LATIHAN
Soal 1
Lakukan prediksi TRI dengan
variabel independen IMT, Umur dan Umur Kuadrat
Bekerja bersama di laboratorium
a.
Lakukan analisa regresi masing-masing independent variable
b.
Hitung SS for Regression (X3│X1, X2)
c.
Hitung SS for Residual
d.
Hitung Means SS for Regression (X3│X1,
X2)
e.
Hitung Means SS for Residual
f.
Hitung nilai F parsial
g.
Hitung nilai r2
h.
Buktikan penambahan X3 berperan dalam memprediksi Y
TRI
|
IMT
|
UM
|
TRI
|
IMT
|
UM
|
TRI
|
IMT
|
UM
|
135
|
28
|
45
|
230
|
32
|
41
|
136
|
31
|
49
|
101
|
37
|
52
|
146
|
29
|
54
|
139
|
28
|
47
|
57
|
37
|
60
|
160
|
36
|
48
|
124
|
23
|
44
|
56
|
46
|
64
|
186
|
39
|
59
|
138
|
40
|
51
|
113
|
41
|
64
|
138
|
36
|
56
|
150
|
35
|
54
|
42
|
30
|
50
|
160
|
34
|
49
|
142
|
30
|
46
|
84
|
32
|
57
|
142
|
34
|
56
|
145
|
37
|
58
|
186
|
33
|
53
|
153
|
32
|
50
|
149
|
33
|
54
|
164
|
30
|
48
|
139
|
28
|
43
|
128
|
29
|
43
|
205
|
38
|
63
|
170
|
41
|
63
|
155
|
39
|
62
|
TRI = Trigliserida, IMT =
Indeks Massa Tubuh, UM = Umur
Jawaban
ESTIMASI
MODEL 1 : TRIG = 167.677 - 0.792 IMT
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
df
|
Mean
Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
601.667
|
1
|
601.667
|
.371
|
.547a
|
||||||
Residual
|
48697.302
|
30
|
1623.243
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), indeksmassatubuh
|
|
|
||||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
167.677
|
46.066
|
|
3.640
|
.001
|
||||||
indeksmassatubuh
|
-.792
|
1.300
|
-.110
|
-.609
|
.547
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|
||||||||
ESTIMASI
MODEL 2 : TRIG = 149.943 - 0.177 UMUR
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
Df
|
Mean
Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
212.189
|
1
|
212.189
|
.130
|
.721a
|
||||||
Residual
|
49086.780
|
30
|
1636.226
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), umur
|
|
|
|
|
||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
149.943
|
28.605
|
|
5.242
|
.000
|
||||||
umur
|
-.177
|
.492
|
-.066
|
-.360
|
.721
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|||||||||
ESTIMASI
MODEL 3 : TRIG = 142.230 + 0.000 UMUR KUADRAT
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
df
|
Mean
Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
85.385
|
1
|
85.385
|
.052
|
.821a
|
||||||
Residual
|
49213.584
|
30
|
1640.453
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), umurkuadrat
|
|
|
|
|||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
142.230
|
12.226
|
|
11.634
|
.000
|
||||||
umurkuadrat
|
.000
|
.003
|
-.042
|
-.228
|
.821
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|||||||||
ESTIMASI
MODEL 4 :167.688 - 0.784 IMT - 0.005 UMUR
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
df
|
Mean
Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
601.777
|
2
|
300.889
|
.179
|
.837a
|
||||||
Residual
|
48697.191
|
29
|
1679.213
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), umur, indeksmassatubuh
|
|
|
||||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
167.688
|
46.872
|
|
3.578
|
.001
|
||||||
indeksmassatubuh
|
-.784
|
1.628
|
-.109
|
-.482
|
.634
|
|||||||
umur
|
-.005
|
.613
|
-.002
|
-.008
|
.994
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|
||||||||
ESTIMASI MODEL 5 :168.623 - 0.841 IMT + 0.000 UMUR KUADRAT
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
609.613
|
2
|
304.806
|
.182
|
.835a
|
||||||
Residual
|
48689.356
|
29
|
1678.943
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), umurkuadrat, indeksmassatubuh
|
|
|
||||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
168.623
|
48.827
|
|
3.453
|
.002
|
||||||
indeksmassatubuh
|
-.841
|
1.505
|
-.117
|
-.559
|
.581
|
|||||||
umurkuadrat
|
.000
|
.003
|
.014
|
.069
|
.946
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|
||||||||
ESTIMASI
MODEL 6 :214.510 - 0.107 IMT - 1.886 UMUR + 0.010
UMUR KUADRAT
ANOVAb
|
||||||||||||
Model
|
Sum of
Squares
|
df
|
Mean
Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
1002.559
|
3
|
334.186
|
.194
|
.900a
|
||||||
Residual
|
48296.409
|
28
|
1724.872
|
|
|
|||||||
Total
|
49298.969
|
31
|
|
|
|
|||||||
a. Predictors: (Constant), umurkuadrat, indeksmassatubuh, umur
|
|
|||||||||||
b. Dependent Variable: trigliserida
|
|
|
|
|||||||||
Coefficientsa
|
||||||||||||
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
||||||||
B
|
Std.
Error
|
Beta
|
||||||||||
1
|
(Constant)
|
214.510
|
108.129
|
|
1.984
|
.057
|
||||||
indeksmassatubuh
|
-.107
|
2.166
|
-.015
|
-.050
|
.961
|
|||||||
umur
|
-1.886
|
3.951
|
-.699
|
-.477
|
.637
|
|||||||
umurkuadrat
|
.010
|
.022
|
.653
|
.482
|
.634
|
|||||||
a. Dependent Variable: trigliserida
|
|
|
|
|
||||||||
Kita lakukanujiparsial
F sepertiberikut (berdasarkanhasil-hasil yang sudahkitalakukandiatas)
ANOVA Tabeluntuk TRIG
dengan IMT danUM , UMSQ
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
X1
|
1
|
601.667
|
601.667
|
0.34881
|
0.900
|
Regresi X2│X1
|
1
|
1.00018
|
1.00018
|
0.00058
|
|
X3│X1, X2
|
1
|
1.66600
|
1.66600
|
0.00966
|
|
Residual
|
28
|
48296.409
|
1724.872
|
|
|
Total
|
31
|
49298.969
|
|
|
Nilai
F untukpenambahan independent variabel X3 = 0.00966 < F 4.02
iniberartihipotesa H0 : β3 = 0
diterimaataugagalditolakartinyapenambahan third order ( X 3)
tidaksecarabermaknadapatmemprediksi Y.
Kita
bersimpulanbahwa :
a. Penambahan
“ second order” sesuai (fit) dengannilai
r2 = 0.021
b. Penambahannilai
r2 menjadi0.900 pada “ thind order” hanyasebesar 0879
adalahkecil
c. Kurva yang
adacukupditerangkandengan “second order”
Soal 2.
Lakukan prediksi CHOL dengan variabel independen TRIGLI,
UM, dan UM kuadrat
Bekerja bersama di laboratorium
a.
Lakukan analisa regresi masing-masing independent variable
b.
Hitung SS for Regression (X3│X1, X2)
c.
Hitung SS for Residual
d.
Hitung Means SS for Regression (X3│X1,
X2)
e.
Hitung Means SS for Residual
f.
Hitung nilai F parsial
g.
Hitung nilai r2
h.
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 :
ESTIMASI
MODEL 1 : CHOL = 203.123 + 0.127 TRIG
ANOVAb
|
||||||||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|||||||
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
|
|
|
|
|||||||||
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
|
|
|
|
|||||||||
ESTIMASI
MODEL 2 :CHOL = 204.048 + 0.445 UMUR
ANOVAb
|
||||||||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|||||||
1
|
Regression
|
655.625
|
1
|
655.625
|
1.007
|
.321a
|
||||||
Residual
|
27990.819
|
43
|
650.949
|
|
|
|||||||
Total
|
28646.444
|
44
|
|
|
|
|||||||
a.
Predictors: (Constant), umur
|
|
|
|
|
||||||||
b.
Dependent Variable: cholesterol
|
|
|
|
|||||||||
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
|
|
|
|
|||||||||
ESTIMASI
MODEL 3 : CHOL = 217.420 + 0.003 UMQS
ANOVAb
|
||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
396.227
|
1
|
396.227
|
.603
|
.442a
|
Residual
|
28250.217
|
43
|
656.982
|
|
|
|
Total
|
28646.444
|
44
|
|
|
|
|
a.
Predictors: (Constant), umurkuadrat
|
|
|
|
|||
b.
Dependent Variable: cholesterol
|
|
|
|
Coefficientsa
|
||||||
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
B
|
Std. Error
|
Beta
|
||||
1
|
(Constant)
|
217.420
|
11.555
|
|
18.816
|
.000
|
umurkuadrat
|
.003
|
.004
|
.118
|
.777
|
.442
|
|
a.
Dependent Variable: cholesterol
|
|
|
|
ESTIMASI
MODEL 4 : CHOL = 192.155 + 0.292 UM + 0.108 TRIG
ANOVAb
|
||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
1437.719
|
2
|
718.860
|
1.110
|
.339a
|
Residual
|
27208.725
|
42
|
647.827
|
|
|
|
Total
|
28646.444
|
44
|
|
|
|
|
a.
Predictors: (Constant), trigliserida, umur
|
|
|
|
|||
b.
Dependent Variable: cholesterol
|
|
|
|
Coefficientsa
|
||||||
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
B
|
Std. Error
|
Beta
|
||||
1
|
(Constant)
|
192.155
|
24.554
|
|
7.826
|
.000
|
Umur
|
.292
|
.464
|
.099
|
.629
|
.533
|
|
trigliserida
|
.108
|
.098
|
.173
|
1.099
|
.278
|
|
a.
Dependent Variable: cholesterol
|
|
|
|
ESTIMASI
MODEL 5 : CHOL = -25.670 + 9.838 UM - 0.093 UMQS
ANOVAb
|
||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
3678.335
|
2
|
1839.167
|
3.094
|
.056a
|
Residual
|
24968.110
|
42
|
594.479
|
|
|
|
Total
|
28646.444
|
44
|
|
|
|
|
a.
Predictors: (Constant), umurkuadrat, umur
|
|
|
||||
b.
Dependent Variable: cholesterol
|
|
|
|
Coefficientsa
|
||||||
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
T
|
Sig.
|
||
B
|
Std. Error
|
Beta
|
||||
1
|
(Constant)
|
-25.670
|
104.039
|
|
-.247
|
.806
|
umur
|
9.838
|
4.187
|
3.342
|
2.350
|
.024
|
|
umurkuadrat
|
-.093
|
.041
|
-3.207
|
-2.255
|
.029
|
|
a.
Dependent Variable: cholesterol
|
|
|
|
ESTIMASI
MODEL 6 : CHOL = -21.969 + 9.220 UM + 0.079 TRIG - 0.088
UMQS
ANOVAb
|
||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
4086.344
|
3
|
1362.115
|
2.274
|
.094a
|
Residual
|
24560.100
|
41
|
599.027
|
|
|
|
Total
|
28646.444
|
44
|
|
|
|
|
a.
Predictors: (Constant), umurkuadrat, trigliserida, umur
|
|
|
||||
b.
Dependent Variable: cholesterol
|
|
|
|
Coefficientsa
|
||||||
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
T
|
Sig.
|
||
B
|
Std. Error
|
Beta
|
||||
1
|
(Constant)
|
-21.969
|
104.532
|
|
-.210
|
.835
|
umur
|
9.220
|
4.269
|
3.132
|
2.160
|
.037
|
|
trigliserida
|
.079
|
.095
|
.126
|
.825
|
.414
|
|
umurkuadrat
|
-.088
|
.042
|
-3.035
|
-2.103
|
.042
|
|
a.
Dependent Variable: cholesterol
|
|
|
|
Kita lakukan ujiparsial F sepertiberikut
(berdasarkanhasil-hasil yang sudahkitalakukandiatas)
ANOVA Tabeluntuk TRIG dengan CHOL danUM , UMSQ
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
X1
|
1
|
1181.676
|
1181.676
|
1.97266
|
0.143
|
Regresi X2│X1
|
1
|
1.21668
|
1.21668
|
0.00203
|
|
X3│X1, X2
|
1
|
2.84224
|
2.84224
|
0.00474
|
|
Residual
|
41
|
24560.100
|
599.027
|
||
Total
|
44
|
28646.444
|
Nilai F
untukpenambahan independent variabel X3 = 0.00474 < F 4.08 iniberartihipotesa H0 : β3
= 0 diterimaataugagalditolakartinyapenambahan third order ( X 3)
tidaksecarabermaknadapatmemprediksi Y.
Kita
bersimpulanbahwa :
a.
Penambahan “ second order” sesuai
(fit) dengannilai r2 = 0.128
b.
Penambahannilai r2 menjadi0.143 pada “ thind
order” hanyasebesar 0.015 adalahkecil
c.
Kurva yang adacukupditerangkandengan “second order”
Soal 3
Andaikan kita
memiliki data informasi sebagai berikut :
Model estimasi 1 :
Y = - 122.345 + 6.227 X
Model estimasi 2 :
Y = 32.901 – 3.051 X + 0.1176 X2
Model estimasi 3 :
Y = 114.621 – 10.620 X + 0.3247 X2 + 0.00173 X3
Source
|
df
|
SS
|
MS
|
F
|
X
|
1
|
174,473.96
|
174.473,96
|
942.88
|
Regresi X2│X
|
1
|
10,515.44
|
10,515,44
|
25,8658
|
X3│X1,
X2
|
1
|
415.19
|
415,19
|
1,02128
|
Residual
|
15
|
6098.08
|
406,539
|
|
Total
|
18
|
190,502.93
|
1.
Lengkapi tabel
Anova diatas
2.
Tentukan besaran r2
untuk ketiga model estimasi dan buat kesimpulannya
3.
Hitung nilai F
untuk ketiga model estimasi dan buat kesimpulannya
4.
Tentukan model yang
terbaik dari ketiganya
Jawaban :
Model
regresi :
Model
estimasi1 : Y = - 122.345 + 6.227 X
Model
estimasi2 : Y = 32.091 – 3.051 X + 0.1176 X2
Model
estimasi3 : Y = 114.621 – 10.620 X + 0.3247 X2 + 0.00173 X3
Jawaban
:
1. Nilai
r2 1 :
2. Nilai
r2 2 :
3. Nilai
r2 3 :
4. Nilai
F model
estimasi 1: 942.64 > F tabel 4.54, maka kesimpulan perubahan penambahan independen variabel X secara bermakna meningkatkan prediksi Y.
5. Nilai
F model estimasi 2
: 25.87 > F tabel 4.54, mak kesimpulan perubahan penambahan independen variabel X2 secara bermakna meningkatkan prediksi Y.
6. Nilai
F model estimasi 3
: 1.02 > F tabel 4.54, maka kesimpulan perubahan penambahan independen variabel X tidak secara bermakna meningkatkan prediksi Y.
7. Model
yang terbaik Y = -122.345 + 6.227 X