Minggu, 21 Mei 2017

anreg pertemuan 9

Latihan 1
Umur
Cholesterol
Trigliserida
UMSQ
40
218
194
1600
46
265
188
2116
69
197
134
4761
44
188
155
1936
41
217
191
1681
56
240
207
3136
48
222
155
2304
49
244
235
2401
41
190
167
1681
38
209
186
1444
36
208
179
1296
39
214
129
1521
59
238
220
3481
56
219
155
3136
44
241
201
1936
37
212
140
1369
40
244
132
1600
32
217
140
1024
56
227
279
3136
49
218
101
2401
50
241
213
2500
46
234
168
2116
52
231
242
2704
51
297
142
2601
46
230
240
2116
60
258
173
3600
47
243
175
2209
58
236
199
3364
66
193
201
4356
52
193
193
2704
55
319
191
3025
58
212
216
3364
41
209
154
1681
60
224
198
3600
50
184
129
2500
48
222
115
2304
49
229
148
2401
39
204
164
1521
40
211
104
1600
47
230
218
2209
67
230
239
4489
57
222
183
3249
50
213
190
2500
43
238
259
1849
55
234
156
3025

Model 1          : Chol =
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
203.123
17.156

11.840
.000
Trigliserida
.127
.093
.203
1.360
.181
a. Dependent Variable: Cholesterol




Coefficient                              Standard Error                                    Partial F
            
                                                              1.850
Estimated model Chol = 203.123 + 0.127 Trig

ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
1181.676
1
1181.676
1.850
.181a

Residual
27464.768
43
638.716



Total
28646.444
44




a. Predictors: (Constant), Trigliserida




b. Dependent Variable: Cholesterol



0.04
 
Model 2          : Chol =
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
204.048
22.093

9.236
.000
Umur
.445
.444
.151
1.004
.321
a. Dependent Variable: Cholesterol




Coefficient                              Standard Error                                    Partial F
            
                                                            1.004
Estimated model Chol = 204.048 + 0.445 UM
ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
655.625
1
655.625
1.007
.321a
0.02
Residual
27990.819
43
650.949



Total
28646.444
44




a. Predictors: (Constant), Umur





b. Dependent Variable: Cholesterol





Model 3          : Chol =
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
217.420
11.555

18.816
.000
Umur Kuadrat
.003
.004
.118
.777
.442
a. Dependent Variable: Cholesterol



Coefficient                              Standard Error                                    Partial F
            
                                                            0.562
Estimated model Chol = 217.420 + 0.003 (UM)2
ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
396.227
1
396.227
.603
.442a
0.013
Residual
28250.217
43
656.982



Total
28646.444
44




a. Predictors: (Constant), Umur Kuadrat




b. Dependent Variable: Cholesterol





Model 4          : Chol =

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
192.155
24.554

7.826
.000
Trigliserida
.108
.098
.173
1.099
.278
Umur
.292
.464
.099
.629
.533
a. Dependent Variable: Cholesterol




Coefficient                              Standard Error                                    Partial F
             
                                                            1.214
                                                           0.396
Estimated model Chol = 192.155 + 0.108 Trig + 0.292 UM

ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
1437.719
2
718.860
1.110
.339a
0.050
Residual
27208.725
42
647.827



Total
28646.444
44




a. Predictors: (Constant), Umur, Trigliserida




b. Dependent Variable: Cholesterol





Model 5          : Chol =

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
200.525
18.433

10.879
.000
Trigliserida
.115
.098
.185
1.173
.247
Umur Kuadrat
.002
.005
.065
.413
.682
a. Dependent Variable: Cholesterol




Coefficient                              Standard Error                                    Partial F
            
                                                            1.377
                                                           0.16
Estimated model Chol = 200.525 + 0.115 Trig + 0.002 (UM)2

ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
1292.618
2
646.309
.992
.379a
0.045
Residual
27353.826
42
651.282



Total
28646.444
44




a. Predictors: (Constant), Umur Kuadrat, Trigliserida



b. Dependent Variable: Cholesterol





Model 6          : Chol =

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-21.969
104.532

-.210
.835
Trigliserida
.079
.095
.126
.825
.414
Umur
9.220
4.269
3.132
2.160
.037
Umur Kuadrat
-.088
.042
-3.035
-2.103
.042
a. Dependent Variable: Cholesterol



Coefficient                              Standard Error                                    Partial F
            
                                                            0.691
                                                           4.664
                                                         4.390
Estimated model Chol = -21.969 + 0.079 Trig + 9.220 UM – 0.088 (UM)2



ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.
R2
1
Regression
4086.344
3
1362.115
2.274
.094a
0.142
Residual
24560.100
41
599.027



Total
28646.444
44




a. Predictors: (Constant), Umur Kuadrat, Trigliserida, Umur



b. Dependent Variable: Cholesterol





Dari ke enam model estimasi di atas kita bisa menduga model estimasi No. 6 dengan independen variable Trig, UM dan (UM)2 adalah yang terbaik bila di lihat dari besaran r2 yaitu 0.05. Namun sebaiknya kita perhatikam uraian di bawah ini.

Kita dapat memperinci nilai-nilai Sum Square of Regression dalam tabel ANOVA sbb :
Sumber
df
SS
MS
F
R2
Regresi
X1
X2 I X1
X3 I X1,X2

1
1
1

1181.676
256.043
2648.625

1181.676
256.043
2648.625

1.972
0.395
4.42

0.05
Residual
41
24560.100
599.027


Total
44
28646.444






Latihan 2.
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.

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
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





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