Nama: Yenaprilia
NIM: 201532290
HAL 221
Soal 1
Lakukan prediksi TRI dengan variabel independen IMT, Umur dan Umur Kuadrat.
- Lakukan analisa regresi masing-masing independen variabel
- Hitung SS for Regression
- Hitung SS for Residual
- Hitung Means SS for Regression
- Hitung Means SS for Residual
- Hitung nilai F parsial
- Hitung nilai r2
- Buktikan penambahan berperan dalam memprediksi Y
TRI | IMT | UM |
135 | 28 | 45 |
101 | 37 | 52 |
57 | 37 | 60 |
56 | 46 | 64 |
113 | 41 | 64 |
42 | 30 | 50 |
84 | 32 | 57 |
186 | 33 | 53 |
164 | 30 | 48 |
205 | 38 | 63 |
230 | 32 | 41 |
146 | 29 | 54 |
160 | 36 | 48 |
186 | 39 | 59 |
138 | 36 | 56 |
160 | 34 | 49 |
142 | 34 | 56 |
153 | 32 | 50 |
139 | 28 | 43 |
170 | 41 | 63 |
136 | 31 | 49 |
139 | 28 | 47 |
124 | 23 | 44 |
138 | 40 | 51 |
150 | 35 | 54 |
142 | 30 | 46 |
145 | 37 | 58 |
149 | 33 | 54 |
128 | 29 | 43 |
155 | 39 | 62 |
MODEL 1 : TRI = β0 + β1 IMT
Variables Entered/Removedb | |||||||
Model | Variables Entered | Variables Removed | Method | ||||
1 | Indeks Massa Tubuha | . | Enter | ||||
a. All requested variables entered. | |||||||
b. Dependent Variable: Trigliserida | |||||||
Model Summary | |||||||
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | |||
1 | .057a | .003 | -.032 | 41.696 | |||
a. Predictors: (Constant), Indeks Massa Tubuh | |||||||
ANOVAb | ||||||||||||
Model | Sum of Squares | Df | Mean Square | F | Sig. | |||||||
1 | Regression | 160.067 | 1 | 160.067 | .092 | .764a | ||||||
Residual | 48678.633 | 28 | 1738.523 | |||||||||
Total | 48838.700 | 29 | ||||||||||
a. Predictors: (Constant), Indeks Massa Tubuh | ||||||||||||
b. Dependent Variable: Trigliserida | ||||||||||||
Coefficientsa | ||||||||||||
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||||||||
B | Std. Error | Beta | ||||||||||
1 | (Constant) | 154.991 | 52.922 | 2.929 | .007 | |||||||
Indeks Massa Tubuh | -.468 | 1.543 | -.057 | -.303 | .764 | |||||||
a. Dependent Variable: Trigliserida | ||||||||||||
MODEL 2 : TRI = β0 + β1 UM
Variables Entered/Removedb | |||||||||||||||||||
Model | Variables Entered | Variables Removed | Method | ||||||||||||||||
1 | Umura | . | Enter | ||||||||||||||||
a. All requested variables entered. | |||||||||||||||||||
b. Dependent Variable: Trigliserida | |||||||||||||||||||
Model Summary | |||||||||||||||||||
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | |||||||||||||||
1 | .170a | .029 | -.006 | 41.154 | |||||||||||||||
a. Predictors: (Constant), Umur | |||||||||||||||||||
ANOVAb | |||||||||||||||||||
Model | Sum of Squares | Df | Mean Square | F | Sig. | ||||||||||||||
1 | Regression | 1416.088 | 1 | 1416.088 | .836 | .368a | |||||||||||||
Residual | 47422.612 | 28 | 1693.665 | ||||||||||||||||
Total | 48838.700 | 29 | |||||||||||||||||
a. Predictors: (Constant), Umur | |||||||||||||||||||
b. Dependent Variable: Trigliserida | |||||||||||||||||||
Coefficientsa | |||||||||||||||||||
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | |||||||||||||||
B | Std. Error | Beta | |||||||||||||||||
1 | (Constant) | 193.196 | 59.636 | 3.240 | .003 | ||||||||||||||
Umur | -1.025 | 1.121 | -.170 | -.914 | .368 | ||||||||||||||
a. Dependent Variable: Trigliserida | |||||||||||||||||||
MODEL 3 : TRI = β0 + β1 UMKWT
Variables Entered/Removedb | ||||||||||||||||||
Model | Variables Entered | Variables Removed | Method | |||||||||||||||
1 | Umur Kuadrata | . | Enter | |||||||||||||||
a. All requested variables entered. | ||||||||||||||||||
b. Dependent Variable: Trigliserida | ||||||||||||||||||
Model Summary | ||||||||||||||||||
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | ||||||||||||||
1 | .162a | .026 | -.008 | 41.210 | ||||||||||||||
a. Predictors: (Constant), Umur Kuadrat | ||||||||||||||||||
ANOVAb | ||||||||||||||||||
Model | Sum of Squares | Df | Mean Square | F | Sig. | |||||||||||||
1 | Regression | 1287.955 | 1 | 1287.955 | .758 | .391a | ||||||||||||
Residual | 47550.745 | 28 | 1698.241 | |||||||||||||||
Total | 48838.700 | 29 | ||||||||||||||||
a. Predictors: (Constant), Umur Kuadrat | ||||||||||||||||||
b. Dependent Variable: Trigliserida | ||||||||||||||||||
Coefficientsa | ||||||||||||||||||
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||||||||||||||
B | Std. Error | Beta | ||||||||||||||||
1 | (Constant) | 165.049 | 30.732 | 5.371 | .000 | |||||||||||||
Umur Kuadrat | -.009 | .011 | -.162 | -.871 | .391 | |||||||||||||
a. Dependent Variable: Trigliserida | ||||||||||||||||||
MODEL 4 : TRI = β0 + β1 IMT + β2 UM
Variables Entered/Removedb | |||||||||||||||||||
Model | Variables Entered | Variables Removed | Method | ||||||||||||||||
1 | Umur, Indeks Massa Tubuha | . | Enter | ||||||||||||||||
a. All requested variables entered. | |||||||||||||||||||
b. Dependent Variable: Trigliserida | |||||||||||||||||||
Model Summary | |||||||||||||||||||
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | |||||||||||||||
1 |
.215a |
.046 |
-.024 |
41.536 |
|||||||||||||||
a. Predictors: (Constant), Umur, Indeks Massa Tubuh |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
2256.283 |
2 |
1128.141 |
.654 |
.528a |
|||||||||||||
Residual |
46582.417 |
27 |
1725.275 |
||||||||||||||||
Total |
48838.700 |
29 |
|||||||||||||||||
a. Predictors: (Constant), Umur, Indeks Massa Tubuh |
|||||||||||||||||||
b. Dependent Variable: Trigliserida |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
T |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
188.027 |
60.643 |
3.101 |
.004 |
||||||||||||||
Indeks Massa Tubuh |
1.785 |
2.558 |
.218 |
.698 |
.491 |
||||||||||||||
Umur |
-2.075 |
1.883 |
-.345 |
-1.102 |
.280 |
||||||||||||||
a. Dependent Variable: Trigliserida |
|||||||||||||||||||
MODEL 5 : TRI = β0 + β1 IMT + β2 UMKWT
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Umur Kuadrat, Indeks Massa Tubuha |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Trigliserida |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.204a |
.042 |
-.029 |
41.634 |
|||||||||||||||
a. Predictors: (Constant), Umur Kuadrat, Indeks Massa Tubuh |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
2036.327 |
2 |
1018.163 |
.587 |
.563a |
|||||||||||||
Residual |
46802.373 |
27 |
1733.421 |
||||||||||||||||
Total |
48838.700 |
29 |
|||||||||||||||||
a. Predictors: (Constant), Umur Kuadrat, Indeks Massa Tubuh |
|||||||||||||||||||
b. Dependent Variable: Trigliserida |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
T |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
133.975 |
56.573 |
2.368 |
.025 |
||||||||||||||
Indeks Massa Tubuh |
1.706 |
2.597 |
.209 |
.657 |
.517 |
||||||||||||||
Umur Kuadrat |
-.019 |
.018 |
-.330 |
-1.040 |
.307 |
||||||||||||||
a. Dependent Variable: Trigliserida |
|||||||||||||||||||
MODEL 6 : TRI = β0 + β1 IMT + β2 UM + β3 UMKWT
Variables Entered/Removedb |
|||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||
1 |
Umur Kuadrat, Indeks Massa Tubuh, Umura |
. |
Enter |
||||
a. All requested variables entered. |
|||||||
b. Dependent Variable: Trigliserida |
|||||||
Model Summary |
|||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||
1 |
.237a |
.056 |
-.053 |
42.103 |
|||
a. Predictors: (Constant), Umur Kuadrat, Indeks Massa Tubuh, Umur |
|||||||
ANOVAb |
||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|||||||
1 |
Regression |
2750.563 |
3 |
916.854 |
.517 |
.674a |
||||||
Residual |
46088.137 |
26 |
1772.621 |
|||||||||
Total |
48838.700 |
29 |
||||||||||
a. Predictors: (Constant), Umur Kuadrat, Indeks Massa Tubuh, Umur |
||||||||||||
b. Dependent Variable: Trigliserida |
||||||||||||
Coefficientsa |
||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
T |
Sig. |
||||||||
B |
Std. Error |
Beta |
||||||||||
1 |
(Constant) |
453.925 |
507.281 |
.895 |
.379 |
|||||||
Indeks Massa Tubuh |
1.511 |
2.644 |
.185 |
.572 |
.573 |
|||||||
Umur |
-12.042 |
18.970 |
-2.000 |
-.635 |
.531 |
|||||||
Umur Kuadrat |
.095 |
.180 |
1.685 |
.528 |
.602 |
|||||||
a. Dependent Variable: Trigliserida |
||||||||||||
- Y = β0 + β1X1
TRI = β0 + β1 IMT
TRI = 154.991 – 0.468 IMT => Nilai F hitung (0.092) < F tabel (4.2) maka Ho diterima sehingga dapat disimpukan bahwa IMT tidak mempengaruhi TRIGLISERIDA.
Y = β0 + β1X1
TRI = β0 + β1 UM
TRI = 193.196 – 1.025 UM => Nilai F hitung (0.836) < F tabel (4.2) maka Ho diterima sehingga dapat disimpukan bahwa UMUR tidak mempengaruhi TRIGLISERIDA.
Y = β0 + β1X1
TRI = β0 + β1 UMKWT
TRI = 1287.955 + 47550.745 UMKWT => Nilai F hitung (0.758) < F tabel (4.2) maka Ho sehingga diterima dapat disimpukan bahwa UMUR Kuadrat tidak mempengaruhi TRIGLISERIDA.
- Nilai SS for Regression adalah 2750.563
- Nilai SS for Residual adalah 46088.137
- Nilai Means SS for Regression adalah 916.854
- Nilai Means SS for Residual adalah 772.621
- Nilai nilai F parsial adalah 0.517
- Nilai r2 adalah 0.056
- Buktikan penambahan berperan dalam memprediksi Y
TRI = 453.925 + 1.511 IMT – 12.042 UM + 0.095 UMKWT
Pada model 6 diatas, nilai F untuk penambahan independen variabel X3 = 0.157 < F tabel (2.98), ini berarti hipotesa Ho : β3 = 0 diterima atau gagal ditolak, artinya penambahan Umur Kuadrat (X3) tidak secara bermakna dapat memprediksi Y.
BAB 8 HAL 187-191
Soal 1.
Pelajari data yang disajikan dibawah ini tentang pengaruh umur serta pemberian makanan tinggi protein dan rendah protein terhadap panjang badan.
Tinggi Protein |
Rendah Protein |
||
Umur (bln) |
Panjang ( cm) |
Umur (bln) |
Panjang ( cm) |
2 |
50 |
4 |
52 |
5 |
54,3 |
7 |
55 |
8 |
63 |
10 |
61 |
10 |
66 |
10 |
63,4 |
10 |
69 |
15 |
66 |
14 |
73 |
20 |
68,5 |
18 |
82 |
20 |
67,9 |
20 |
83 |
24 |
72 |
20 |
80,3 |
28 |
78 |
25 |
85 |
30 |
74 |
25 |
84 |
13 |
65 |
30 |
86 |
18 |
69 |
27 |
85 |
20 |
74 |
- Tentukan persamaan garis untuk kelompok tinggi protein dan rendah protein secara terpisah
- Tentukan satu persamaan garis dengan memasukkan semua independen variabel
- Buktikan bahwa jenis makanan sangat berpengaruh terhadap panjang badan
- Bila umur dikelompokkan menjadi 2 kelompok yaitu <20 dan > 20 bulan, lakukan uji regresi untuk membuktikan jenis makanan dan umur berpengaruh terhadap panjang badan (ingat ada interaksi!)
Jawaban:
- Persamaan garis
- Kelompok tinggi protein
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Umur (bln)a |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.954a |
.911 |
.903 |
3.8651 |
|||||||||||||||
a. Predictors: (Constant), Umur (bln) |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
1681.302 |
1 |
1681.302 |
112.546 |
.000a |
|||||||||||||
Residual |
164.327 |
11 |
14.939 |
||||||||||||||||
Total |
1845.629 |
12 |
|||||||||||||||||
a. Predictors: (Constant), Umur (bln) |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
52.211 |
2.308 |
22.624 |
.000 |
||||||||||||||
Umur (bln) |
1.317 |
.124 |
.954 |
10.609 |
.000 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Persamaan garis kelompok tinggi protein:
Y = β0 + β1X1
Y = β0 + β1 Umur => Panjang Badan = 52,211 + 1, 317 Umur
- Kelompok rendah protein
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Umur (bln)a |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.940a |
.883 |
.872 |
2.6769 |
|||||||||||||||
a. Predictors: (Constant), Umur (bln) |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
593.115 |
1 |
593.115 |
82.769 |
.000a |
|||||||||||||
Residual |
78.825 |
11 |
7.166 |
||||||||||||||||
Total |
671.940 |
12 |
|||||||||||||||||
a. Predictors: (Constant), Umur (bln) |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
51.656 |
1.803 |
28.656 |
.000 |
||||||||||||||
Umur (bln) |
.887 |
.098 |
.940 |
9.098 |
.000 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Persamaan garis kelompok rendah protein:
Y = β0 + β1X1
Y = β0 + β1 Umur => Panjang Badan = 51,656 + 0,887 Umur
- Persamaan garis semua independen variabel
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Jenis Protein, Umur (bl)a |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.942a |
.888 |
.878 |
3.7390 |
|||||||||||||||
a. Predictors: (Constant), Jenis Protein, Umur (bl) |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
2541.687 |
2 |
1270.844 |
90.905 |
.000a |
|||||||||||||
Residual |
321.538 |
23 |
13.980 |
||||||||||||||||
Total |
2863.225 |
25 |
|||||||||||||||||
a. Predictors: (Constant), Jenis Protein, Umur (bl) |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
47.581 |
1.838 |
25.888 |
.000 |
||||||||||||||
Umur (bl) |
1.129 |
.090 |
.876 |
12.533 |
.000 |
||||||||||||||
Jenis Protein |
7.727 |
1.467 |
.368 |
5.267 |
.000 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Persamaan garis kelompok tinggi protein:
Y = β0 + β1X1
Y = β0 + β1 Umur + β2 Jenis Protein
Panjang Badan = 47,581 + 1, 129 Umur + 7,727 Jenis Protein
- Buktikan jenis makanan sangat berpengaruh terhadap panjang badan
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Jenis Proteina |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.347a |
.121 |
.084 |
10.2420 |
|||||||||||||||
a. Predictors: (Constant), Jenis Protein |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
345.655 |
1 |
345.655 |
3.295 |
.082a |
|||||||||||||
Residual |
2517.569 |
24 |
104.899 |
||||||||||||||||
Total |
2863.225 |
25 |
|||||||||||||||||
a. Predictors: (Constant), Jenis Protein |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
66.600 |
2.841 |
23.446 |
.000 |
||||||||||||||
Jenis Protein |
7.292 |
4.017 |
.347 |
1.815 |
.082 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Kesimpulan: Fhitung = 3,295 < Ftabel = 4,26 maka Ho diterima artinya bahwa jenis makanan (jenis protein) sangat tidak berpengaruh terhadap panjang badan.
- Uji regresi membuktikan jenis protein dan umur berpengaruh terhadap panjang badan
- Sebelum Interaksi
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
Jenis Protein, UmurKategoria |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.778a |
.606 |
.572 |
7.0040 |
|||||||||||||||
a. Predictors: (Constant), Jenis Protein, UmurKategori |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
1734.927 |
2 |
867.464 |
17.683 |
.000a |
|||||||||||||
Residual |
1128.297 |
23 |
49.056 |
||||||||||||||||
Total |
2863.225 |
25 |
|||||||||||||||||
a. Predictors: (Constant), Jenis Protein, UmurKategori |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
59.832 |
2.322 |
25.770 |
.000 |
||||||||||||||
Jenis Protein |
7.292 |
2.747 |
.347 |
2.654 |
.014 |
||||||||||||||
Umur Kategori |
14.663 |
2.755 |
.697 |
5.322 |
.000 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Kesimpulan: Fhitung = 17,683 > Ftabel = 3,42 maka Ho ditolak artinya bahwa jenis makanan (jenis protein) dan umur (berdasarkan kategori) sangat berpengaruh terhadap panjang badan.
- Setelah Interaksi
Variables Entered/Removedb |
|||||||||||||||||||
Model |
Variables Entered |
Variables Removed |
Method |
||||||||||||||||
1 |
UmurKategori*Jenis Protein, Jenis Protein, Umur Kategoria |
. |
Enter |
||||||||||||||||
a. All requested variables entered. |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Model Summary |
|||||||||||||||||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|||||||||||||||
1 |
.800a |
.640 |
.591 |
6.8438 |
|||||||||||||||
a. Predictors: (Constant), UmurKategori*Jenis Protein, Jenis Protein, Umur Kategori |
|||||||||||||||||||
ANOVAb |
|||||||||||||||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
||||||||||||||
1 |
Regression |
1832.788 |
3 |
610.929 |
13.043 |
.000a |
|||||||||||||
Residual |
1030.437 |
22 |
46.838 |
||||||||||||||||
Total |
2863.225 |
25 |
|||||||||||||||||
a. Predictors: (Constant), UmurKategori*Jenis Protein, Jenis Protein, Umur Kategori |
|||||||||||||||||||
b. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Coefficientsa |
|||||||||||||||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|||||||||||||||
B |
Std. Error |
Beta |
|||||||||||||||||
1 |
(Constant) |
61.629 |
2.587 |
23.825 |
.000 |
||||||||||||||
Jenis Protein |
3.700 |
3.658 |
.176 |
1.011 |
.323 |
||||||||||||||
Umur Kategori |
10.771 |
3.808 |
.512 |
2.829 |
.010 |
||||||||||||||
UmurKategori*Jenis Protein |
7.783 |
5.385 |
.312 |
1.445 |
.162 |
||||||||||||||
a. Dependent Variable: Panjang (cm) |
|||||||||||||||||||
Kesimpulan: Fhitung = 13,043 > Ftabel = 3,05 maka Ho ditolak artinya bahwa jenis makanan (jenis protein) dan umur (berdasarkan kategori) serta interaksi jenis protein*umur kategori sangat berpengaruh terhadap panjang badan.
Soal 2
Dengan pengetahuan biomedik yang saudara miliki, gunakan data dibawah ini untuk membuat beberapa persamaan garis regresi dan membuktikan hipotesa tentang slop dan intersep. (Buat dulu hipotesis yang akan dibuktikan)
SKL : Jenis Sekolah: 1 = Swasta; 0 = Negeri
JK : Jenis Kelamin: 1 = Laki-laki; 0 = Perempuan
UM : Umur dalam Tahun
BB : Berat Badan
TB : Tinggi Badan
IMT : Indeks Massa Tubuh
BJ : Berat Jenis Urin
AMA : Jumlah Air Dari Makanan
TKAR : Total Konsumsi Air
SKL |
JK |
UMUR |
BB |
TB |
IMT |
BJ |
AMA |
TKAR |
0 |
2 |
10 |
65 |
148 |
29,7 |
1025 |
402 |
1943 |
0 |
1 |
11 |
27 |
129 |
16,2 |
1020 |
634 |
2135 |
0 |
2 |
10 |
26 |
138 |
13,7 |
1015 |
359 |
1951 |
0 |
2 |
11 |
28 |
142 |
13,9 |
1020 |
679 |
2205 |
0 |
2 |
10 |
23 |
125 |
14,7 |
1030 |
273 |
2116 |
0 |
1 |
11 |
29 |
145 |
13,8 |
1025 |
352 |
2272 |
0 |
2 |
11 |
36 |
145 |
17,1 |
1025 |
454 |
2204 |
0 |
2 |
11 |
41 |
148 |
18,7 |
1020 |
635 |
2177 |
0 |
2 |
10 |
38 |
142 |
18,8 |
1025 |
473 |
2043 |
0 |
2 |
10 |
55 |
146 |
25,8 |
1020 |
562 |
2244 |
0 |
2 |
11 |
30 |
140 |
15,3 |
1035 |
382 |
1924 |
0 |
2 |
11 |
32 |
143 |
15,7 |
1020 |
569 |
2182 |
0 |
2 |
11 |
31 |
131 |
18,1 |
1015 |
711 |
2253 |
0 |
2 |
11 |
53 |
150 |
23,6 |
1010 |
386 |
2237 |
0 |
1 |
11 |
66 |
144 |
31,9 |
1025 |
290 |
2042 |
0 |
2 |
11 |
43 |
147 |
19,9 |
1020 |
522 |
2255 |
0 |
1 |
11 |
25 |
134 |
14 |
1010 |
260 |
2071 |
0 |
2 |
10 |
30 |
134 |
16,7 |
1010 |
529 |
2180 |
0 |
2 |
11 |
41 |
151 |
18 |
1030 |
293 |
1904 |
0 |
1 |
11 |
24 |
133 |
14 |
1025 |
256 |
2077 |
0 |
2 |
12 |
27 |
136 |
14,6 |
1020 |
409 |
2282 |
0 |
2 |
11 |
40 |
150 |
17,8 |
1025 |
350 |
2034 |
0 |
2 |
11 |
37 |
144 |
17,8 |
1010 |
832 |
2105 |
0 |
2 |
10 |
32 |
136 |
17,3 |
1025 |
480 |
2164 |
0 |
2 |
11 |
41 |
147 |
19 |
1030 |
457 |
2139 |
0 |
2 |
11 |
27 |
137 |
14,4 |
1025 |
317 |
2009 |
0 |
2 |
11 |
33 |
141 |
16,5 |
1040 |
289 |
1549 |
0 |
2 |
11 |
25 |
135 |
13,7 |
1020 |
593 |
1976 |
0 |
2 |
10 |
48 |
148 |
22 |
1025 |
812 |
2005 |
0 |
2 |
11 |
36 |
151 |
16 |
1025 |
458 |
2280 |
0 |
2 |
10 |
36 |
149 |
16,2 |
1005 |
815 |
2077 |
1 |
2 |
11 |
33 |
139 |
17,1 |
1020 |
482 |
2321 |
1 |
2 |
11 |
25 |
130 |
14,8 |
1005 |
596 |
2679 |
1 |
1 |
11 |
31 |
147 |
14,3 |
1005 |
868 |
3018 |
1 |
2 |
11 |
35 |
147 |
16,2 |
1025 |
661 |
2112 |
1 |
2 |
11 |
51 |
149 |
23 |
1015 |
694 |
2547 |
1 |
2 |
11 |
39 |
148 |
17,8 |
1005 |
709 |
2958 |
1 |
2 |
10 |
52 |
158 |
20,8 |
1015 |
604 |
2917 |
1 |
2 |
11 |
58 |
158 |
23,2 |
1020 |
580 |
2477 |
1 |
2 |
11 |
49 |
153 |
21 |
1015 |
592 |
2488 |
1 |
2 |
11 |
43 |
147 |
19,9 |
1010 |
693 |
2894 |
1 |
1 |
10 |
42 |
153 |
18 |
1010 |
547 |
2591 |
1 |
1 |
11 |
43 |
146 |
20,2 |
1020 |
379 |
2232 |
1 |
1 |
11 |
35 |
141 |
17,6 |
1015 |
1000 |
2786 |
1 |
1 |
11 |
51 |
152 |
22,1 |
1010 |
636 |
2785 |
1 |
2 |
11 |
27 |
128 |
16,5 |
1010 |
446 |
2927 |
1 |
1 |
11 |
39 |
151 |
17,1 |
1015 |
631 |
3072 |
1 |
2 |
12 |
38 |
154 |
16,1 |
1015 |
458 |
2741 |
1 |
1 |
10 |
35 |
140 |
17,9 |
1020 |
578 |
2312 |
1 |
1 |
11 |
31 |
147 |
14,3 |
1020 |
267 |
2388 |
1 |
2 |
11 |
35 |
148 |
16 |
1010 |
605 |
2468 |
1 |
1 |
11 |
18 |
119 |
12,7 |
1015 |
388 |
2521 |
1 |
1 |
12 |
54 |
147 |
25 |
1025 |
492 |
2384 |
1 |
2 |
11 |
36 |
149 |
16,2 |
1020 |
407 |
2447 |
1 |
1 |
11 |
28 |
148 |
12,8 |
1010 |
715 |
2503 |
1 |
2 |
10 |
38 |
142 |
18,8 |
1020 |
909 |
2750 |
1 |
2 |
10 |
33 |
144 |
16 |
1020 |
436 |
2756 |
1 |
2 |
11 |
32 |
149 |
14,4 |
1005 |
1067 |
3547 |
1 |
1 |
11 |
40 |
148 |
18,3 |
1015 |
596 |
3373 |
1 |
1 |
11 |
38 |
147 |
17,6 |
1005 |
560 |
2710 |
1 |
1 |
11 |
39 |
148 |
17,8 |
1010 |
545 |
2328 |
1 |
1 |
10 |
45 |
147 |
20,8 |
1030 |
513 |
2343 |
0 |
2 |
10 |
65 |
148 |
29,7 |
1025 |
402 |
1943 |
0 |
1 |
11 |
27 |
129 |
16,2 |
1020 |
634 |
2135 |
0 |
2 |
10 |
26 |
138 |
13,7 |
1015 |
359 |
1951 |
0 |
2 |
11 |
28 |
142 |
13,9 |
1020 |
679 |
2205 |
0 |
2 |
10 |
23 |
125 |
14,7 |
1030 |
273 |
2116 |
0 |
1 |
11 |
29 |
145 |
13,8 |
1025 |
352 |
2272 |
0 |
2 |
11 |
36 |
145 |
17,1 |
1025 |
454 |
2204 |
0 |
2 |
11 |
41 |
148 |
18,7 |
1020 |
635 |
2177 |
0 |
2 |
10 |
38 |
142 |
18,8 |
1025 |
473 |
2043 |
0 |
2 |
10 |
55 |
146 |
25,8 |
1020 |
562 |
2244 |
0 |
2 |
11 |
30 |
140 |
15,3 |
1035 |
382 |
1924 |
X1 = SKL : 1 bila sekolah swasta
0 bila sekolah Negeri
X2 = JK : 1 bila laki-laki
0 bila Perempuan
X3 = UM
X4 = BB
X5 = TB
X6 = IMT
X7 = AMA
X8 = TKAR
X9 = SKL*JK
Jawab:
H0 : µ1 = µ2 atau H0 : β1 = 0
Tidak ada hubungan antara jenis sekolah, jenis kelamin, umur, berat badan, tinggi badan, indeks massa tubuh, jumlah air dari makanan dan total konsumsi air dengan berat jenis urin.
Ha : µ1 ≠ µ2 atau H0 : β1 ≠ 0
Ada hubungan antara jenis sekolah, jenis kelamin, umur, berat badan, tinggi badan, indeks massa tubuh, jumlah air dari makanan dan total konsumsi air dengan berat jenis urin.
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9
Persamaan garis untuk jenis sekolah swasta dan jenis kelamin laki-laki:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9
Y = β0 + β1(1) + β2(1) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9(1*1)
Y = (β0 + β1 + β2 + β9) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8
Model Regresi:
BJ = (978,545 + 1,878 + 1,881 – 1,283) + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT
– 0,014 AMA – 0,009 TKAR
= 981,021 + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
Persamaan garis untuk jenis sekolah swasta dan jenis kelamin perempuan:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9
Y = β0 + β1(1) + β2(0) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9(1*0)
Y = (β0 + β1) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8
Model Regresi:
BJ = (978,545 + 1,878) + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
= 980,423 + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
Persamaan garis untuk jenis sekolah negeri dan jenis kelamin laki-laki:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9
Y = β0 + β1(0) + β2(1) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9(0*1)
Y = (β0 + β2) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8
Model Regresi:
BJ = (978,545 + 1,881) + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
= 980,426 + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
Persamaan garis untuk jenis sekolah negeri dan jenis kelamin perempuan:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9
Y = β0 + β1(0) + β2(0) + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9(0*0)
Y = β0 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8
Model Regresi:
BJ = 978,545 + 0,289 UM – 0,857 BB + 0,419 TB + 1,967 IMT – 0,014 AMA
– 0,009 TKAR
Variables Entered/Removedb |
|||
Model |
Variables Entered |
Variables Removed |
Method |
1 |
Jenis Sekolah*Jenis Kelamin, Indeks Massa Tubuh, Jenis Kelamin, Umur dalam Tahun, Jumlah Air Dari Makanan, Tinggi Badan, Total Konsumsi Air, Jenis Sekolah, Berat Badana |
. |
Enter |
a. All requested variables entered. |
|||
b. Dependent Variable: Berat Jenis Urin |
Model Summary |
||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
1 |
.686a |
.471 |
.395 |
6.103 |
a. Predictors: (Constant), Jenis Sekolah*Jenis Kelamin, Indeks Massa Tubuh, Jenis Kelamin, Umur dalam Tahun, Jumlah Air Dari Makanan, Tinggi Badan, Total Konsumsi Air, Jenis Sekolah, Berat Badan |
ANOVAb |
||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
1 |
Regression |
2086.687 |
9 |
231.854 |
6.226 |
.000a |
Residual |
2346.190 |
63 |
37.241 |
|||
Total |
4432.877 |
72 |
||||
a. Predictors: (Constant), Jenis Sekolah*Jenis Kelamin, Indeks Massa Tubuh, Jenis Kelamin, Umur dalam Tahun, Jumlah Air Dari Makanan, Tinggi Badan, Total Konsumsi Air, Jenis Sekolah, Berat Badan |
||||||
b. Dependent Variable: Berat Jenis Urin |
Coefficientsa |
||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
B |
Std. Error |
Beta |
||||
1 |
(Constant) |
978.545 |
75.754 |
12.917 |
.000 |
|
Jenis Sekolah |
1.878 |
6.239 |
.119 |
.301 |
.764 |
|
Jenis Kelamin |
1.881 |
2.719 |
.111 |
.692 |
.492 |
|
Umur dalam Tahun |
.289 |
1.512 |
.019 |
.191 |
.849 |
|
Berat Badan |
-.857 |
1.120 |
-1.157 |
-.765 |
.447 |
|
Tinggi Badan |
.419 |
.510 |
.419 |
.821 |
.415 |
|
Indeks Massa Tubuh |
1.967 |
2.410 |
1.008 |
.816 |
.417 |
|
Jumlah Air Dari Makanan |
-.014 |
.005 |
-.320 |
-2.805 |
.007 |
|
Total Konsumsi Air |
-.009 |
.003 |
-.431 |
-2.713 |
.009 |
|
Jenis Sekolah*Jenis Kelamin |
-1.283 |
3.471 |
-.135 |
-.370 |
.713 |
|
a. Dependent Variable: Berat Jenis Urin |
Pembuktian hipotesa tentang slop dan intersep:
Dari keempat persamaan garis dan model regresi diatas menunjukkan intersep masing-masing berbeda namun slopenya sama. Hal ini dikarenakan variabel jenis sekolah dan jenis kelamin mengalami interaksi.
Dari penyataan diatas dapat disimpulkan bahwa H0 ditolak karena nilai Fhitung (6,226) > Ftabel (2,03). Sehingga dapat disimpulkan ada pengaruh antara variabel indeks massa tubuh, jenis kelamin, umur dalam tahun, jumlah air dari makanan, tinggi badan, total konsumsi air, jenis sekolah, berat badan dan interaksi jenis sekolah-jenis kelamin dengan berat jenis urin.
Namun, untuk masing – masing variabel hanya variabel AMA dan TKAR yang berpengaruh terhadap berat jenis urin karena nilai Thitung > Ttabel (1,96) sedangkan variabel lain tidak berpengaruh.
Soal 3
Variabel |
β |
Sβ |
Partial F |
t |
Umur |
1.02892 |
0.50177 |
4.205 |
2.05 |
IMT |
10.45104 |
9.13111 |
1.310 |
1.144 |
RKK |
-0.53744 |
23.23004 |
0.0005 |
0.022 |
Umur*RKK |
0.43733 |
0.71320 |
0.376 |
0.613 |
IMT*RKK |
-3.70682 |
10.76763 |
0.11851 |
0.344 |
Intersep |
48.61271 |
Parsial F1 = (β1 : Sβ1)2 = (1.02892 : 0.50177)2 = 4.205
Sβ2 = β2 : = 10.45104 : = 9.13111
Parsial F3 = (β3 : Sβ3)2 = (-0.53744 : 23.23004)2 = 0.0005
Sβ4 = β4 : = 0.43733 : = 0.71320
Parsial F5 = (β5 : Sβ5)2 = (-3.70682 : 10.76763)2 = 0.11851
X1 = Umur
X2 = IMT
X3 = RKK
X4 = Umur*RKK
X5 = IMT*RKK
Persamaan garis:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5
= 48.61271 + 1.02892 X1 + 10.45104 X2 + -0.53744 X3 + 0.43733 X4 + -3.70682 X5
= 48.61271 + 1.02892 Umur + 10.45104 IMT – 0.53744 RKK + 0.43733 Umur*RKK
– 3.70682 IMT*RKK
Kesimpulan:
Penambahan variabel X1 (Umur) kedalam model bermakna karena Thitung (2,05) > Ttabel (1,96) dengan kata lain perlu menambahkan variabel tersebut kedalam model regresi. Sedangkan variabel selain itu tidak perlu ditambahkan kedalam model regresi sehingga model regresi akhir adalah sebagai berikut:
Y = β0 + β1X1
Y = 48.61271 + 1.02892 Umur