Penerapan Analisis Regresi dan Asumsi-Asumsi : Menentukan Model Persamaan Regresi untuk Diabetes Mellitus Berdasarkan Faktor Tekanan Darah dan Kadar Insulin
Rafelyno Mulfazal Ardana - 225090501111004
01 Juni 2024
1 PENDAHULUAN
1.1 Latar Belakang
Diabetes mellitus adalah salah satu penyakit metabolik kronis yang ditandai dengan kadar glukosa darah yang tinggi akibat gangguan pada sekresi insulin, kerja insulin, atau keduanya. Kondisi ini telah menjadi masalah kesehatan global yang signifikan, mempengaruhi jutaan orang di seluruh dunia. Peningkatan prevalensi diabetes, baik tipe 1 maupun tipe 2, telah menimbulkan kekhawatiran di kalangan ahli kesehatan dan pemerintah karena dampaknya terhadap kualitas hidup individu yang terkena serta beban ekonomi yang dihasilkan dari biaya pengobatan dan komplikasi terkait.
Diabetes mellitus dapat diklasifikasikan menjadi beberapa tipe, dengan yang paling umum adalah diabetes tipe 1 dan tipe 2. Diabetes tipe 1 biasanya disebabkan oleh autoimun yang mengakibatkan kerusakan sel-sel beta pankreas yang memproduksi insulin, sehingga tubuh tidak mampu memproduksi insulin secara cukup. Di sisi lain, diabetes tipe 2 lebih sering diakibatkan oleh resistensi insulin, di mana tubuh tidak dapat menggunakan insulin secara efektif.
Analisis regresi adalah salah satu teknik statistik yang paling umum dan penting dalam penelitian kuantitatif, yang digunakan untuk memahami dan memodelkan hubungan antara satu atau lebih variabel independen (prediktor) dan variabel dependen (respon). Dengan analisis tersebut, kita dapat menentukan hubungan antara beberapa faktor yang mempengaruhi Diabetes Mellitus melalui pemodelan regresi.
2 TINJAUAN PUSTAKA
2.1 Statistika Deskriptif
tatistika deskriptif adalah cabang dari statistika yang digunakan untuk meringkas dan menggambarkan data. Alat-alat yang sering digunakan dalam statistika deskriptif meliputi tabel, grafik, dan ukuran-ukuran numerik seperti rata-rata, median, modus, varians, dan standar deviasi. Tujuan utama dari statistika deskriptif adalah memberikan gambaran yang jelas tentang karakteristik utama dari kumpulan data.
- Ukuran Pemusatan:
Rata-rata (Mean): Menunjukkan nilai rata-rata dari data. Median: Nilai tengah dari data yang telah diurutkan. Modus: Nilai yang paling sering muncul dalam data.
- Ukuran Dispersi:
Range (Jangkauan): Selisih antara nilai maksimum dan minimum. Varians: Rata-rata kuadrat dari deviasi setiap nilai data terhadap rata-rata. Standar Deviasi: Akar kuadrat dari varians, memberikan gambaran tentang penyebaran data di sekitar rata-rata.
- Visualisasi Data:
Histogram: Grafik yang menunjukkan distribusi frekuensi dari data. Boxplot: Menampilkan median, kuartil, dan potensi outlier dalam data.
2.2 Analisis Regresi
Analisis regresi adalah metode statistik yang digunakan untuk memodelkan hubungan antara satu atau lebih variabel independen (prediktor) dan variabel dependen (respon). Analisis ini membantu dalam memahami bagaimana variabel-variabel tersebut saling terkait dan memungkinkan untuk membuat prediksi.
- Regresi Linear Sederhana:
Model : \[ Y = \beta0 + \beta1 X + \epsilon \]
- Regresi Linear Berganda
Model : \[ Y = \beta0 + \beta1X1 + \beta2X2 + ... + \beta(p)X(p) + \epsilon \]
- Regresi Non-linear
Model yang digunakan untuk data yang tidak sesuai dengan asumsi linearitas. Model bisa berbentuk kuadratik, eksponensial, logaritmik, atau lainnya, tergantung pada pola data.
2.3 Asumsi
2.3.1 Asumsi Normalitas
Asumsi normalitas adalah salah satu asumsi penting dalam analisis regresi, yang menyatakan bahwa residual (kesalahan prediksi) dari model regresi harus berdistribusi normal. Asumsi ini penting karena sebagian besar metode inferensial dalam analisis regresi memerlukan normalitas residual untuk memberikan hasil yang valid.
2.3.2 Asumsi Homoskedastisitas
Asumsi homoskedastisitas dalam analisis regresi menyatakan bahwa varians dari residual, yang merupakan selisih antara nilai aktual dan nilai yang diprediksi oleh model, harus tetap konstan di semua tingkat nilai variabel independen. Dengan kata lain, tidak boleh terdapat pola yang teratur dalam variasi residual seiring dengan perubahan nilai variabel independen (Sulistyorini & Wijayanto, 2019).
Jika terjadi pelanggaran terhadap asumsi homoskedastisitas, yang disebut heteroskedastisitas, maka hasil regresi dapat menjadi tidak konsisten dan tidak dapat diandalkan. Heteroskedastisitas dapat menghasilkan estimasi koefisien yang efisien dan tidak akurat, serta mengganggu pengujian statistik dan interval kepercayaan.
Untuk menguji asumsi homoskedastisitas, digunakan berbagai metode statistik seperti uji White, uji Glejser, atau uji Breusch-Pagan. Jika hasil pengujian menunjukkan adanya heteroskedastisitas, langkah-langkah perbaikan yang mungkin dilakukan termasuk transformasi variabel, penggunaan metode regresi yang lebih sesuai (seperti regresi heteroskedastik), atau penggunaan metode estimasi robust yang mengabaikan asumsi homoskedastisitas.
2.3.3 Asumsi Kolinearitas
Asumsi Kolinearitas adalah kondisi di mana dua atau lebih variabel independen dalam sebuah model regresi memiliki hubungan linear yang tinggi. Kolinearitas yang parah dapat menyebabkan masalah dalam interpretasi model regresi, karena sulit untuk menentukan efek individu dari setiap variabel independen terhadap variabel dependen.
2.4 Data
Data yang digunakan pada laporan ini ialah data sekunder. Data diambil dari https://www.kaggle.com/datasets/vikasukani/diabetes-data-set
3 SOURCE CODE
3.1 Library
3.2 Data
3.3 Plot
3.3.1 Box Plot
> par(mfrow=c(1,2))
> boxplot(diabetes_dataset$`BloodPressure`, main="Gambar 2.1. Boxplot Tekanan Darah",sub=paste("Outlier rows: ", boxplot.stats(diabetes_dataset$`BloodPressure`)$out), col="green4")
> boxplot(diabetes_dataset$`Insulin`, main="Gambar 2.2. Boxplot Kadar Insulin",sub=paste("Outlier rows: ", boxplot.stats(diabetes_dataset$`Insulin`)$out), col="darkgrey")
3.3.2 Scatter Plot
> scatter.smooth(x=diabetes_dataset$`Glucose`,y=diabetes_dataset$`BloodPressure`, main = "Gambar 1. Smooth Scatter Plot Glucose~Tekanan Darah", xlab ="Glucose", ylab ="Blood Pressure", pch=20, col="aquamarine4")
Dari scatter plot tersebut, data menyebar secara acak dan banyak data
yang berada jauh dari rentang garis regresi.
> scatter.smooth(x=diabetes_dataset$`Glucose`,y=diabetes_dataset$`Insulin`, main = "Gambar 2. Smooth Scatter Plot Glucose~Kadar Insulin", xlab ="Glucose", ylab ="Kadar Insulin", pch=20, col="purple3")
Dari scatter plot tersebut, data menyebar secara acak dan banyak data
yang berada jauh dari rentang garis regresi.
4 HASIL DAN PEMBAHASAN
4.1 Analisis Deskriptif
> summary(diabetes_dataset)
Pregnancies Glucose BloodPressure SkinThickness
Min. : 0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 63.50 1st Qu.: 0.00
Median : 3.000 Median :117.0 Median : 72.00 Median : 23.00
Mean : 3.704 Mean :121.2 Mean : 69.15 Mean : 20.93
3rd Qu.: 6.000 3rd Qu.:141.0 3rd Qu.: 80.00 3rd Qu.: 32.00
Max. :17.000 Max. :199.0 Max. :122.00 Max. :110.00
Insulin BMI DiabetesPedigreeFunction Age
Min. : 0.00 Min. : 0.00 Min. :0.0780 Min. :21.00
1st Qu.: 0.00 1st Qu.:27.38 1st Qu.:0.2440 1st Qu.:24.00
Median : 40.00 Median :32.30 Median :0.3760 Median :29.00
Mean : 80.25 Mean :32.19 Mean :0.4709 Mean :33.09
3rd Qu.:130.00 3rd Qu.:36.80 3rd Qu.:0.6240 3rd Qu.:40.00
Max. :744.00 Max. :80.60 Max. :2.4200 Max. :81.00
Outcome
Min. :0.000
1st Qu.:0.000
Median :0.000
Mean :0.342
3rd Qu.:1.000
Max. :1.000 Dari hasil tersebut diketahui bahwa rata-rata kadar glukosa darah pada data penelitian adalah sebesar 121.2 mg/dL
4.2 Analisis Korelasi
Dari hasil tersebut dapat disimpulkan bahwa hubungan antara tekanan darah dengan terjadinya diabetes mellitus sangat rendah yaitu sebesar 0.13804 atau 13.804%
Dari hasil tersebut dapat disimpulkan bahwa hubungan antara kadar insulin dengan terjadinya diabetes mellitus tidak terlalu tinggi yaitu sebesar 0.32037 atau 32.037%
“cor()” adalah fungsi dalam bahasa pemrograman yang digunakan untuk menghitung koefisien korelasi antara dua variabel atau lebih.
4.3 Analisis Regresi
> ### Membentuk Matriks
> X1 <- diabetes_dataset$`BloodPressure`
> X2 <- diabetes_dataset$`Insulin`
> Y <- diabetes_dataset$`Glucose`
> X <- cbind(1, X1, X2)
> X
X1 X2
[1,] 1 62 0
[2,] 1 82 125
[3,] 1 0 0
[4,] 1 68 250
[5,] 1 62 480
[6,] 1 78 265
[7,] 1 72 0
[8,] 1 80 0
[9,] 1 65 66
[10,] 1 90 0
[11,] 1 68 0
[12,] 1 70 122
[13,] 1 0 0
[14,] 1 74 0
[15,] 1 68 0
[16,] 1 72 76
[17,] 1 70 145
[18,] 1 74 193
[19,] 1 90 71
[20,] 1 72 0
[21,] 1 68 0
[22,] 1 64 79
[23,] 1 78 0
[24,] 1 82 0
[25,] 1 90 90
[26,] 1 60 170
[27,] 1 50 76
[28,] 1 78 0
[29,] 1 72 0
[30,] 1 62 210
[31,] 1 68 0
[32,] 1 62 0
[33,] 1 54 86
[34,] 1 70 105
[35,] 1 78 0
[36,] 1 60 192
[37,] 1 76 0
[38,] 1 76 0
[39,] 1 68 0
[40,] 1 72 207
[41,] 1 64 70
[42,] 1 84 0
[43,] 1 92 0
[44,] 1 110 240
[45,] 1 64 0
[46,] 1 66 0
[47,] 1 56 0
[48,] 1 70 0
[49,] 1 66 0
[50,] 1 0 0
[51,] 1 80 82
[52,] 1 50 36
[53,] 1 66 23
[54,] 1 90 300
[55,] 1 66 342
[56,] 1 50 0
[57,] 1 68 304
[58,] 1 88 110
[59,] 1 82 0
[60,] 1 64 142
[61,] 1 0 0
[62,] 1 72 0
[63,] 1 62 0
[64,] 1 58 128
[65,] 1 66 0
[66,] 1 74 0
[67,] 1 88 0
[68,] 1 92 0
[69,] 1 66 38
[70,] 1 85 100
[71,] 1 66 90
[72,] 1 64 140
[73,] 1 90 0
[74,] 1 86 270
[75,] 1 75 0
[76,] 1 48 0
[77,] 1 78 0
[78,] 1 72 0
[79,] 1 0 0
[80,] 1 66 0
[81,] 1 44 0
[82,] 1 0 0
[83,] 1 78 71
[84,] 1 65 0
[85,] 1 108 0
[86,] 1 74 125
[87,] 1 72 0
[88,] 1 68 71
[89,] 1 70 110
[90,] 1 68 0
[91,] 1 55 0
[92,] 1 80 176
[93,] 1 78 48
[94,] 1 72 0
[95,] 1 82 64
[96,] 1 72 228
[97,] 1 62 0
[98,] 1 48 76
[99,] 1 50 64
[100,] 1 90 220
[101,] 1 72 0
[102,] 1 60 0
[103,] 1 96 0
[104,] 1 72 40
[105,] 1 65 0
[106,] 1 56 152
[107,] 1 122 0
[108,] 1 58 140
[109,] 1 58 18
[110,] 1 85 36
[111,] 1 72 135
[112,] 1 62 495
[113,] 1 76 37
[114,] 1 62 0
[115,] 1 54 175
[116,] 1 92 0
[117,] 1 74 0
[118,] 1 48 0
[119,] 1 60 0
[120,] 1 76 51
[121,] 1 76 100
[122,] 1 64 0
[123,] 1 74 100
[124,] 1 80 0
[125,] 1 76 0
[126,] 1 30 99
[127,] 1 70 135
[128,] 1 58 94
[129,] 1 88 145
[130,] 1 84 0
[131,] 1 70 168
[132,] 1 56 0
[133,] 1 64 225
[134,] 1 74 0
[135,] 1 68 49
[136,] 1 60 140
[137,] 1 70 50
[138,] 1 60 92
[139,] 1 80 0
[140,] 1 72 325
[141,] 1 78 0
[142,] 1 82 0
[143,] 1 52 63
[144,] 1 66 0
[145,] 1 62 284
[146,] 1 75 0
[147,] 1 80 0
[148,] 1 64 119
[149,] 1 78 0
[150,] 1 70 0
[151,] 1 74 204
[152,] 1 65 0
[153,] 1 86 155
[154,] 1 82 485
[155,] 1 78 0
[156,] 1 88 0
[157,] 1 52 94
[158,] 1 56 135
[159,] 1 74 53
[160,] 1 72 114
[161,] 1 90 0
[162,] 1 74 105
[163,] 1 80 285
[164,] 1 64 0
[165,] 1 88 0
[166,] 1 74 156
[167,] 1 66 0
[168,] 1 68 0
[169,] 1 66 0
[170,] 1 90 78
[171,] 1 82 0
[172,] 1 70 130
[173,] 1 0 0
[174,] 1 60 48
[175,] 1 64 55
[176,] 1 72 130
[177,] 1 78 0
[178,] 1 110 130
[179,] 1 78 0
[180,] 1 82 0
[181,] 1 80 0
[182,] 1 64 92
[183,] 1 74 23
[184,] 1 60 0
[185,] 1 74 0
[186,] 1 68 0
[187,] 1 68 495
[188,] 1 98 58
[189,] 1 76 114
[190,] 1 80 160
[191,] 1 62 0
[192,] 1 70 94
[193,] 1 66 0
[194,] 1 0 0
[195,] 1 55 0
[196,] 1 84 210
[197,] 1 58 0
[198,] 1 62 48
[199,] 1 64 99
[200,] 1 60 318
[201,] 1 80 0
[202,] 1 82 0
[203,] 1 68 0
[204,] 1 70 44
[205,] 1 72 190
[206,] 1 72 0
[207,] 1 76 280
[208,] 1 104 0
[209,] 1 64 87
[210,] 1 84 0
[211,] 1 60 0
[212,] 1 85 0
[213,] 1 95 0
[214,] 1 65 130
[215,] 1 82 175
[216,] 1 70 271
[217,] 1 62 129
[218,] 1 68 120
[219,] 1 74 0
[220,] 1 66 0
[221,] 1 60 478
[222,] 1 90 0
[223,] 1 0 0
[224,] 1 60 190
[225,] 1 66 56
[226,] 1 78 32
[227,] 1 76 0
[228,] 1 52 0
[229,] 1 70 744
[230,] 1 80 53
[231,] 1 86 0
[232,] 1 80 370
[233,] 1 80 37
[234,] 1 68 0
[235,] 1 68 45
[236,] 1 72 0
[237,] 1 84 192
[238,] 1 90 0
[239,] 1 84 0
[240,] 1 76 0
[241,] 1 64 0
[242,] 1 70 88
[243,] 1 54 0
[244,] 1 50 176
[245,] 1 76 194
[246,] 1 85 0
[247,] 1 68 0
[248,] 1 90 680
[249,] 1 70 402
[250,] 1 86 0
[251,] 1 52 0
[252,] 1 84 0
[253,] 1 80 55
[254,] 1 68 0
[255,] 1 62 258
[256,] 1 64 0
[257,] 1 56 0
[258,] 1 68 0
[259,] 1 50 375
[260,] 1 76 150
[261,] 1 68 130
[262,] 1 0 0
[263,] 1 70 0
[264,] 1 80 0
[265,] 1 62 0
[266,] 1 74 67
[267,] 1 0 0
[268,] 1 64 0
[269,] 1 52 0
[270,] 1 0 0
[271,] 1 86 0
[272,] 1 62 56
[273,] 1 78 0
[274,] 1 78 45
[275,] 1 70 0
[276,] 1 70 57
[277,] 1 60 0
[278,] 1 64 116
[279,] 1 74 0
[280,] 1 62 278
[281,] 1 70 0
[282,] 1 76 122
[283,] 1 88 155
[284,] 1 86 0
[285,] 1 80 0
[286,] 1 74 135
[287,] 1 84 545
[288,] 1 86 220
[289,] 1 56 49
[290,] 1 72 75
[291,] 1 88 40
[292,] 1 62 74
[293,] 1 78 182
[294,] 1 48 194
[295,] 1 50 0
[296,] 1 62 120
[297,] 1 70 360
[298,] 1 84 215
[299,] 1 78 184
[300,] 1 72 0
[301,] 1 0 0
[302,] 1 58 135
[303,] 1 82 42
[304,] 1 98 0
[305,] 1 76 0
[306,] 1 76 105
[307,] 1 68 132
[308,] 1 68 148
[309,] 1 68 180
[310,] 1 68 205
[311,] 1 66 0
[312,] 1 70 148
[313,] 1 74 96
[314,] 1 50 85
[315,] 1 80 0
[316,] 1 68 94
[317,] 1 80 64
[318,] 1 74 0
[319,] 1 66 140
[320,] 1 78 0
[321,] 1 60 231
[322,] 1 74 0
[323,] 1 70 0
[324,] 1 90 29
[325,] 1 75 0
[326,] 1 72 168
[327,] 1 64 156
[328,] 1 70 0
[329,] 1 86 120
[330,] 1 70 68
[331,] 1 72 0
[332,] 1 58 52
[333,] 1 0 0
[334,] 1 80 0
[335,] 1 60 58
[336,] 1 76 255
[337,] 1 0 0
[338,] 1 76 0
[339,] 1 78 171
[340,] 1 84 0
[341,] 1 70 105
[342,] 1 74 73
[343,] 1 68 0
[344,] 1 86 0
[345,] 1 72 0
[346,] 1 88 108
[347,] 1 46 83
[348,] 1 0 0
[349,] 1 62 74
[350,] 1 80 0
[351,] 1 80 0
[352,] 1 84 0
[353,] 1 82 0
[354,] 1 62 43
[355,] 1 78 0
[356,] 1 88 0
[357,] 1 50 167
[358,] 1 0 0
[359,] 1 74 54
[360,] 1 76 249
[361,] 1 64 325
[362,] 1 70 0
[363,] 1 108 0
[364,] 1 78 0
[365,] 1 74 293
[366,] 1 54 83
[367,] 1 72 0
[368,] 1 64 0
[369,] 1 86 66
[370,] 1 102 140
[371,] 1 82 465
[372,] 1 64 89
[373,] 1 64 66
[374,] 1 58 94
[375,] 1 52 158
[376,] 1 82 325
[377,] 1 82 84
[378,] 1 60 75
[379,] 1 75 0
[380,] 1 100 72
[381,] 1 72 82
[382,] 1 68 0
[383,] 1 60 182
[384,] 1 62 59
[385,] 1 70 110
[386,] 1 54 50
[387,] 1 74 0
[388,] 1 100 0
[389,] 1 82 285
[390,] 1 68 81
[391,] 1 66 196
[392,] 1 76 0
[393,] 1 64 415
[394,] 1 72 87
[395,] 1 78 0
[396,] 1 58 275
[397,] 1 56 115
[398,] 1 66 0
[399,] 1 70 0
[400,] 1 70 0
[401,] 1 64 0
[402,] 1 61 0
[403,] 1 84 88
[404,] 1 78 0
[405,] 1 64 0
[406,] 1 48 165
[407,] 1 72 0
[408,] 1 62 0
[409,] 1 74 0
[410,] 1 68 579
[411,] 1 90 0
[412,] 1 72 176
[413,] 1 84 310
[414,] 1 74 61
[415,] 1 60 167
[416,] 1 84 474
[417,] 1 68 0
[418,] 1 82 0
[419,] 1 68 0
[420,] 1 64 115
[421,] 1 88 170
[422,] 1 68 76
[423,] 1 64 78
[424,] 1 64 0
[425,] 1 78 210
[426,] 1 78 277
[427,] 1 0 0
[428,] 1 64 180
[429,] 1 94 145
[430,] 1 82 180
[431,] 1 0 0
[432,] 1 74 85
[433,] 1 74 60
[434,] 1 75 0
[435,] 1 68 0
[436,] 1 0 0
[437,] 1 85 0
[438,] 1 75 0
[439,] 1 70 0
[440,] 1 88 0
[441,] 1 104 0
[442,] 1 66 50
[443,] 1 64 120
[444,] 1 70 0
[445,] 1 62 0
[446,] 1 78 14
[447,] 1 72 70
[448,] 1 80 92
[449,] 1 64 64
[450,] 1 74 63
[451,] 1 64 95
[452,] 1 70 0
[453,] 1 68 210
[454,] 1 0 0
[455,] 1 54 105
[456,] 1 62 0
[457,] 1 54 0
[458,] 1 68 71
[459,] 1 84 237
[460,] 1 74 60
[461,] 1 72 56
[462,] 1 62 0
[463,] 1 70 49
[464,] 1 78 0
[465,] 1 98 0
[466,] 1 56 105
[467,] 1 52 36
[468,] 1 64 100
[469,] 1 0 0
[470,] 1 78 140
[471,] 1 82 0
[472,] 1 70 0
[473,] 1 66 0
[474,] 1 90 0
[475,] 1 64 0
[476,] 1 84 0
[477,] 1 80 191
[478,] 1 76 110
[479,] 1 74 75
[480,] 1 86 0
[481,] 1 70 328
[482,] 1 88 0
[483,] 1 58 49
[484,] 1 82 125
[485,] 1 0 0
[486,] 1 68 250
[487,] 1 62 480
[488,] 1 78 265
[489,] 1 72 0
[490,] 1 80 0
[491,] 1 65 66
[492,] 1 90 0
[493,] 1 68 0
[494,] 1 70 122
[495,] 1 0 0
[496,] 1 74 0
[497,] 1 68 0
[498,] 1 72 76
[499,] 1 70 145
[500,] 1 74 193
[501,] 1 90 71
[502,] 1 72 0
[503,] 1 68 0
[504,] 1 64 79
[505,] 1 78 0
[506,] 1 82 0
[507,] 1 90 90
[508,] 1 60 170
[509,] 1 50 76
[510,] 1 78 0
[511,] 1 72 0
[512,] 1 62 210
[513,] 1 68 0
[514,] 1 62 0
[515,] 1 54 86
[516,] 1 70 105
[517,] 1 88 165
[518,] 1 86 0
[519,] 1 60 0
[520,] 1 90 326
[521,] 1 70 66
[522,] 1 80 130
[523,] 1 0 0
[524,] 1 70 0
[525,] 1 58 0
[526,] 1 60 0
[527,] 1 64 82
[528,] 1 74 105
[529,] 1 66 188
[530,] 1 65 0
[531,] 1 60 106
[532,] 1 76 0
[533,] 1 66 65
[534,] 1 0 0
[535,] 1 56 56
[536,] 1 0 0
[537,] 1 90 0
[538,] 1 60 0
[539,] 1 80 210
[540,] 1 92 155
[541,] 1 74 215
[542,] 1 72 190
[543,] 1 85 0
[544,] 1 90 56
[545,] 1 78 76
[546,] 1 90 225
[547,] 1 76 207
[548,] 1 68 166
[549,] 1 82 67
[550,] 1 110 0
[551,] 1 70 0
[552,] 1 68 106
[553,] 1 88 0
[554,] 1 62 44
[555,] 1 64 115
[556,] 1 70 215
[557,] 1 70 0
[558,] 1 76 0
[559,] 1 68 0
[560,] 1 74 0
[561,] 1 76 0
[562,] 1 66 274
[563,] 1 68 77
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[1416,] 1 68 0
[1417,] 1 50 375
[1418,] 1 76 150
[1419,] 1 68 130
[1420,] 1 0 0
[1421,] 1 70 0
[1422,] 1 80 0
[1423,] 1 62 0
[1424,] 1 74 67
[1425,] 1 0 0
[1426,] 1 64 0
[1427,] 1 52 0
[1428,] 1 0 0
[1429,] 1 86 0
[1430,] 1 62 56
[1431,] 1 78 0
[1432,] 1 78 45
[1433,] 1 70 0
[1434,] 1 70 57
[1435,] 1 60 0
[1436,] 1 64 116
[1437,] 1 74 0
[1438,] 1 62 278
[1439,] 1 70 0
[1440,] 1 76 122
[1441,] 1 88 155
[1442,] 1 86 0
[1443,] 1 80 0
[1444,] 1 74 135
[1445,] 1 84 545
[1446,] 1 86 220
[1447,] 1 56 49
[1448,] 1 72 75
[1449,] 1 88 40
[1450,] 1 62 74
[1451,] 1 78 182
[1452,] 1 48 194
[1453,] 1 50 0
[1454,] 1 62 120
[1455,] 1 70 360
[1456,] 1 84 215
[1457,] 1 78 184
[1458,] 1 70 0
[1459,] 1 70 0
[1460,] 1 64 0
[1461,] 1 61 0
[1462,] 1 84 88
[1463,] 1 78 0
[1464,] 1 64 0
[1465,] 1 48 165
[1466,] 1 72 0
[1467,] 1 62 0
[1468,] 1 74 0
[1469,] 1 68 579
[1470,] 1 90 0
[1471,] 1 72 176
[1472,] 1 84 310
[1473,] 1 74 61
[1474,] 1 60 167
[1475,] 1 84 474
[1476,] 1 68 0
[1477,] 1 82 0
[1478,] 1 68 0
[1479,] 1 64 115
[1480,] 1 88 170
[1481,] 1 68 76
[1482,] 1 64 78
[1483,] 1 64 0
[1484,] 1 78 210
[1485,] 1 78 277
[1486,] 1 0 0
[1487,] 1 64 180
[1488,] 1 94 145
[1489,] 1 82 180
[1490,] 1 0 0
[1491,] 1 74 85
[1492,] 1 74 60
[1493,] 1 75 0
[1494,] 1 68 0
[1495,] 1 0 0
[1496,] 1 85 0
[1497,] 1 75 0
[1498,] 1 70 0
[1499,] 1 88 0
[1500,] 1 104 0
[1501,] 1 66 50
[1502,] 1 64 120
[1503,] 1 70 0
[1504,] 1 62 0
[1505,] 1 78 14
[1506,] 1 72 70
[1507,] 1 80 92
[1508,] 1 64 64
[1509,] 1 74 63
[1510,] 1 64 95
[1511,] 1 70 0
[1512,] 1 68 210
[1513,] 1 0 0
[1514,] 1 54 105
[1515,] 1 62 0
[1516,] 1 54 0
[1517,] 1 68 71
[1518,] 1 84 237
[1519,] 1 74 60
[1520,] 1 72 56
[1521,] 1 62 0
[1522,] 1 70 49
[1523,] 1 78 0
[1524,] 1 98 0
[1525,] 1 56 105
[1526,] 1 52 36
[1527,] 1 64 100
[1528,] 1 0 0
[1529,] 1 78 140
[1530,] 1 82 0
[1531,] 1 70 0
[1532,] 1 66 0
[1533,] 1 90 0
[1534,] 1 64 0
[1535,] 1 84 0
[1536,] 1 80 191
[1537,] 1 76 110
[1538,] 1 74 75
[1539,] 1 86 0
[1540,] 1 70 328
[1541,] 1 88 0
[1542,] 1 58 49
[1543,] 1 82 125
[1544,] 1 0 0
[1545,] 1 68 250
[1546,] 1 62 480
[1547,] 1 78 265
[1548,] 1 72 0
[1549,] 1 80 0
[1550,] 1 65 66
[1551,] 1 90 0
[1552,] 1 68 0
[1553,] 1 70 122
[1554,] 1 0 0
[1555,] 1 74 0
[1556,] 1 68 0
[1557,] 1 72 76
[1558,] 1 70 145
[1559,] 1 74 193
[1560,] 1 74 220
[1561,] 1 84 215
[1562,] 1 64 225
[1563,] 1 94 177
[1564,] 1 66 215
[1565,] 1 62 0
[1566,] 1 40 64
[1567,] 1 84 0
[1568,] 1 44 140
[1569,] 1 0 215
[1570,] 1 78 265
[1571,] 1 72 0
[1572,] 1 80 0
[1573,] 1 65 66
[1574,] 1 90 0
[1575,] 1 68 0
[1576,] 1 70 122
[1577,] 1 0 0
[1578,] 1 74 0
[1579,] 1 68 0
[1580,] 1 72 76
[1581,] 1 70 145
[1582,] 1 74 193
[1583,] 1 74 220
[1584,] 1 84 215
[1585,] 1 64 225
[1586,] 1 94 177
[1587,] 1 66 215
[1588,] 1 62 0
[1589,] 1 40 64
[1590,] 1 84 0
[1591,] 1 44 140
[1592,] 1 0 215
[1593,] 1 84 0
[1594,] 1 70 105
[1595,] 1 74 73
[1596,] 1 68 0
[1597,] 1 86 0
[1598,] 1 72 0
[1599,] 1 88 108
[1600,] 1 46 83
[1601,] 1 0 0
[1602,] 1 62 74
[1603,] 1 80 0
[1604,] 1 80 0
[1605,] 1 84 0
[1606,] 1 82 0
[1607,] 1 62 43
[1608,] 1 78 0
[1609,] 1 88 0
[1610,] 1 50 167
[1611,] 1 0 0
[1612,] 1 74 54
[1613,] 1 76 249
[1614,] 1 64 325
[1615,] 1 70 0
[1616,] 1 108 0
[1617,] 1 78 0
[1618,] 1 74 293
[1619,] 1 54 83
[1620,] 1 72 0
[1621,] 1 64 0
[1622,] 1 86 66
[1623,] 1 102 140
[1624,] 1 82 465
[1625,] 1 64 89
[1626,] 1 64 66
[1627,] 1 58 94
[1628,] 1 52 158
[1629,] 1 82 325
[1630,] 1 82 84
[1631,] 1 60 75
[1632,] 1 75 0
[1633,] 1 100 72
[1634,] 1 72 82
[1635,] 1 68 0
[1636,] 1 60 182
[1637,] 1 62 59
[1638,] 1 70 110
[1639,] 1 54 50
[1640,] 1 74 0
[1641,] 1 100 0
[1642,] 1 82 285
[1643,] 1 68 81
[1644,] 1 66 196
[1645,] 1 76 0
[1646,] 1 64 415
[1647,] 1 72 87
[1648,] 1 78 0
[1649,] 1 58 275
[1650,] 1 56 115
[1651,] 1 66 0
[1652,] 1 70 0
[1653,] 1 70 0
[1654,] 1 64 0
[1655,] 1 61 0
[1656,] 1 84 88
[1657,] 1 78 0
[1658,] 1 64 0
[1659,] 1 48 165
[1660,] 1 72 0
[1661,] 1 62 0
[1662,] 1 74 0
[1663,] 1 68 579
[1664,] 1 90 0
[1665,] 1 72 176
[1666,] 1 84 310
[1667,] 1 74 61
[1668,] 1 60 167
[1669,] 1 84 474
[1670,] 1 68 0
[1671,] 1 82 0
[1672,] 1 68 0
[1673,] 1 64 115
[1674,] 1 88 170
[1675,] 1 68 76
[1676,] 1 64 78
[1677,] 1 64 0
[1678,] 1 78 210
[1679,] 1 78 277
[1680,] 1 0 0
[1681,] 1 64 180
[1682,] 1 94 145
[1683,] 1 82 180
[1684,] 1 0 0
[1685,] 1 74 85
[1686,] 1 74 60
[1687,] 1 74 0
[1688,] 1 38 120
[1689,] 1 88 0
[1690,] 1 0 0
[1691,] 1 74 0
[1692,] 1 78 126
[1693,] 1 0 0
[1694,] 1 60 0
[1695,] 1 78 293
[1696,] 1 62 41
[1697,] 1 82 272
[1698,] 1 62 182
[1699,] 1 54 158
[1700,] 1 58 194
[1701,] 1 88 321
[1702,] 1 80 0
[1703,] 1 74 144
[1704,] 1 72 0
[1705,] 1 96 0
[1706,] 1 62 15
[1707,] 1 82 0
[1708,] 1 0 0
[1709,] 1 86 160
[1710,] 1 76 0
[1711,] 1 94 0
[1712,] 1 70 115
[1713,] 1 64 0
[1714,] 1 88 54
[1715,] 1 68 0
[1716,] 1 78 0
[1717,] 1 80 0
[1718,] 1 65 0
[1719,] 1 64 0
[1720,] 1 78 90
[1721,] 1 60 0
[1722,] 1 82 183
[1723,] 1 62 0
[1724,] 1 72 0
[1725,] 1 74 0
[1726,] 1 76 66
[1727,] 1 76 91
[1728,] 1 74 46
[1729,] 1 86 105
[1730,] 1 70 0
[1731,] 1 80 0
[1732,] 1 0 0
[1733,] 1 72 152
[1734,] 1 74 440
[1735,] 1 74 144
[1736,] 1 50 159
[1737,] 1 84 130
[1738,] 1 60 0
[1739,] 1 54 100
[1740,] 1 60 106
[1741,] 1 74 77
[1742,] 1 54 0
[1743,] 1 70 135
[1744,] 1 52 540
[1745,] 1 58 90
[1746,] 1 80 200
[1747,] 1 106 0
[1748,] 1 82 70
[1749,] 1 84 0
[1750,] 1 76 0
[1751,] 1 106 231
[1752,] 1 80 130
[1753,] 1 60 0
[1754,] 1 80 132
[1755,] 1 82 0
[1756,] 1 70 0
[1757,] 1 58 190
[1758,] 1 78 100
[1759,] 1 68 168
[1760,] 1 58 0
[1761,] 1 106 49
[1762,] 1 100 240
[1763,] 1 82 0
[1764,] 1 70 0
[1765,] 1 86 0
[1766,] 1 60 0
[1767,] 1 52 0
[1768,] 1 58 265
[1769,] 1 56 45
[1770,] 1 76 0
[1771,] 1 64 105
[1772,] 1 80 0
[1773,] 1 82 0
[1774,] 1 74 205
[1775,] 1 64 0
[1776,] 1 50 0
[1777,] 1 74 180
[1778,] 1 82 180
[1779,] 1 80 0
[1780,] 1 114 0
[1781,] 1 70 95
[1782,] 1 68 125
[1783,] 1 60 0
[1784,] 1 90 480
[1785,] 1 74 125
[1786,] 1 0 0
[1787,] 1 88 155
[1788,] 1 70 0
[1789,] 1 76 200
[1790,] 1 78 0
[1791,] 1 88 0
[1792,] 1 0 0
[1793,] 1 76 100
[1794,] 1 80 0
[1795,] 1 0 0
[1796,] 1 46 335
[1797,] 1 78 0
[1798,] 1 64 160
[1799,] 1 64 387
[1800,] 1 78 22
[1801,] 1 62 0
[1802,] 1 58 291
[1803,] 1 74 0
[1804,] 1 50 392
[1805,] 1 78 185
[1806,] 1 72 0
[1807,] 1 60 178
[1808,] 1 76 0
[1809,] 1 86 0
[1810,] 1 66 200
[1811,] 1 68 127
[1812,] 1 86 105
[1813,] 1 94 0
[1814,] 1 78 0
[1815,] 1 78 180
[1816,] 1 84 0
[1817,] 1 88 0
[1818,] 1 52 0
[1819,] 1 78 79
[1820,] 1 86 0
[1821,] 1 88 120
[1822,] 1 56 165
[1823,] 1 75 0
[1824,] 1 60 0
[1825,] 1 86 120
[1826,] 1 72 0
[1827,] 1 60 160
[1828,] 1 74 0
[1829,] 1 80 150
[1830,] 1 44 94
[1831,] 1 58 116
[1832,] 1 94 0
[1833,] 1 88 140
[1834,] 1 84 105
[1835,] 1 94 0
[1836,] 1 74 57
[1837,] 1 70 200
[1838,] 1 62 0
[1839,] 1 70 0
[1840,] 1 78 74
[1841,] 1 62 0
[1842,] 1 88 510
[1843,] 1 78 0
[1844,] 1 88 110
[1845,] 1 90 0
[1846,] 1 72 0
[1847,] 1 76 0
[1848,] 1 92 0
[1849,] 1 58 16
[1850,] 1 74 0
[1851,] 1 62 0
[1852,] 1 76 180
[1853,] 1 70 0
[1854,] 1 72 112
[1855,] 1 60 0
[1856,] 1 78 0
[1857,] 1 60 192
[1858,] 1 76 0
[1859,] 1 76 0
[1860,] 1 68 0
[1861,] 1 72 207
[1862,] 1 64 70
[1863,] 1 84 0
[1864,] 1 92 0
[1865,] 1 110 240
[1866,] 1 64 0
[1867,] 1 66 0
[1868,] 1 56 0
[1869,] 1 70 0
[1870,] 1 66 0
[1871,] 1 0 0
[1872,] 1 80 82
[1873,] 1 50 36
[1874,] 1 66 23
[1875,] 1 90 300
[1876,] 1 66 342
[1877,] 1 50 0
[1878,] 1 68 304
[1879,] 1 88 110
[1880,] 1 82 0
[1881,] 1 64 142
[1882,] 1 0 0
[1883,] 1 72 0
[1884,] 1 62 0
[1885,] 1 58 128
[1886,] 1 66 0
[1887,] 1 74 0
[1888,] 1 88 0
[1889,] 1 92 0
[1890,] 1 66 38
[1891,] 1 85 100
[1892,] 1 66 90
[1893,] 1 64 140
[1894,] 1 90 0
[1895,] 1 86 270
[1896,] 1 75 0
[1897,] 1 48 0
[1898,] 1 78 0
[1899,] 1 72 0
[1900,] 1 0 0
[1901,] 1 66 0
[1902,] 1 44 0
[1903,] 1 0 0
[1904,] 1 78 71
[1905,] 1 65 0
[1906,] 1 108 0
[1907,] 1 74 125
[1908,] 1 72 0
[1909,] 1 68 71
[1910,] 1 70 110
[1911,] 1 68 0
[1912,] 1 55 0
[1913,] 1 80 176
[1914,] 1 78 48
[1915,] 1 72 0
[1916,] 1 82 64
[1917,] 1 72 228
[1918,] 1 62 0
[1919,] 1 48 76
[1920,] 1 50 64
[1921,] 1 90 220
[1922,] 1 72 0
[1923,] 1 60 0
[1924,] 1 96 0
[1925,] 1 72 40
[1926,] 1 65 0
[1927,] 1 56 152
[1928,] 1 122 0
[1929,] 1 58 140
[1930,] 1 58 18
[1931,] 1 85 36
[1932,] 1 72 135
[1933,] 1 62 495
[1934,] 1 76 37
[1935,] 1 62 0
[1936,] 1 54 175
[1937,] 1 92 0
[1938,] 1 74 0
[1939,] 1 48 0
[1940,] 1 60 0
[1941,] 1 76 51
[1942,] 1 76 100
[1943,] 1 64 0
[1944,] 1 74 100
[1945,] 1 80 0
[1946,] 1 76 0
[1947,] 1 30 99
[1948,] 1 70 135
[1949,] 1 58 94
[1950,] 1 88 145
[1951,] 1 84 0
[1952,] 1 70 168
[1953,] 1 56 0
[1954,] 1 64 225
[1955,] 1 74 0
[1956,] 1 68 49
[1957,] 1 60 140
[1958,] 1 70 50
[1959,] 1 60 92
[1960,] 1 80 0
[1961,] 1 72 325
[1962,] 1 78 0
[1963,] 1 82 0
[1964,] 1 52 63
[1965,] 1 66 0
[1966,] 1 62 284
[1967,] 1 75 0
[1968,] 1 80 0
[1969,] 1 64 119
[1970,] 1 78 0
[1971,] 1 70 0
[1972,] 1 74 204
[1973,] 1 65 0
[1974,] 1 86 155
[1975,] 1 82 485
[1976,] 1 78 0
[1977,] 1 88 0
[1978,] 1 52 94
[1979,] 1 56 135
[1980,] 1 74 53
[1981,] 1 72 114
[1982,] 1 90 0
[1983,] 1 74 105
[1984,] 1 80 285
[1985,] 1 64 0
[1986,] 1 88 0
[1987,] 1 74 156
[1988,] 1 66 0
[1989,] 1 68 0
[1990,] 1 66 0
[1991,] 1 90 78
[1992,] 1 82 0
[1993,] 1 70 130
[1994,] 1 0 0
[1995,] 1 60 48
[1996,] 1 64 55
[1997,] 1 72 130
[1998,] 1 78 0
[1999,] 1 110 130
[2000,] 1 72 76>
> ### Penduga Koefisien
> beta_duga <- (solve(t(X)%*%X))%*%(t(X)%*%Y)
> beta_duga
[,1]
101.17570544
X1 0.18533504
X2 0.08961186atau dapat menggunakan cara lain yaitu :
> model_regresi <- lm(Y~X1 +X2)
> model_regresi
Call:
lm(formula = Y ~ X1 + X2)
Coefficients:
(Intercept) X1 X2
101.17571 0.18534 0.08961 Dari model regresi tersebut, dapat disimpulkan bahwa antara tekanan darah dan kadar insulin memiliki hubungan yang linear dan searah. Setiap terjadinya kenaikan 1 satuan untuk tekanan darah, maka kemungkinan terjadinya diabetes akan bertambah sebanyak 0.18534 dan ketika bertambah 1 satuan kadar insulin juga akan meningkatkan kemungkinan diabetes sebesar 0.08961.
Maka persamaan regresi yang diperoleh adalah : \[ Y = \beta0 + \beta1X1 + \beta2X2 + \epsilon \] \[ Y = 101.17571 + 0.18534X1 + 0.08961X2 + \epsilon \]
> # Uji F
> JKT <- sum((Y - mean(Y))^2)
> JKR <- sum((predict(model_regresi) - mean(Y))^2)
> JKG <- JKT - JKR
> dbR <- 2
> dbG <- length(Y) - dbR - 1
> F <- (JKR / dbR) / (JKG / dbG)
> # Menghitung nilai p
> p_value <- pf(F, df1 = dbR, df2 = dbG, lower.tail = FALSE)
>
> # Menampilkan hasil
> cat("Nilai F:", F, "\n")
Nilai F: 129.5464 Karena pvalue < alpha, maka dapat disimpulkan bahwa setidaknya satu variabel independen dalam model regresi secara signifikan mempengaruhi variabel dependen.
4.4 Analisis Asumsi
> # Uji normalitas
> shapiro.test(model_regresi$residuals)
Shapiro-Wilk normality test
data: model_regresi$residuals
W = 0.9676, p-value < 2.2e-16Karena pvalue < alpha, maka dapat disimpulkan bahwa residual tidak berdistribusi normal. Ini menunjukkan pelanggaran asumsi normalitas.
> # Uji homoskedastisitas
> library(lmtest)
> bptest(model_regresi)
studentized Breusch-Pagan test
data: model_regresi
BP = 31.241, df = 2, p-value = 1.644e-07Karena pvalue < alpha, maka dapat disimpulkan bahwa ada heteroskedastisitas, yang berarti variasi residual tidak konstan dan melanggar asumsi homoskedastisitas.
Dikarenakan nilai VIF < 5 maka dapat disimpulkan bahwa tidak terdapat kolinearitas yang signifikan.
5 KESIMPULAN
Dari data yang diperoleh dapat disimpulkan bahwa tekanan darah dan kadar insulin mempengaruhi kemungkinan terjadinya diabetes mellitus dengan hubungan yang searah. Pada data tersebut terjadi pelanggaran asumsi yaitu asumsi normalitas, homoskedastisitas, dan kolinearitas.
6 DAFTAR PUSTAKA
Rahman, M. S., & Kusumawati, I. (2019). Analisis Korelasi Serial (Autokorelasi) Pada Data Time Series Harga Saham. Jurnal Ilmu Komputer Dan Informatika, 12(1), 9-18. Sholikhah, A. (2016) STATISTIK DESKRIPTIF DALAM PENELITIAN KUALITATIF. KOMUNIKA, Vol. 10, No. 2 hal. 324-362
Sulistyorini, E., & Wijayanto, H. (2019). Analisis Heteroskedastisitas pada Model Regresi Data Panel dengan Uji White. Jurnal Ekonomi Pembangunan, 20(2), 152-163.