Tugas Analisis Regresi Halaman 154 Pertemuan 10
Nama : fentria
angraeni
NIM : 20160302163
Seksi : 10 (Analisis Regresi/Kelas Paralel)
Latihan 2.
Lakukan prediksi BB
dengan variable independen TB, BTL, dan AK.
a.
Hitung
SS for Regression (X3ІX1,X2);
b.
Hitung
SS for Residual;
c.
Hitung
Means SS for Regression (X3ІX1,X2);
d.
Hitung
Means SS for Residual;
e.
Hitung
nilai F parsial;
f.
Hitung
nilai r2;
g.
Buktikan
bahwa penambahan X3 berperan dalam memprediksi Y.
BB
|
TB
|
BTL
|
AK
|
79.2
|
149.0
|
54.1
|
2670
|
64.0
|
152.0
|
44.3
|
820
|
67.0
|
155.7
|
47.8
|
1210
|
78.4
|
159.0
|
53.9
|
2678
|
66.0
|
163.3
|
47.5
|
1205
|
63.0
|
166.0
|
43.0
|
815
|
65.9
|
169.0
|
47.1
|
1200
|
63.1
|
172.0
|
44.0
|
1180
|
73.2
|
174.5
|
44.1
|
1850
|
66.5
|
176.1
|
48.3
|
1260
|
61.9
|
176.5
|
43.5
|
1170
|
72.5
|
179.0
|
43.3
|
1852
|
101.1
|
182.0
|
66.4
|
1790
|
66.2
|
170.4
|
47.5
|
1250
|
99.9
|
184.9
|
66.0
|
1889
|
63.0
|
169.0
|
44.0
|
915
|
BB =
Berat Badan
TB =
Tinggi Badan
BTL =
Berat Badan Tanpa Lemak
AK =
Asupan Kalori
Model 1. BB = β0 +
β1 TB
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Tinggi Badana
|
.
|
Enter
|
a. All requested
variables entered.
b. Dependent Variable: Berat Badan
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.378a
|
.143
|
.081
|
11.8405
|
a. Predictors:
(Constant), Tinggi Badan
|
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
326.204
|
1
|
326.204
|
2.327
|
.149a
|
Residual
|
1962.751
|
14
|
140.196
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Tinggi Badan
|
|
|
|
b. Dependent
Variable: Berat Badan
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
-2.492
|
48.880
|
|
-.051
|
.960
|
Tinggi Badan
|
.441
|
.289
|
.378
|
1.525
|
.149
|
a. Dependent
Variable: Berat Badan
|
|
|
|
Estimasi model 1 BB = -2.492 +
0.441 TB
Model 2. BB = β0 +
β1 BTL
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Berat Badan Tanpa
Lemaka
|
.
|
Enter
|
a. All requested
variables entered.
|
|
b. Dependent
Variable: Berat Badan
|
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.945a
|
.893
|
.886
|
4.1735
|
a. Predictors:
(Constant), Berat Badan Tanpa Lemak
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
2045.099
|
1
|
2045.099
|
117.411
|
.000a
|
Residual
|
243.855
|
14
|
17.418
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Berat Badan Tanpa Lemak
|
|
|
b. Dependent
Variable: Berat Badan
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
-4.303
|
7.112
|
|
-.605
|
.555
|
Berat Badan Tanpa Lemak
|
1.554
|
.143
|
.945
|
10.836
|
.000
|
a. Dependent
Variable: Berat Badan
|
|
|
|
|
Estimasi model 2 BB = -4.303 + 1.554 BTL
Model 3. BB = β0 +
β1 AK
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Asupan Kaloria
|
.
|
Enter
|
a. All requested
variables entered.
|
|
b. Dependent
Variable: Berat Badan
|
Model Summary
|
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.617a
|
.381
|
.337
|
10.0593
|
|
a. Predictors:
(Constant), Asupan Kalori
|
|
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
872.301
|
1
|
872.301
|
8.620
|
.011a
|
Residual
|
1416.653
|
14
|
101.190
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Asupan Kalori
|
|
|
|
b. Dependent
Variable: Berat Badan
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
52.517
|
7.074
|
|
7.423
|
.000
|
Asupan Kalori
|
.013
|
.004
|
.617
|
2.936
|
.011
|
a. Dependent
Variable: Berat Badan
|
|
|
|
Estimasi model 3 BB = 52.517 +
0.013 AK
Model 4. BB = β0 +
β1 TB + β2 BTL
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Berat Badan Tanpa
Lemak, Tinggi Badana
|
.
|
Enter
|
a. All requested
variables entered.
|
|
b. Dependent
Variable: Berat Badan
|
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.954a
|
.910
|
.896
|
3.9870
|
a. Predictors:
(Constant), Berat Badan Tanpa Lemak, Tinggi Badan
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
2082.309
|
2
|
1041.154
|
65.499
|
.000a
|
Residual
|
206.645
|
13
|
15.896
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Berat Badan Tanpa Lemak, Tinggi Badan
|
|
b. Dependent
Variable: Berat Badan
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
-27.527
|
16.631
|
|
-1.655
|
.122
|
Tinggi Badan
|
.155
|
.101
|
.132
|
1.530
|
.150
|
Berat Badan Tanpa
Lemak
|
1.496
|
.142
|
.910
|
10.511
|
.000
|
a. Dependent
Variable: Berat Badan
|
|
|
|
|
Estimasi model 4 BB = -27.527 +
0.155 TB + 1.496 BTL
Model 5. BB = β0 +
β1 TB + β3 AK
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Asupan Kalori,
Tinggi Badana
|
.
|
Enter
|
a. All requested
variables entered.
|
|
b. Dependent
Variable: Berat Badan
|
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.747a
|
.557
|
.489
|
8.8280
|
a. Predictors:
(Constant), Asupan Kalori, Tinggi Badan
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
1275.821
|
2
|
637.911
|
8.185
|
.005a
|
Residual
|
1013.133
|
13
|
77.933
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Asupan Kalori, Tinggi Badan
|
|
|
b. Dependent
Variable: Berat Badan
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
-31.333
|
37.369
|
|
-.838
|
.417
|
Tinggi Badan
|
.492
|
.216
|
.421
|
2.275
|
.040
|
Asupan Kalori
|
.014
|
.004
|
.646
|
3.491
|
.004
|
a. Dependent
Variable: Berat Badan
|
|
|
|
Estimasi model 5 BB = -31.333 +
0.492 TB + 0.014 AK
Model 6. BB = β0 +
β1 TB + β2 BTL + β3 AK
Variables Entered/Removedb
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
1
|
Asupan Kalori,
Tinggi Badan, Berat Badan Tanpa Lemaka
|
.
|
Enter
|
a. All requested
variables entered.
|
|
b. Dependent
Variable: Berat Badan
|
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.969a
|
.939
|
.923
|
3.4224
|
a. Predictors:
(Constant), Asupan Kalori, Tinggi Badan, Berat Badan Tanpa Lemak
|
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
|
Regression
|
2148.400
|
3
|
716.133
|
61.141
|
.000a
|
Residual
|
140.554
|
12
|
11.713
|
|
|
Total
|
2288.954
|
15
|
|
|
|
a. Predictors:
(Constant), Asupan Kalori, Tinggi Badan, Berat Badan Tanpa Lemak
|
b. Dependent
Variable: Berat Badan
|
|
|
|
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
1
|
(Constant)
|
-33.412
|
14.489
|
|
-2.306
|
.040
|
Tinggi Badan
|
.210
|
.090
|
.180
|
2.339
|
.037
|
Berat Badan Tanpa
Lemak
|
1.291
|
.150
|
.785
|
8.631
|
.000
|
Asupan Kalori
|
.004
|
.002
|
.209
|
2.375
|
.035
|
a. Dependent
Variable: Berat Badan
|
|
|
|
|
Estimasi model 6 BB = -33.412 +
0.210 TB + 1.291 BTL + 0.004 AK
Kita lakukan uji
parsial F seperti berikut (berdasarkan hasil-hasil yang sudah kita lakukan di
atas).
ANOVA Tabel untuk BB
dengan TB, BTL, dan AK.
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
X1
Regresi X2ІX1
X3ІX1X2
|
1
1
1
|
326.204
2082.309- 326.204 =
1756.105
2148.400 - 2082.309
= 66.091
|
326.204
1756.105
66.091
|
326.204/11.713 =
27.85
1756.105/15.896=
110.475
66.091/11.713 =
5.643
|
0.000
|
Residual
|
12
|
140.554
|
11.713
|
|
|
Total
|
15
|
2288.954
|
|
|
|
*p<0.05
Berikut ringkasan
table analisis yang dapat membantu kita dalam pemilihan model estimasi yang
terbaik.
No.
|
Model Estimasi
|
F
|
r2
|
1.
|
Y = -2.49 + 0.44 TB
|
2.33
|
0.15
|
2.
|
Y = -4.30 + 1.55 BTL
|
117.41
|
0.00
|
3.
|
Y = 52.52 + 0.01 AK
|
8.62
|
0.01
|
4.
|
Y = -27.53 + 0.16 TB + 1.50 BTL
|
65.50
|
0.00
|
5.
|
Y = -31.33 + 0.49 TB +
0.01 AK
|
8.19
|
0.00
|
6.
|
Y = -33.41 + 0.21 TB + 1.29 BTL + 0.00 AK
|
61.14
|
0.00
|
Angka dalam tanda
kurung adalah Standar Error dari parameter
*bermakna (p<0.05)
Dari ke enam model
estimasi terlihat bahwa variable Tinggi Badan secara konsisten sangat
berpengaruh terhadap Berat Badan (p<0.05). Pada model estimasi 1 tampak
nilai r2 sebesar 0.149 dan bila disbanding dengan model
esimasi 4,5, dan 6 penambahan nilai r2 relatif kecil
masing-masing 0.000, 0.005, dan 0.000 atau hanya bertambah sekitar -0.149,
-0.144, dan -0.149, ini sangat tidak berarti.
Dengan demikian kita
bias berkesimpulan variable Tinggi Badan sangat bermakna pengaruhnya terhadap
Berat Badan. Sebaliknya penambahan variable UM dan UMSQ tidak berperan dalam
menjelaskan variasi Berat Badan dan kita tidak perlu menambahkan kedua
variable tersebut ke dalam model. Model akhir yaitu : Y = -2.49 +
0.44 TB
|
|
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