tugas pertemuan 10



Nama : Ade B. Aliandu
NIM : 20160302229
 Halaman : 153-154

Latihan 1
Lakukan prediksi TDS dengan variabel independen IMT, Umur dan Umur Kuadrat
a.       Hitung SS for Regression (X3 X1, X2)
b.      Hitung SS for Residual
c.       Hitung Means SS for Regression (X3 X1, X2)
d.      Hitung Means SS for Residual
e.       Hitung nilai F parsial
f.       Hitung nilai r2
g.      Buktikan penambahan X3 berperan dalam memprediksi Y
UM
CHOL
TRIG
UM
CHOL
TRIG
UM
CHOL
TRIG
40
218
194
37
212
140
55
319
191
46
265
188
40
244
132
58
212
216
69
197
134
32
217
140
41
209
154
44
188
155
56
227
279
60
224
198
41
217
191
49
218
101
50
184
129
56
240
207
50
241
213
48
222
115
48
222
155
46
234
168
49
229
148
49
244
235
52
231
242
39
204
164
41
190
167
51
297
142
40
211
104
38
209
186
46
230
240
47
230
218
36
208
179
60
258
173
67
230
239
39
214
129
47
243
175
57
222
183
59
238
220
58
236
199
50
213
190
56
219
155
66
193
201
43
238
259
44
241
201
52
193
193
55
234
156
UM      = Umur
CHOL  = Cholesterol
TRIG   = Trigliserida

Jawaban :
Regression
Model 1
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Trigliseridab
.
Enter
a. Dependent Variable: Cholesterol
b. All requested variables entered.



Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.203a
.041
.019
25.273
a. Predictors: (Constant), Trigliserida


ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
1181.676
1
1181.676
1.850
.181b
Residual
27464.768
43
638.716


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Trigliserida










Estimasi Model 1 : Chol= 203.123 + 0.127 Trigliserida
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


Model 2
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Umurb
.
Enter
a. Dependent Variable: Cholesterol
b. All requested variables entered.

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.151a
.023
.000
25.514
a. Predictors: (Constant), Umur
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
655.625
1
655.625
1.007
.321b
Residual
27990.819
43
650.949


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Umur









Estimasi Model 2: CHOL= 204.408 + 0.445 UM
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

Model 3
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Umur kuadratb
.
Enter
a. Dependent Variable: Cholesterol
b. All requested variables entered.

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.118a
.014
-.009
25.632
a. Predictors: (Constant), Umur kuadrat

ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
396.227
1
396.227
.603
.442b
Residual
28250.217
43
656.982


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Umur kuadrat
Estimasi model 3: CHOL= 217.420 + 0.003 UMSQ
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

Model 4
Variables Entered/Removeda

Model
Variables Entered
Variables Removed
Method

1
Umur, Trigliseridab
.
Enter

a. Dependent Variable: Cholesterol

b. All requested variables entered.

Model Summary

Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.224a
.050
.005
25.452
a. Predictors: (Constant), Umur, Trigliserida









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


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Umur, Trigliserida
Estimasi model 4 = CHOL= 192.155 + 0.108 TRIG + 0.292 UM
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

Model 5
Variables Entered/Removeda

Model
Variables Entered
Variables Removed
Method

1
Umur kuadrat, Trigliseridab
.
Enter

a. Dependent Variable: Cholesterol

b. All requested variables entered.

Model Summary

Model
R
R Square
Adjusted R Square
Std. Error of the Estimate

1
.212a
.045
.000
25.520

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

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


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Umur kuadrat, Trigliserida















Estimasi model 5: CHOL= 200.525 + 0.115 TRIG + 0.002 UMSQ
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
Model 6
Variables Entered/Removeda

Model
Variables Entered
Variables Removed
Method

1
Umur kuadrat, Trigliserida, Umurb
.
Enter

a. Dependent Variable: Cholesterol

b. All requested variables entered.

Model Summary

Model
R
R Square
Adjusted R Square
Std. Error of the Estimate

1
.378a
.143
.080
24.475

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

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


Total
28646.444
44



a. Dependent Variable: Cholesterol
b. Predictors: (Constant), Umur kuadrat, Trigliserida, Umur















Estimasi model 6: CHOL= -21.969 + 0.079 TRIG + 9.220 UM – 0.088 UMSQ
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
























ANOVA Tabel untuk CHOL dengan TRIG,UM,UMSQ
Sumber
df
SS
MS
F
Regresi X1
X2│X1
X3│X1,X2
1
1
1
1181.676
256.043
2648.625
1181.676
256.043
2648.625
1.97
0.43
4.42

0.143
Residual
41
24560.100
599.027


Total
44
28646.444





No
Model Estimasi
F
1
Y= 203.123 + 0.127 TRIG (.093)*
1.850
.041
2
Y = 204.408 + 0.445 UM (.444)*
1.007
.023
3
Y= 217.420 + 0.003 UMSQ(.004)
.603
.014
4
Y= 192.155 + 0.108 TRIG + 0.292 UM (.098 )* (.464)*
1.110
.050
5
Y= 200.525 + 0.115 TRIG + 0.002 UMSQ (.098)*  (.005)
.992
.045
6
Y= -21.969 + 0.079 TRIG + 9.220 UM – 0.088 UMSQ (.095)* (4.269)* (.042)
2.274
.143
Angka dalam tanda kurung adalah standar error dari parameter
*bermakna (p<0.05)










Latihan 2
Lakukan prediksi TDS dengan variabel independen IMT, Umur dan Umur Kuadrat
a.       Hitung SS for Regression (X3 X1, X2)
b.      Hitung SS for Residual
c.       Hitung Means SS for Regression (X3 X1, X2)
d.      Hitung Means SS for Residual
e.       Hitung nilai F parsial
f.       Hitung nilai r2
g.      Buktikan penambahan X3 berperan dalam memprediksi Y

BB
TB
BTL
AK
79.2
149
54.1
2670
64.0
152
44.3
820
67.0
155.7
47.8
1210
78.4
159
53.9
2678
66.0
163.3
47.5
1205
63.0
166
43
815
65.9
169
47.1
1200
63.1
172
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
43.3
1852
101.1
182
66.4
1790
66.2
170.4
47.5
1250
99.9
184.9
66
1889
63.0
169
44
915












BB       = Berat Badan
TB      = Tinggi Badan
BTL     = Berat Tanpa Lemak
AK                  = Asupan Kalori







Jawaban :
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Tinggi Badanb
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


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

ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
326.204
1
326.204
2.327
.149b
Residual
1962.751
14
140.196


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), Tinggi 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

Model 1: BB = β + β TB
Estimasi model 1: BB = -2.492 + 0.441 TB

Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
BB Tanpa Lemakb
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.945a
.893
.886
4.1735
a. Predictors: (Constant), BB Tanpa Lemak





ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
2045.099
1
2045.099
117.411
.000b
Residual
243.855
14
17.418


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), BB Tanpa Lemak


Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-4.303
7.112

-.605
.555
BB Tanpa Lemak
1.554
.143
.945
10.836
.000
a. Dependent Variable: Berat Badan
Model 2: BB = β + β BTL
Estimasi model 2: BB = -4.303 + 1.554 BTL
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Asupan Kalorib
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


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


ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
872.301
1
872.301
8.620
.011b
Residual
1416.653
14
101.190


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), Asupan Kalori


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








Model 3: BB = β + β AK
Estimasi model 3: BB = 52.517 + 0.013 AK
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
BB Tanpa Lemak, Tinggi Badanb
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.954a
.910
.896
3.9870
a. Predictors: (Constant), BB Tanpa Lemak, Tinggi Badan


ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
2082.309
2
1041.154
65.499
.000b
Residual
206.645
13
15.896


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), BB Tanpa Lemak, Tinggi 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
BB 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
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Asupan Kalori, BB Tanpa Lemakb
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.954a
.911
.897
3.9676

a. Predictors: (Constant), Asupan Kalori, BB Tanpa Lemak

ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
2084.306
2
1042.153
66.201
.000b
Residual
204.649
13
15.742


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), Asupan Kalori, BB Tanpa Lemak


Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-2.474
6.860

-.361
.724
BB Tanpa Lemak
1.418
.162
.862
8.774
.000
Asupan Kalori
.003
.002
.155
1.578
.139
a. Dependent Variable: Berat Badan

Estimasi model 5: BB = -2.474 + 1.418 BTL + 0.003 AK
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Asupan Kalori, Tinggi Badan, BB Tanpa Lemakb
.
Enter
a. Dependent Variable: Berat Badan
b. All requested variables entered.


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, BB Tanpa Lemak


ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
2148.400
3
716.133
61.141
.000b
Residual
140.554
12
11.713


Total
2288.954
15



a. Dependent Variable: Berat Badan
b. Predictors: (Constant), Asupan Kalori, Tinggi Badan, BB Tanpa Lemak


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
BB 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

 

Uji parsial F dari hasil-hasil yang sudah didapat.
Tabel ANOVA utk BB dgn TB, BTL, dan AK:
Model
Sumber
df
Sum of Square (SS)
Mean of Square (MS)
F
r2
Regression
X1
1
326.204
326.204
27.85
0.939
X2ǀX1
1
1756.105
714.95
61.04
X3ǀX1, X2
1
66.091
-325.021
-27.75
Residual

12
140.554
11.713


TOTAL

15
2288.954




Dibawah ini adalah tabel pemilihan model estimasi yg terbaik.
No.
Model Estimasi
F
r2
1.
Y = -2.492 + 0.441 TB (0.289)*
2.327
0.143
2.
Y = -4.303 + 1.554 BTL (0.143)*
117.411
0.893
3.
Y = 52.517 + 0.013 AK (0.004)
8.620
0.381
4.
Y = -27.527 + 0.155 TB + 1.496 BTL (0.101)* (0.142)*
65.499
0.910
5.
Y = -2.474 + 1.418 BTL + 0.003 AK (0.162)* (0.002)
66.201
0.911
6.
Y = -33.412 + 0.210 TB + 1.291 BTL + 0.004 AK (0.090)* (0.150)* (0.002)
61.141
0.923
Angka dalam tanda kurung adalah standar error dari parameter
*bermakna (p<0.05)

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