Rabu, 31 Mei 2017

Tugas Analisis Regresi Pertemuan 10

                                                TUGAS ANALISIS REGRESI HALAMAN 154


Lakukan prediksi BB dengan variable independen TB, BTL, dan AK.
  1. Hitung SS for Regression (X3ІX1,X2);
  2. Hitung SS for Residual;
  3. Hitung Means SS for Regression (X3ІX1,X2);
  4. Hitung Means SS for Residual;
  5. Hitung nilai F parsial;
  6. Hitung nilai r2;
  7. 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