Tugas Analisis Regresi Pertemuan 10
TUGAS ANALISIS REGRESI HALAMAN 154
Lakukan prediksi BB
dengan variable independen TB, BTL, dan AK.
- Hitung SS for
Regression (X3ІX1,X2);
- Hitung SS for
Residual;
- Hitung Means SS
for Regression (X3ІX1,X2);
- Hitung Means SS
for Residual;
- Hitung nilai F
parsial;
- Hitung nilai r2;
- 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.
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
1
|
.378a
|
.143
|
.081
|
11.8405
|
b. Dependent Variable: Berat 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
X3ІX1
X2
|
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
|
