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 lakukan uji parsial F seperti
berikut (berdasarkan hasil-hasil yang sudah kita lakukan diatas)
ANOVA Tabeluntuk TRIG dengan IMT
dan UM , 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 untuk penambahan independent variabel X3 = 0.00966 < F 4.02
ini berarti hipotesa H0 : β3 = 0 diterima atau
gagal ditolak artinya penambahan third order ( X 3) tidak secara
bermakna dapat memprediksi Y.
Kita
bersimpulan bahwa :
a. Penambahan
“ second order” sesuai (fit) dengannilai
r2 = 0.021
b. Penambahan
nilai r2 menjadi0.900 pada “ thind order” hanya sebesar 0879 adalah kecil
c. Kurva yang ada cukup
diterangkan dengan “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
lakukanujiparsial F sepertiberikut (berdasarkanhasil-hasil yang sudah kita lakukan diatas)
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, maka 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