 155 260.4 115 57.0 7.30 11.5
## 156 178.7 116 56.0 14.61 9.8
## 157 337.4 120 77.0 11.37 15.8
## 158 157.6 129 85.0 12.35 13.7
## 159 183.6 117 54.0 12.84 10.2
## 160 142.1 124 65.9 9.17 9.6
## 161 136.3 97 41.1 8.61 7.1
## 162 217.1 110 58.0 12.08 12.0
## 163 187.5 99 81.4 12.07 10.5
## 164 98.9 103 29.0 6.77 12.2
## 165 206.3 151 48.0 7.43 6.1
## 166 243.1 92 92.7 10.69 12.1
## 167 189.8 126 67.3 8.17 7.5
## 168 202.0 102 59.9 12.16 10.9
## 169 170.1 124 80.6 9.67 12.8
## 170 230.9 87 56.0 9.37 6.3
## 171 237.1 105 60.0 11.18 13.2
## 172 182.1 91 74.6 8.49 10.6
## 173 119.3 87 40.4 10.58 10.5
## 174 116.8 87 36.0 8.95 14.1
## 175 219.2 92 50.0 7.47 6.1
## 176 252.6 104 58.0 8.45 11.1
## 177 147.1 91 42.0 9.52 12.2
## 178 202.1 103 54.0 11.47 11.5
## 179 173.5 93 48.3 9.71 16.2
## 180 232.1 122 65.0 14.62 0.0
## 181 197.1 125 77.7 10.73 9.5
## 182 58.2 94 22.0 6.94 11.9
## 183 115.6 111 66.7 11.89 9.9
## 184 186.1 98 55.4 12.72 14.6
## 185 259.9 68 66.0 12.25 8.4
## 186 214.3 145 60.0 13.43 10.8
## 187 158.7 74 33.0 3.22 10.2
## 188 271.6 71 67.9 11.47 10.9
## 189 160.6 111 44.7 8.16 9.0
## 190 232.4 109 56.0 9.37 9.1
## 191 133.8 85 39.0 9.03 8.9
## 192 176.9 109 41.5 4.54 9.5
## 193 209.9 74 53.0 9.76 8.8
## 194 137.5 118 43.2 10.16 13.4
## 195 289.5 52 89.7 8.33 9.5
## 196 198.1 86 67.4 8.85 6.8
## 197 149.7 119 41.0 9.11 9.7
## 198 326.5 67 74.3 8.82 10.7
## 199 292.9 101 104.3 9.99 13.8
## 200 83.0 64 30.0 8.85 13.0
## 201 145.7 146 79.4 11.03 13.1
## 202 182.3 101 59.0 16.41 11.2
## 203 218.0 86 53.0 9.20 6.4
## 204 140.6 109 40.0 8.93 6.8
## 205 152.7 105 48.0 12.88 9.4
## 206 106.7 76 68.7 10.49 12.1
## 207 243.8 98 49.0 4.20 13.7
## 208 194.4 94 49.0 9.34 10.8
## 209 213.9 95 50.0 7.60 12.2
## 210 217.2 112 58.0 12.34 15.8
## 211 241.1 72 55.0 7.78 11.6
## 212 203.5 100 56.0 12.38 11.9
## 213 155.2 131 76.9 12.23 10.7
## 214 167.6 139 71.9 5.65 12.2
## 215 226.7 98 58.0 11.41 17.6
## 216 179.3 93 46.0 8.93 11.5
## 217 151.4 89 45.1 9.32 10.9
## 218 180.0 80 50.0 11.21 4.7
## 219 250.2 121 66.0 13.36 13.0
## 220 223.0 121 52.0 5.51 7.1
## 221 183.6 116 45.0 7.63 12.2
## 222 166.0 114 71.5 8.73 10.2
## 223 136.1 112 47.0 13.65 4.4
## 224 149.3 113 49.2 12.11 8.9
## 225 65.4 97 26.0 8.41 13.8
## 226 213.4 111 57.0 11.73 2.7
## 227 206.9 85 56.0 12.24 7.7
## 228 186.2 78 73.9 9.48 9.6
## 229 280.2 136 102.9 11.03 13.3
## 230 196.6 84 93.1 15.66 11.9
## 231 312.0 109 65.0 6.47 10.5
## 232 199.0 110 88.7 14.57 11.0
## 233 203.1 96 55.5 10.85 13.5
## 234 168.8 97 48.0 11.02 10.9
## 235 173.1 140 50.0 12.02 9.0
## 236 134.4 106 41.0 10.57 10.2
## 237 202.6 103 69.3 5.94 9.0
## 238 74.5 117 33.1 10.04 9.8
## 239 83.6 148 28.1 6.05 10.7
## 240 192.2 86 47.0 8.43 9.4
## 241 220.2 89 45.0 4.42 12.9
## 242 135.1 95 35.0 6.71 12.3
## 243 253.4 77 61.5 9.12 8.4
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## 1623 184.8 83 53.0 12.43 9.6
## 1624 176.3 140 48.0 10.05 11.3
## 1625 241.7 115 56.0 8.43 11.1
## 1626 224.7 121 90.5 14.70 9.8
## 1627 207.3 115 56.7 9.92 8.6
## 1628 196.8 81 48.0 8.40 12.7
## 1629 110.9 74 29.0 5.78 15.8
## 1630 122.5 145 45.0 13.67 8.0
## 1631 226.9 144 57.4 10.08 13.2
## 1632 187.0 65 44.0 7.07 10.0
## 1633 170.5 113 46.0 9.66 11.2
## 1634 204.8 101 49.0 8.05 9.5
## 1635 165.9 114 49.0 11.80 12.0
## 1636 154.0 133 44.0 9.95 9.5
## 1637 158.1 104 79.0 16.11 8.9
## 1638 225.2 93 61.5 10.76 9.1
## 1639 159.4 79 43.0 8.98 9.7
## 1640 172.7 95 44.0 6.96 11.7
## 1641 222.8 99 54.1 8.79 11.0
## 1642 214.1 77 57.0 12.03 10.1
## 1643 54.8 92 25.0 8.65 7.5
## 1644 134.0 104 38.0 8.73 7.3
## 1645 184.8 74 47.0 8.76 10.5
## 1646 283.1 112 103.5 14.31 11.3
## 1647 291.8 143 68.0 10.72 9.9
## 1648 222.7 94 50.0 5.29 13.5
## 1649 174.5 79 50.0 11.84 8.5
## 1650 68.4 86 29.0 9.67 10.4
## 1651 273.0 78 90.9 10.78 9.6
## 1652 225.3 134 48.0 5.41 17.3
## 1653 283.2 130 81.4 8.13 7.2
## 1654 131.4 78 42.0 10.99 11.1
## 1655 89.7 87 56.9 6.93 10.7
## 1656 127.1 102 43.0 12.39 5.0
## 1657 105.9 132 66.9 11.59 10.7
## 1658 142.3 79 41.0 7.90 6.0
## 1659 191.3 80 47.5 6.93 6.4
## 1660 201.9 93 85.0 7.82 13.7
## 1661 247.3 91 61.6 9.14 14.7
## 1662 242.2 96 79.0 7.99 8.9
## 1663 127.3 80 42.2 11.12 13.7
## 1664 162.0 104 49.0 12.06 10.9
## 1665 179.1 93 79.6 11.92 10.6
## 1666 197.4 125 78.2 6.17 12.3
## 1667 148.2 82 54.9 15.44 6.4
## 1668 193.1 85 48.0 8.61 10.2
## 1669 171.7 99 46.6 8.74 7.8
## 1670 198.5 123 78.9 13.53 8.1
## 1671 121.7 87 71.3 9.20 12.7
## 1672 130.2 105 47.6 13.90 14.0
## 1673 203.4 96 49.0 8.43 13.7
## 1674 174.7 83 54.0 14.04 10.5
## 1675 241.0 120 64.4 11.59 9.9
## 1676 141.7 95 45.1 11.05 10.2
## 1677 134.8 96 38.0 8.36 7.7
## 1678 163.1 119 49.0 12.47 9.0
## 1679 145.5 116 48.1 11.42 8.9
## 1680 329.8 73 74.0 10.42 10.6
## 1681 194.5 97 49.0 9.32 12.7
## 1682 131.9 93 46.0 13.64 7.1
## 1683 150.0 91 63.0 7.97 8.5
## 1684 196.6 93 88.8 12.07 12.9
## 1685 99.7 107 30.0 7.26 14.1
## 1686 143.6 88 39.7 7.09 10.8
## 1687 231.9 56 91.2 10.59 12.3
## 1688 37.8 80 20.0 7.77 14.2
## 1689 72.8 107 29.0 9.32 10.5
## 1690 94.8 89 65.8 10.96 11.4
## 1691 221.8 143 89.5 10.53 12.4
## 1692 269.0 120 66.0 11.69 7.3
## 1693 268.3 114 65.1 9.28 6.3
## 1694 198.7 127 88.8 12.45 12.5
## 1695 115.5 75 39.0 10.91 11.5
## 1696 202.1 100 51.0 9.79 13.3
## 1697 215.6 113 54.0 10.03 12.4
## 1698 169.9 107 47.0 10.47 11.5
## 1699 201.7 85 49.0 8.47 6.0
## 1700 221.1 133 52.0 8.01 8.4
## 1701 218.7 117 72.4 5.75 9.4
## 1702 293.7 89 76.9 13.63 11.0
## 1703 120.3 108 41.0 12.02 7.7
## 1704 175.8 96 78.0 10.33 11.1
## 1705 278.5 95 68.0 12.04 11.6
## 1706 236.3 105 76.4 9.54 7.2
## 1707 273.8 113 57.0 5.98 11.7
## 1708 131.1 129 36.0 8.03 5.6
## 1709 167.4 83 81.2 12.93 11.2
## 1710 197.7 68 55.0 12.53 10.5
## 1711 169.5 93 49.0 11.55 9.0
## 1712 225.2 116 85.6 8.67 11.7
## 1713 174.5 73 48.0 10.69 10.3
## 1714 129.7 84 41.6 8.88 7.5
## 1715 200.0 66 44.0 5.40 11.4
## 1716 95.9 87 74.9 13.08 13.3
## 1717 152.8 110 71.6 12.14 9.1
## 1718 129.9 102 40.0 10.44 14.3
## 1719 268.4 85 59.0 7.53 9.7
## 1720 188.5 152 45.0 7.42 15.2
## 1721 170.6 97 45.4 8.11 6.1
## 1722 191.4 124 50.0 10.04 8.2
## 1723 75.3 96 29.0 9.00 12.3
## 1724 149.8 123 53.0 13.82 10.9
## 1725 115.9 87 30.0 5.57 7.1
## 1726 128.8 86 40.0 10.20 14.1
## 1727 131.7 108 41.0 10.83 11.0
## 1728 101.4 48 31.0 7.96 12.2
## 1729 149.0 104 71.7 11.79 9.5
## 1730 96.8 123 67.2 8.53 13.4
## 1731 107.5 121 41.0 12.82 12.6
## 1732 232.8 95 66.0 15.17 12.9
## 1733 121.1 105 65.4 13.01 8.3
## 1734 124.3 70 45.0 13.54 3.5
## 1735 157.7 101 53.0 14.93 13.8
## 1736 124.3 68 39.0 10.36 14.8
## 1737 286.4 125 67.0 10.29 6.9
## 1738 141.7 95 42.0 10.28 8.8
## 1739 173.0 91 64.0 12.29 4.8
## 1740 268.7 120 72.0 15.05 5.8
## 1741 218.5 130 74.4 6.71 9.4
## 1742 255.3 114 60.0 9.73 3.7
## 1743 41.9 124 26.0 10.55 11.4
## 1744 260.8 87 67.0 12.91 5.8
## 1745 239.4 94 83.8 12.97 7.7
## 1746 226.7 94 56.3 8.42 10.2
## 1747 179.3 147 49.0 10.45 13.5
## 1748 158.0 110 44.0 9.85 10.0
## 1749 175.7 82 90.1 12.95 14.1
## 1750 157.4 107 42.0 8.39 8.8
## 1751 113.1 74 34.0 8.44 6.9
## 1752 182.7 142 53.0 12.33 8.8
## 1753 161.3 83 40.1 6.22 14.1
## 1754 142.5 92 42.0 10.42 7.5
## 1755 190.5 108 58.8 12.99 9.7
## 1756 159.3 110 74.1 8.53 11.9
## 1757 153.8 106 61.8 6.17 9.2
## 1758 180.7 127 46.0 8.73 12.0
## 1759 202.7 105 54.0 11.25 12.1
## 1760 190.8 100 79.0 13.07 8.9
## 1761 205.1 102 58.1 11.64 9.2
## 1762 235.6 124 81.8 11.84 7.7
## 1763 189.3 77 46.0 7.80 7.4
## 1764 166.9 101 83.1 13.66 11.5
## 1765 245.2 87 64.0 12.71 7.5
## 1766 132.6 125 42.0 11.06 12.7
## 1767 182.3 64 43.0 6.99 11.6
## 1768 192.3 86 69.4 4.44 10.5
## 1769 122.0 110 40.0 11.01 10.8
## 1770 193.0 101 55.0 12.50 9.6
## 1771 158.6 112 46.0 11.00 9.1
## 1772 91.5 125 69.3 11.00 12.7
## 1773 153.6 92 45.9 10.28 12.5
## 1774 221.6 79 83.1 7.86 11.5
## 1775 244.7 81 59.0 8.40 6.6
## 1776 239.8 103 91.7 14.30 9.5
## 1777 172.4 132 49.0 11.53 11.0
## 1778 242.5 83 63.0 12.27 10.0
## 1779 117.6 82 64.5 7.96 11.3
## 1780 174.5 127 52.0 12.97 11.3
## 1781 157.3 83 46.0 11.05 12.0
## 1782 192.0 97 93.8 11.96 15.1
## 1783 218.2 76 52.0 8.47 8.0
## 1784 144.6 97 66.4 7.00 10.9
## 1785 153.6 108 46.0 11.65 14.1
## 1786 135.8 104 63.3 11.13 7.9
## 1787 160.7 69 40.0 7.34 8.2
## 1788 202.5 91 76.1 12.07 7.8
## 1789 152.2 119 79.2 11.36 12.3
## 1790 227.4 90 45.0 3.66 4.7
## 1791 191.6 115 51.0 10.28 9.2
## 1792 138.9 111 42.0 10.58 10.8
## 1793 127.0 102 41.8 10.35 6.1
## 1794 168.6 87 51.0 12.96 7.3
## 1795 286.6 73 68.0 11.16 11.5
## 1796 164.6 121 92.0 13.14 15.2
## 1797 144.0 90 39.4 6.79 13.0
## 1798 141.6 95 69.5 10.40 10.2
## 1799 204.3 65 56.0 12.37 12.0
## 1800 163.2 80 45.2 8.38 6.2
## 1801 225.0 110 60.0 12.21 10.7
## 1802 176.1 103 49.3 9.99 8.5
## 1803 254.2 78 100.3 11.41 13.8
## 1804 174.9 105 52.0 13.10 8.5
## 1805 187.3 118 46.0 8.04 9.6
## 1806 211.8 84 58.7 11.55 10.7
## 1807 241.9 102 52.0 6.35 11.7
## 1808 196.1 103 51.0 9.99 12.9
## 1809 231.3 100 58.0 10.52 12.4
## 1810 161.6 104 49.2 9.82 13.8
## 1811 194.0 103 54.0 12.05 11.9
## 1812 109.7 148 38.0 11.19 15.4
## 1813 277.0 119 70.0 11.92 8.3
## 1814 192.1 83 48.5 8.18 6.1
## 1815 198.4 147 53.0 10.85 13.1
## 1816 209.2 82 75.7 7.99 9.5
## 1817 184.8 98 50.0 10.82 18.4
## 1818 167.8 119 41.0 7.10 7.3
## 1819 139.2 140 40.0 9.57 11.8
## 1820 221.3 82 63.9 8.38 4.4
## 1821 121.6 84 35.0 8.27 8.9
## 1822 270.4 99 108.6 12.26 15.4
## 1823 139.6 94 45.0 12.05 8.8
## 1824 253.0 78 86.9 6.95 11.8
## 1825 183.9 83 92.5 12.04 15.0
## 1826 203.3 108 57.0 13.00 7.8
## 1827 200.6 106 48.0 7.63 7.7
## 1828 167.6 96 44.0 8.80 13.4
## 1829 156.5 67 44.0 10.22 9.9
## 1830 215.1 140 82.6 9.87 10.6
## 1831 301.7 82 68.1 8.36 10.5
## 1832 152.3 90 79.5 13.38 11.3
## 1833 195.4 116 52.0 10.61 15.1
## 1834 208.7 97 59.0 13.78 8.0
## 1835 190.1 87 90.3 11.16 14.2
## 1836 185.4 87 68.6 8.93 8.0
## 1837 183.2 95 79.2 12.64 9.7
## 1838 54.2 100 35.0 15.16 8.6
## 1839 208.0 115 73.9 9.25 8.1
## 1840 230.3 110 46.0 3.90 13.2
## 1841 240.8 102 67.2 3.80 7.1
## 1842 195.7 119 57.3 5.31 5.3
## 1843 276.1 82 69.0 10.06 8.9
## 1844 166.1 93 44.0 8.80 16.2
## 1845 135.9 117 75.1 12.23 11.5
## 1846 189.1 122 52.0 11.16 13.9
## 1847 177.9 117 77.1 8.76 11.5
## 1848 143.9 73 76.8 10.52 12.5
## 1849 148.2 138 39.0 7.98 8.6
## 1850 287.1 115 63.0 7.97 13.9
## 1851 179.7 144 75.1 10.91 9.3
## 1852 165.8 96 45.0 9.50 10.9
## 1853 144.1 144 78.2 8.38 14.5
## 1854 172.5 85 51.0 12.66 5.9
## 1855 199.8 138 49.0 8.36 5.5
## 1856 109.1 134 31.0 7.12 10.9
## 1857 171.8 106 55.0 15.09 9.7
## 1858 222.3 101 63.0 14.30 12.1
## 1859 245.8 102 65.0 13.24 11.2
## 1860 164.6 110 51.0 13.53 8.0
## 1861 211.7 107 63.6 13.59 7.4
## 1862 147.2 103 59.8 8.01 7.7
## 1863 254.7 103 65.0 12.61 8.0
## 1864 170.1 113 53.0 13.59 8.7
## 1865 195.1 91 60.1 13.08 11.4
## 1866 149.3 83 42.0 9.36 7.9
## 1867 81.9 75 36.0 12.69 8.9
## 1868 191.1 109 72.5 7.48 9.8
## 1869 206.9 115 55.0 11.22 8.3
## 1870 239.0 156 64.0 13.65 13.5
## 1871 179.3 97 55.5 12.64 8.0
## 1872 185.3 91 51.0 10.96 5.5
## 1873 141.4 80 35.0 6.20 8.1
## 1874 248.6 91 85.4 5.97 12.0
## 1875 152.5 131 48.0 12.62 4.9
## 1876 145.6 102 47.8 11.55 11.4
## 1877 164.2 116 45.0 9.81 8.1
## 1878 221.0 115 52.0 8.27 9.7
## 1879 295.4 126 70.0 11.61 11.5
## 1880 139.8 98 39.0 8.75 9.4
## 1881 162.3 99 42.6 7.46 14.8
## 1882 272.7 97 67.0 11.82 7.7
## 1883 200.3 75 88.8 11.33 12.9
## 1884 157.1 77 72.0 8.62 11.1
## 1885 135.8 60 74.2 10.03 12.3
## 1886 236.7 110 61.6 11.60 12.7
## 1887 111.4 133 36.1 8.75 5.5
## 1888 156.1 89 75.7 5.36 14.7
## 1889 191.1 93 57.0 14.14 12.0
## 1890 153.0 123 38.0 7.06 10.3
## 1891 218.8 123 58.0 12.14 10.3
## 1892 205.4 101 47.0 6.75 10.3
## 1893 225.2 111 54.0 9.25 9.9
## 1894 249.9 127 65.0 12.73 8.9
## 1895 131.6 89 39.1 6.85 10.2
## 1896 197.9 99 75.3 8.28 10.1
## 1897 166.5 129 47.0 10.51 9.9
## 1898 225.4 79 89.8 9.36 12.9
## 1899 275.8 103 63.0 9.48 7.4
## 1900 142.9 105 61.2 4.43 10.8
## 1901 207.2 113 57.0 12.80 9.9
## 1902 206.2 100 53.0 10.56 10.2
## 1903 210.3 66 53.0 9.79 11.2
## 1904 225.7 117 86.8 5.98 14.0
## 1905 167.8 91 85.2 10.27 14.5
## 1906 197.7 118 47.0 7.61 7.0
## 1907 169.8 105 64.4 3.26 10.9
## 1908 190.6 104 79.5 11.87 9.8
## 1909 80.3 140 61.6 7.67 12.8
## 1910 231.7 110 91.7 11.26 12.1
## 1911 69.1 114 32.0 11.52 6.5
## 1912 188.8 60 51.0 10.87 8.2
## 1913 150.6 125 40.0 8.46 10.4
## 1914 192.0 89 47.8 6.98 5.5
## 1915 163.7 78 64.7 5.66 9.9
## 1916 211.7 100 53.0 9.94 6.5
## 1917 175.5 103 42.0 6.62 11.8
## 1918 150.1 120 43.0 10.01 11.0
## 1919 189.5 99 48.0 8.82 14.2
## 1920 70.8 94 31.0 10.78 9.5
## 1921 215.5 102 56.5 9.54 8.6
## 1922 101.7 105 35.0 10.14 9.4
## 1923 258.4 132 57.3 6.34 9.7
## 1924 242.4 126 55.0 7.65 11.8
## 1925 131.8 82 47.0 14.22 11.3
## 1926 190.2 102 52.6 9.89 9.8
## 1927 154.1 104 44.0 10.21 9.8
## 1928 188.0 127 40.0 4.53 15.3
## 1929 103.1 70 41.0 13.75 11.2
## 1930 175.4 130 44.0 7.98 11.6
## 1931 145.4 93 43.0 10.46 10.9
## 1932 250.6 85 59.0 9.40 7.8
## 1933 161.5 123 46.0 10.71 8.6
## 1934 260.1 101 67.0 12.83 10.0
## 1935 281.3 124 74.0 15.08 8.7
## 1936 130.1 90 73.7 8.35 13.6
## 1937 102.0 118 27.0 5.67 11.4
## 1938 218.7 104 83.7 7.75 12.1
## 1939 128.5 86 56.4 9.42 6.8
## 1940 128.7 100 42.0 11.36 9.2
## 1941 172.2 92 47.6 8.13 8.7
## 1942 199.2 124 45.0 6.30 7.6
## 1943 184.5 98 49.0 10.03 8.8
## 1944 168.6 99 44.0 8.78 10.9
## 1945 174.0 118 66.1 10.27 6.7
## 1946 230.4 65 62.0 12.87 8.5
## 1947 198.2 73 51.0 10.14 5.1
## 1948 186.1 96 50.0 10.58 8.0
## 1949 148.5 105 46.0 12.15 6.8
## 1950 157.1 109 50.0 13.44 10.0
## 1951 155.0 110 38.0 6.67 7.0
## 1952 129.3 123 62.9 8.83 9.6
## 1953 188.5 77 48.0 9.10 6.1
## 1954 208.8 120 55.0 11.27 11.1
## 1955 238.0 82 65.0 13.93 11.8
## 1956 211.1 103 54.0 10.35 5.6
## 1957 198.9 87 86.0 10.35 12.6
## 1958 212.8 79 57.3 10.21 10.2
## 1959 137.4 126 34.0 6.00 12.4
## 1960 191.8 75 90.6 13.39 12.8
## 1961 149.0 92 30.0 2.46 13.9
## 1962 117.1 118 42.0 12.48 11.1
## 1963 108.0 79 39.0 12.10 10.4
## 1964 112.8 133 37.0 9.97 10.1
## 1965 175.9 105 49.3 9.42 11.0
## 1966 236.6 109 55.0 8.50 11.1
## 1967 169.4 102 45.0 9.25 2.0
## 1968 129.6 79 45.8 12.31 9.4
## 1969 177.1 97 46.0 9.24 8.0
## 1970 133.3 63 75.5 9.21 13.5
## 1971 167.8 121 49.4 10.65 13.0
## 1972 174.6 107 81.3 15.53 9.0
## 1973 150.3 101 48.0 12.80 12.5
## 1974 283.2 110 86.0 11.99 6.3
## 1975 157.8 83 64.5 8.08 8.7
## 1976 141.2 132 37.0 7.46 7.0
## 1977 230.2 106 84.1 9.81 10.4
## 1978 237.8 92 61.6 10.45 15.6
## 1979 204.0 84 49.0 8.43 13.3
## 1980 221.1 106 53.0 8.93 7.4
## 1981 177.2 93 43.0 7.13 12.7
## 1982 118.0 133 42.0 12.41 5.3
## 1983 163.8 73 50.0 12.78 15.7
## 1984 141.3 96 69.4 11.52 9.4
## 1985 272.5 119 66.0 11.31 16.4
## 1986 118.9 112 62.1 11.42 8.2
## 1987 7.9 100 15.7 6.82 12.1
## 1988 159.5 96 43.9 8.36 10.2
## 1989 150.2 70 46.2 9.29 12.1
## 1990 144.5 35 79.4 13.12 12.0
## 1991 140.7 88 42.0 10.55 12.4
## 1992 169.2 123 48.0 10.84 12.6
## 1993 220.8 77 53.8 7.43 7.6
## 1994 216.3 96 63.5 13.32 4.5
## 1995 169.5 96 43.0 7.88 10.6
## 1996 256.3 119 97.6 12.91 11.7
## 1997 179.7 128 57.0 14.99 7.6
## 1998 266.0 120 57.0 6.51 13.1
## 1999 96.7 97 33.0 9.69 9.7
## 2000 82.7 116 31.0 9.73 10.9
## 2001 168.2 87 43.0 8.09 10.1
## 2002 286.4 109 64.0 8.91 10.7
## 2003 174.3 95 46.0 9.33 12.9
## 2004 190.6 100 47.0 8.09 13.0
## 2005 175.5 86 50.1 10.26 17.8
## 2006 133.4 102 41.0 10.23 11.1
## 2007 204.6 96 64.8 6.80 6.6
## 2008 242.2 88 61.0 11.66 6.2
## 2009 253.1 112 93.1 10.51 11.9
## 2010 130.0 110 38.0 9.27 8.3
## 2011 105.9 151 35.0 9.48 12.7
## 2012 194.2 98 50.0 9.69 9.3
## 2013 183.8 111 42.0 6.18 6.1
## 2014 196.5 82 52.5 9.50 10.8
## 2015 184.5 81 46.0 8.60 13.7
## 2016 261.9 113 58.0 7.41 13.8
## 2017 202.4 118 59.3 13.01 9.2
## 2018 167.4 113 69.7 8.64 9.5
## 2019 167.7 104 70.3 12.34 7.5
## 2020 191.7 109 79.0 9.65 11.1
## 2021 240.2 78 61.0 11.52 5.2
## 2022 189.1 112 78.0 8.91 11.1
## 2023 127.7 67 38.0 9.15 10.6
## 2024 205.2 106 44.0 4.98 13.4
## 2025 153.6 93 79.0 10.85 12.6
## 2026 154.5 129 45.3 9.68 13.4
## 2027 153.7 109 43.0 9.70 14.1
## 2028 171.2 138 74.2 9.29 10.8
## 2029 328.1 106 71.9 7.59 8.7
## 2030 145.9 69 46.6 10.41 14.4
## 2031 201.2 76 90.9 14.01 11.8
## 2032 139.1 72 45.0 12.30 11.4
## 2033 118.9 128 44.0 13.92 13.2
## 2034 217.6 87 64.3 13.95 10.4
## 2035 145.0 133 43.0 10.46 14.6
## 2036 203.5 89 60.0 14.48 8.7
## 2037 240.1 115 57.0 9.02 8.0
## 2038 83.8 121 35.0 12.01 6.7
## 2039 269.8 106 70.5 11.44 10.1
## 2040 126.3 84 68.6 10.48 10.6
## 2041 88.1 125 56.2 8.80 9.7
## 2042 218.5 61 80.7 9.84 9.9
## 2043 236.8 61 93.2 13.17 11.2
## 2044 124.1 117 40.6 9.64 6.4
## 2045 184.2 132 73.0 8.38 10.0
## 2046 222.7 133 62.0 13.85 13.6
## 2047 149.2 98 42.0 9.68 11.1
## 2048 206.5 125 51.0 9.01 12.2
## 2049 159.7 102 67.9 8.44 9.6
## 2050 204.7 118 71.9 10.47 7.0
## 2051 213.2 79 50.2 6.04 7.5
## 2052 269.6 121 61.0 8.59 8.2
## 2053 116.7 92 39.0 10.69 9.7
## 2054 263.4 101 65.0 11.78 13.0
## 2055 140.2 97 43.0 10.70 7.1
## 2056 197.7 101 45.0 6.38 13.5
## 2057 136.2 92 45.1 11.05 13.3
## 2058 88.5 87 62.1 8.94 11.5
## 2059 215.3 58 58.0 12.12 12.1
## 2060 269.2 104 65.8 9.69 8.9
## 2061 203.8 118 77.7 13.36 7.3
## 2062 268.4 112 92.8 11.11 10.3
## 2063 159.1 104 50.0 13.49 10.3
## 2064 114.4 122 33.8 6.39 10.1
## 2065 138.9 65 42.0 10.45 9.2
## 2066 186.0 55 52.0 11.87 12.2
## 2067 170.4 91 91.8 12.73 15.1
## 2068 164.5 95 48.0 11.55 9.9
## 2069 168.6 121 43.0 8.43 12.3
## 2070 261.2 119 69.1 12.54 9.8
## 2071 190.5 91 48.0 8.92 13.1
## 2072 181.1 121 58.0 15.72 4.2
## 2073 177.1 131 40.0 5.74 6.5
## 2074 160.5 114 48.0 12.03 11.3
## 2075 134.7 116 48.0 14.77 6.6
## 2076 198.2 107 69.8 6.96 8.8
## 2077 228.9 134 61.0 12.79 10.1
## 2078 241.7 137 53.0 6.79 13.1
## 2079 131.1 108 38.0 8.81 4.3
## 2080 234.1 101 57.0 10.01 13.1
## 2081 200.1 72 60.0 15.05 11.9
## 2082 154.0 107 35.0 4.72 10.1
## 2083 224.2 106 81.5 9.48 9.8
## 2084 148.3 83 41.0 9.08 8.3
## 2085 174.6 76 68.8 8.83 8.8
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## 2990 115.1 114 41.8 10.57 13.8
## 2991 172.9 109 64.4 6.88 8.3
## 2992 156.4 116 38.0 6.52 7.3
## 2993 128.1 104 65.3 7.17 11.6
## 2994 196.6 73 48.0 8.51 12.5
## 2995 227.9 130 65.0 15.13 5.5
## 2996 194.9 63 85.6 9.58 13.2
## 2997 44.9 63 55.9 6.71 13.3
## 2998 262.8 114 85.1 10.79 7.8
## 2999 211.2 70 60.1 12.64 12.3
## 3000 204.0 69 54.0 11.26 9.6
## 3001 223.2 109 53.2 6.38 14.5
## 3002 119.0 82 40.9 9.38 11.5
## 3003 266.1 91 65.0 11.26 8.9
## 3004 134.4 104 36.0 7.62 9.4
## 3005 171.1 78 51.0 12.86 16.2
## 3006 170.5 103 51.0 12.72 10.5
## 3007 178.5 124 45.3 7.35 9.9
## 3008 205.2 145 49.0 7.74 14.1
## 3009 232.8 97 91.1 9.18 13.0
## 3010 239.9 107 81.1 12.69 6.7
## 3011 55.6 97 34.0 14.44 12.1
## 3012 153.5 78 75.6 12.10 10.6
## 3013 109.8 100 35.0 9.48 11.1
## 3014 196.1 89 50.0 9.28 5.2
## 3015 166.8 127 41.0 7.18 11.8
## 3016 113.2 96 62.2 13.50 7.1
## 3017 203.0 92 49.5 7.55 14.6
## 3018 242.8 90 62.0 11.71 6.0
## 3019 156.5 102 39.0 7.01 12.2
## 3020 266.7 105 61.5 7.91 13.8
## 3021 182.0 80 76.5 10.81 9.8
## 3022 85.9 92 32.0 9.70 10.1
## 3023 146.6 87 42.8 5.74 2.9
## 3024 110.5 101 74.5 10.42 13.9
## 3025 118.6 89 38.0 9.98 11.5
## 3026 197.6 105 83.1 4.00 15.6
## 3027 210.3 116 82.2 9.61 10.8
## 3028 220.3 96 87.4 14.29 9.4
## 3029 150.0 98 46.0 11.62 12.5
## 3030 161.7 114 70.8 10.38 9.2
## 3031 191.4 116 47.0 8.37 14.0
## 3032 146.7 83 40.6 7.42 12.5
## 3033 109.4 103 28.0 5.07 7.8
## 3034 144.1 115 49.3 12.49 13.6
## 3035 248.9 93 87.2 8.54 11.2
## 3036 85.7 112 34.0 11.08 11.6
## 3037 214.8 112 55.0 10.49 9.4
## 3038 158.9 137 48.0 12.14 6.5
## 3039 110.0 94 48.3 7.08 6.4
## 3040 152.8 145 42.0 9.18 10.5
## 3041 145.6 103 44.2 9.86 10.5
## 3042 93.3 83 33.0 9.98 6.5
## 3043 216.8 134 57.2 9.39 8.3
## 3044 201.9 101 51.2 7.74 9.0
## 3045 146.4 81 48.0 11.26 8.5
## 3046 272.7 74 66.0 11.25 10.5
## 3047 18.9 92 28.4 12.92 14.8
## 3048 172.8 81 46.0 9.67 12.8
## 3049 190.2 119 46.0 7.86 14.0
## 3050 130.6 83 40.0 10.41 15.6
## 3051 158.4 92 43.0 9.40 13.5
## 3052 166.5 111 49.0 11.81 15.6
## 3053 129.3 103 40.0 10.14 12.9
## 3054 199.3 112 51.0 9.67 7.0
## 3055 185.1 126 52.0 11.65 9.1
## 3056 175.4 80 47.0 9.87 9.7
## 3057 263.4 123 58.0 7.60 10.7
## 3058 94.2 108 39.0 13.21 7.3
## 3059 189.4 83 53.6 10.95 7.1
## 3060 118.0 103 66.9 8.36 11.8
## 3061 212.1 98 53.0 9.47 8.4
## 3062 222.0 93 56.2 9.35 12.4
## 3063 222.8 98 89.1 9.03 13.0
## 3064 190.0 137 75.9 5.83 12.2
## 3065 271.8 129 70.3 11.86 8.7
## 3066 195.4 83 79.7 13.41 8.4
## 3067 199.6 93 53.0 10.72 7.2
## 3068 100.0 98 32.0 8.68 10.1
## 3069 160.6 85 72.7 11.16 9.5
## 3070 158.7 91 67.7 8.03 9.9
## 3071 154.5 122 45.0 10.71 12.0
## 3072 192.3 114 61.0 6.47 6.3
## 3073 305.1 106 68.0 9.40 8.5
## 3074 193.0 106 66.0 7.68 7.4
## 3075 72.5 88 32.7 10.20 6.6
## 3076 105.2 61 64.0 17.07 6.3
## 3077 180.5 88 43.0 6.74 10.0
## 3078 214.7 86 102.6 15.72 14.3
## 3079 86.8 95 24.0 5.41 13.2
## 3080 131.5 99 38.0 8.74 7.9
## 3081 135.4 102 46.1 11.86 17.5
## 3082 174.3 85 52.0 12.71 5.9
## 3083 203.9 63 51.0 9.59 12.1
## 3084 235.5 108 53.0 7.12 12.5
## 3085 157.0 113 49.0 12.85 12.1
## 3086 111.9 55 38.0 11.15 10.0
## 3087 236.3 91 54.0 7.64 11.2
## 3088 163.6 88 52.0 14.17 8.6
## 3089 213.6 127 76.0 8.80 8.9
## 3090 143.4 72 64.4 8.50 9.4
## 3091 78.3 119 34.5 9.91 12.1
## 3092 97.1 98 36.0 11.40 10.6
## 3093 94.1 93 29.0 7.38 10.1
## 3094 226.3 95 65.6 13.72 8.2
## 3095 133.8 61 37.0 7.94 10.5
## 3096 190.3 93 82.6 12.45 10.6
## 3097 294.9 106 91.5 8.29 9.8
## 3098 185.4 114 48.0 9.57 10.0
## 3099 179.5 121 47.0 9.60 12.0
## 3100 158.0 94 45.0 10.40 10.1
## 3101 173.0 131 46.0 9.52 10.4
## 3102 134.2 101 63.1 10.60 8.2
## 3103 125.2 123 75.0 11.55 12.6
## 3104 195.9 111 53.0 11.35 13.2
## 3105 214.2 61 79.8 9.06 10.3
## 3106 221.1 101 58.0 11.84 9.5
## 3107 132.0 100 69.3 8.67 11.6
## 3108 157.6 92 48.1 9.92 9.1
## 3109 110.3 71 64.7 9.12 11.0
## 3110 161.5 121 44.0 9.65 11.2
## 3111 171.8 116 78.6 12.04 10.6
## 3112 211.0 99 80.8 7.76 11.4
## 3113 139.3 89 41.0 9.62 9.3
## 3114 291.6 99 71.7 11.06 14.0
## 3115 139.0 110 38.5 6.65 12.1
## 3116 234.8 125 57.0 9.96 10.0
## 3117 187.6 83 50.0 10.07 8.8
## 3118 159.8 143 46.0 10.51 13.1
## 3119 177.1 100 61.0 9.70 5.2
## 3120 117.9 101 34.0 8.02 11.4
## 3121 247.6 95 93.2 12.82 10.8
## 3122 169.9 77 41.0 6.92 8.5
## 3123 185.0 120 49.0 10.19 14.1
## 3124 204.9 84 82.5 10.05 11.3
## 3125 225.5 119 79.4 9.10 9.4
## 3126 169.7 115 41.0 7.07 10.5
## 3127 239.3 102 60.0 11.17 10.6
## 3128 113.3 96 37.0 9.90 11.7
## 3129 161.9 100 51.3 11.51 10.2
## 3130 133.3 110 54.1 9.29 5.6
## 3131 170.7 88 62.5 5.50 8.7
## 3132 189.7 76 48.1 7.81 8.3
## 3133 322.3 100 75.0 11.52 7.8
## 3134 124.4 74 51.6 16.05 10.4
## 3135 146.9 94 35.0 5.72 11.4
## 3136 192.6 123 53.6 10.32 10.8
## 3137 96.3 83 59.8 8.98 10.3
## 3138 131.9 96 37.0 8.38 14.7
## 3139 147.2 121 40.0 8.76 13.3
## 3140 143.1 139 45.0 11.98 7.1
## 3141 280.4 127 65.7 8.97 15.2
## 3142 237.2 85 87.9 10.66 10.7
## 3143 184.2 95 49.2 9.08 12.8
## 3144 109.1 141 38.4 9.36 10.0
## 3145 138.1 115 37.0 7.91 10.3
## 3146 186.8 94 50.0 10.38 8.8
## 3147 155.4 112 52.0 14.55 13.9
## 3148 245.3 91 53.0 6.15 8.5
## 3149 205.9 97 59.0 13.87 11.0
## 3150 207.2 138 54.0 10.71 11.9
## 3151 151.5 100 75.9 12.44 10.7
## 3152 221.9 112 64.5 13.91 7.1
## 3153 190.0 100 56.8 12.33 9.5
## 3154 220.8 111 51.0 7.81 10.5
## 3155 173.7 117 64.0 10.20 6.3
## 3156 114.8 94 33.0 7.50 9.6
## 3157 113.8 97 38.9 9.62 10.4
## 3158 143.2 60 40.0 8.98 6.2
## 3159 184.4 111 49.0 10.19 9.3
## 3160 227.4 67 60.0 12.40 7.8
## 3161 224.0 99 56.0 10.54 2.1
## 3162 216.2 95 53.0 9.29 10.0
## 3163 129.9 121 42.0 11.51 13.3
## 3164 230.1 108 82.6 14.38 6.9
## 3165 204.4 97 58.0 13.66 11.0
## 3166 216.6 101 76.6 8.66 9.1
## 3167 247.5 85 64.1 11.27 10.2
## 3168 228.1 93 51.0 6.82 9.0
## 3169 225.9 110 64.0 14.96 11.2
## 3170 103.5 115 32.0 5.90 12.0
## 3171 115.5 70 43.4 12.61 7.5
## 3172 218.8 125 50.0 7.42 9.7
## 3173 223.8 67 59.0 12.24 12.3
## 3174 143.8 71 41.0 9.20 12.9
## 3175 29.9 123 40.2 6.46 8.6
## 3176 276.7 121 87.4 10.19 8.3
## 3177 141.4 128 37.0 7.32 8.1
## 3178 153.9 102 73.6 7.04 12.8
## 3179 190.5 128 50.0 10.28 13.8
## 3180 192.6 102 51.4 8.95 9.4
## 3181 151.8 115 35.0 5.18 12.2
## 3182 215.6 74 54.0 9.65 10.1
## 3183 180.0 100 54.1 11.45 7.8
## 3184 157.3 116 44.0 9.88 8.4
## 3185 196.5 88 49.8 7.93 6.8
## 3186 240.3 130 58.1 8.13 11.9
## 3187 193.3 126 50.3 7.74 9.4
## 3188 211.9 40 74.6 13.72 5.4
## 3189 218.7 111 51.0 7.78 8.2
## 3190 246.8 110 60.0 10.32 13.2
## 3191 174.7 151 43.0 7.40 15.8
## 3192 240.0 83 53.0 6.71 9.3
## 3193 181.2 76 59.5 8.88 5.0
## 3194 113.7 67 34.0 8.26 10.8
## 3195 174.7 86 80.2 8.03 13.4
## 3196 211.1 89 81.2 11.18 9.7
## 3197 169.3 108 44.0 8.93 12.2
## 3198 247.4 107 58.0 8.80 11.3
## 3199 131.2 63 76.6 11.37 12.8
## 3200 161.4 84 44.3 8.18 11.8
## 3201 107.2 98 26.0 4.34 9.7
## 3202 211.9 120 77.8 10.15 8.8
## 3203 160.4 120 52.0 14.30 6.9
## 3204 230.7 101 79.3 12.84 6.4
## 3205 232.6 96 64.3 12.67 10.5
## 3206 294.7 90 76.0 14.73 10.8
## 3207 133.4 107 42.0 11.20 10.2
## 3208 306.2 123 100.6 9.49 11.7
## 3209 236.8 135 57.0 9.32 10.4
## 3210 125.7 92 83.3 13.80 14.2
## 3211 168.4 114 56.2 13.80 11.4
## 3212 70.9 134 27.8 6.73 12.0
## 3213 105.0 86 39.0 6.09 3.7
## 3214 152.1 141 46.9 10.78 12.0
## 3215 180.9 79 50.7 9.75 8.8
## 3216 156.6 84 66.4 8.08 9.4
## 3217 180.5 85 56.5 11.21 2.4
## 3218 238.8 100 96.6 11.50 13.2
## 3219 182.1 66 86.2 10.68 13.4
## 3220 139.6 72 76.8 16.64 8.8
## 3221 200.3 76 83.5 12.68 10.2
## 3222 153.5 94 51.1 12.59 8.5
## 3223 128.2 119 68.6 8.59 11.7
## 3224 159.5 145 45.0 10.12 16.7
## 3225 226.4 101 63.0 13.84 12.3
## 3226 251.9 81 60.0 9.73 8.4
## 3227 264.5 117 64.0 9.70 7.5
## 3228 153.7 105 43.0 9.43 10.7
## 3229 232.1 81 58.0 10.54 15.0
## 3230 201.9 86 55.2 10.62 7.8
## 3231 186.9 79 48.0 9.13 4.2
## 3232 196.6 89 66.8 9.03 6.6
## 3233 232.1 102 54.0 8.41 9.9
## 3234 166.0 79 35.0 3.73 6.3
## 3235 200.6 96 55.8 8.21 2.5
## 3236 141.0 101 55.2 10.60 4.9
## 3237 245.0 95 81.3 10.85 7.5
## 3238 140.8 140 44.0 11.43 10.9
## 3239 255.1 93 67.0 13.35 8.8
## 3240 125.0 99 69.5 11.77 10.2
## 3241 180.6 65 55.0 14.02 5.0
## 3242 248.7 118 57.0 8.62 11.3
## 3243 178.1 111 73.7 11.84 8.4
## 3244 122.2 112 32.0 6.59 10.3
## 3245 231.3 87 59.0 11.24 7.2
## 3246 111.2 101 30.0 6.11 12.6
## 3247 103.2 117 70.1 11.82 11.9
## 3248 138.4 104 38.0 7.95 3.9
## 3249 146.3 85 44.0 10.83 11.5
## 3250 206.3 66 56.0 12.06 11.7
## 3251 132.0 103 47.0 13.98 13.5
## 3252 274.6 105 61.0 8.06 9.2
## 3253 185.3 87 51.0 11.27 11.7
## 3254 154.8 69 66.3 8.86 9.0
## 3255 179.2 105 94.7 14.16 14.7
## 3256 286.2 61 65.0 9.36 11.0
## 3257 268.0 115 61.3 7.68 17.0
## 3258 137.5 110 44.1 9.91 13.3
## 3259 243.0 115 60.9 9.59 13.4
## 3260 134.9 79 45.5 11.08 15.0
## 3261 234.2 76 61.0 10.84 13.9
## 3262 175.1 73 45.0 8.60 7.3
## 3263 142.2 107 47.0 13.12 10.1
## 3264 132.4 81 42.6 10.02 6.0
## 3265 97.8 98 50.9 10.36 5.9
## 3266 266.9 83 65.0 11.49 11.0
## 3267 155.2 139 76.2 13.42 9.7
## 3268 200.2 92 55.0 12.25 8.8
## 3269 289.1 100 70.0 11.69 12.7
## 3270 198.4 121 55.0 12.48 10.5
## 3271 180.3 67 49.0 10.40 12.8
## 3272 86.3 84 35.0 11.94 12.5
## 3273 295.0 141 70.0 11.18 12.9
## 3274 240.9 108 58.8 8.37 14.7
## 3275 207.7 109 54.0 10.88 8.0
## 3276 128.5 115 36.0 8.19 0.0
## 3277 224.4 114 74.8 7.30 8.8
## 3278 164.9 115 39.0 6.33 10.0
## 3279 238.0 97 55.0 8.23 10.6
## 3280 231.0 85 81.4 11.12 8.3
## 3281 107.3 140 39.0 11.91 10.0
## 3282 185.0 122 47.0 9.13 5.1
## 3283 244.1 71 79.8 10.17 7.7
## 3284 238.4 96 62.0 12.33 12.4
## 3285 141.1 109 79.6 11.24 13.2
## 3286 158.1 117 37.0 5.76 11.8
## 3287 220.1 105 92.4 11.11 13.1
## 3288 199.5 119 75.4 6.75 10.9
## 3289 109.5 105 44.7 14.31 4.9
## 3290 187.2 110 42.0 5.74 13.2
## 3291 107.9 128 35.0 9.35 0.0
## 3292 172.1 119 86.5 11.18 13.9
## 3293 203.8 85 44.2 4.39 11.7
## 3294 160.0 133 46.0 10.77 9.1
## 3295 51.1 106 27.0 10.43 12.3
## 3296 227.7 88 54.0 8.50 11.7
## 3297 203.8 77 53.0 10.26 9.0
## 3298 241.7 84 86.5 8.29 11.3
## 3299 78.1 70 34.0 11.97 12.3
## 3300 187.8 95 45.0 7.46 11.0
## 3301 127.1 94 61.2 11.42 7.1
## 3302 280.0 113 65.0 10.11 10.4
## 3303 153.2 78 46.9 10.54 7.8
## 3304 137.1 88 68.1 7.79 11.5
## 3305 186.1 114 49.0 9.93 13.8
## 3306 224.1 127 90.1 11.94 11.5
## 3307 83.6 131 53.9 10.20 8.1
## 3308 203.9 109 55.0 11.70 17.8
## 3309 211.3 87 50.0 8.29 13.3
## 3310 219.4 112 57.0 11.29 12.0
## 3311 190.4 91 43.1 4.60 13.6
## 3312 147.7 94 50.0 14.17 6.9
## 3313 229.9 130 54.6 7.22 14.2
## 3314 102.8 128 30.0 7.19 10.0
## 3315 178.7 81 53.9 11.69 9.1
## 3316 148.5 106 52.6 5.73 6.5
## 3317 164.1 111 80.2 10.96 12.3
## 3318 197.2 90 50.0 9.43 7.8
## 3319 124.9 131 50.4 15.03 11.6
## 3320 115.4 99 40.5 10.50 15.9
## 3321 140.0 101 44.0 9.82 9.7
## 3322 193.9 118 41.0 4.25 13.2
## 3323 321.1 105 78.0 13.28 11.5
## 3324 118.4 126 45.9 12.47 13.6
## 3325 169.8 114 46.0 9.89 11.6
## 3326 193.4 99 45.3 5.85 9.3
## 3327 106.6 128 46.6 14.24 14.9
## 3328 134.7 98 40.0 9.49 11.8
## 3329 156.2 77 71.7 10.78 9.9
## 3330 231.1 57 56.4 7.67 9.6
## 3331 180.8 109 56.0 14.44 14.1
## 3332 213.8 105 50.0 7.98 5.0
## 3333 234.4 113 100.0 13.30 13.7head(data2)## Churn AccountWeeks ContractRenewal DataPlan DataUsage CustServCalls DayMins
## 1 0 128 1 1 2.7 1 265.1
## 2 0 107 1 1 3.7 1 161.6
## 3 0 137 1 0 0.0 0 243.4
## 4 0 84 0 0 0.0 2 299.4
## 5 0 75 0 0 0.0 3 166.7
## 6 0 118 0 0 0.0 0 223.4
## DayCalls MonthlyCharge OverageFee RoamMins
## 1 110 89 9.87 10.0
## 2 123 82 9.78 13.7
## 3 114 52 6.06 12.2
## 4 71 57 3.10 6.6
## 5 113 41 7.42 10.1
## 6 98 57 11.03 6.3HIPOTESIS
H0 ; Rata-rata contact renewal dan data plan yang dilakukan customer dari faktor 1 (AccountWeeks & OverageFee) dengan faktor 2 (DayMins) sama, dan tidak ada interaksi antar faktor
H1 ; Setidaknya terdapat satu perbedaan rata-rata antara contact renewal dengan data plan, dan terdapat interaksi antar faktor
ASUMSI KENORMALAN
Uji Normalitas Univariat dengan Uji Shapiro-Wilks dan Uji Normalitas Multivariat dengan MardiaDB Test
dengan hipotesis :
H0 : Galat data berdistribusi normal
H1 : Galat data tidak berdistribusi normal
Tolak H0 jika p-value < α. Terima dalam hal lainnya.
x1 <- data2[,2]
x2 <- data2[,7]
x3 <- data2[,10]
data2_fix <- data.frame(x1=x1, x2=x2, x3=x3)
head(data2_fix)## x1 x2 x3
## 1 128 265.1 9.87
## 2 107 161.6 9.78
## 3 137 243.4 6.06
## 4 84 299.4 3.10
## 5 75 166.7 7.42
## 6 118 223.4 11.03library(MVN)
test = mvn(data2_fix, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 8.52476566981408 0.577718086276414 YES
## 2 Mardia Kurtosis -0.808275176317635 0.418932189423078 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk x1 0.9983 0.0012 NO
## 2 Shapiro-Wilk x2 0.9995 0.6401 YES
## 3 Shapiro-Wilk x3 0.9996 0.7100 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## x1 3333 101.06481 39.822106 101.00 1 243.00 74.00 127.00 0.09651936
## x2 3333 179.77510 54.467389 179.40 0 350.80 143.70 216.40 -0.02905090
## x3 3333 10.05149 2.535712 10.07 0 18.19 8.33 11.77 -0.02382388
## Kurtosis
## x1 -0.11120815
## x2 -0.02349700
## x3 0.02204686
Didapatkan bahwa variabel x2 dan x3 memenuhi asumsi normal secara univariat sedangkan x1 tidak memenuhi asumsi normal secara univariat, dan data secara simultan memenuhi asumsi normal multivariat dengan p-value 0,5777 (skewness) dan 0,418 (kurtosis) sehingga p-value > α dan H0 diterima. Dengan taraf signifikansi 5%, data dinyatakan normal secara multivariat
ASUMSI HOMOGENITAS
Uji Homogenitas
dengan hipotesis :
H0 : Data homogen
H1 : Data heterogen
Tolak H0 jika p-value < α. Terima dalam hal lainnya.
library(biotools)
# Contract Renewal
head(data2[,3])## [1] 1 1 1 0 0 0boxM(data = data2_fix, grouping = data2$ContractRenewal)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_fix
## Chi-Sq (approx.) = 4.2496, df = 6, p-value = 0.6429# Data Plan
head(data2[,4])## [1] 1 1 0 0 0 0boxM(data = data2_fix, grouping = data2$DataPlan)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_fix
## Chi-Sq (approx.) = 6.9814, df = 6, p-value = 0.3226Didapatkan bahwa dengan taraf signifikansi 5%, p-value (0,3226) > α (0,05) sehingga H0 diterima. Data dinyatakan homogen.
UJI TWO WAY MANOVA
Two Way MANOVA untuk mengetahui signifikansi >1 faktor independen terhadap variabel dependen.
contract <- as.factor(data2$ContractRenewal)
plan <- as.factor(data2$DataPlan)
manova <- manova(cbind(x1, x2, x3) ~ data2$ContractRenewal * data2$DataPlan, data = data2_fix)
summary(manova)## Df Pillai approx F num Df den Df
## data2$ContractRenewal 1 0.0033950 3.7779 3 3327
## data2$DataPlan 1 0.0004717 0.5234 3 3327
## data2$ContractRenewal:data2$DataPlan 1 0.0000923 0.1024 3 3327
## Residuals 3329
## Pr(>F)
## data2$ContractRenewal 0.01013 *
## data2$DataPlan 0.66622
## data2$ContractRenewal:data2$DataPlan 0.95866
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Karena terdapat variabel yang signifikan (*) maka akan dilakukan uji lanjut
UJI LANJUT
Uji lanjut untuk mengetahui mana variabel faktor yang signifikan. Jika p-value < α maka variabel faktor signifikan berpengaruh.
summary.aov(manova)## Response x1 :
## Df Sum Sq Mean Sq F value Pr(>F)
## data2$ContractRenewal 1 3233 3232.7 2.0381 0.1535
## data2$DataPlan 1 41 40.5 0.0256 0.8730
## data2$ContractRenewal:data2$DataPlan 1 460 460.3 0.2902 0.5901
## Residuals 3329 5280152 1586.1
##
## Response x2 :
## Df Sum Sq Mean Sq F value Pr(>F)
## data2$ContractRenewal 1 24119 24119.0 8.1425 0.004351 **
## data2$DataPlan 1 39 38.8 0.0131 0.908906
## data2$ContractRenewal:data2$DataPlan 1 7 6.6 0.0022 0.962394
## Residuals 3329 9860868 2962.1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response x3 :
## Df Sum Sq Mean Sq F value Pr(>F)
## data2$ContractRenewal 1 7.8 7.8196 1.2160 0.2702
## data2$DataPlan 1 9.8 9.8217 1.5274 0.2166
## data2$ContractRenewal:data2$DataPlan 1 0.1 0.0920 0.0143 0.9048
## Residuals 3329 21406.5 6.4303KESIMPULAN & INTERPRETASI
Hasil analisis Two Way Manova menunjukkan p-value (0,01013) < α (0,05) untuk kontrak renewal sehingga H0 ditolak dan p-value (0,66622) > α (0,05) untuk data plan sehingga H0 diterima. Dengan taraf signifikansi 5% dapat dinyatakan setidaknya terdapat satu variabel yang signifikan sehingga perlu dilakukan uji lanjut.
Dari hasil uji lanjut, didapatkan bahwa x2 (DayMins) signifikan terhadap variabel contract renewal.