NAMA : HARMAIDAR
NIM : 201532269
SESI : 10
Tugas halaman 153-154
Lakukan
prediksi CHOL dengan variable indepedenden TRIG,UM dan UM 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
bahwa penambahan X₃
Berperan dalam memprediksi Y
|
UM
|
CHOL
|
TGIG
|
|
40
|
218
|
194
|
|
46
|
265
|
188
|
|
69
|
197
|
134
|
|
44
|
188
|
155
|
|
41
|
217
|
191
|
|
56
|
240
|
207
|
|
48
|
222
|
155
|
|
49
|
244
|
235
|
|
41
|
190
|
167
|
|
38
|
209
|
186
|
|
36
|
208
|
179
|
|
39
|
214
|
129
|
|
59
|
238
|
220
|
|
56
|
219
|
155
|
|
44
|
214
|
201
|
|
37
|
212
|
140
|
|
40
|
244
|
132
|
|
32
|
217
|
140
|
|
56
|
227
|
279
|
|
49
|
218
|
101
|
|
50
|
241
|
213
|
|
46
|
234
|
168
|
|
52
|
231
|
242
|
|
51
|
297
|
142
|
|
46
|
230
|
240
|
|
60
|
258
|
173
|
|
47
|
243
|
175
|
|
58
|
236
|
199
|
|
66
|
193
|
201
|
|
52
|
193
|
193
|
|
55
|
319
|
191
|
|
58
|
212
|
216
|
|
41
|
209
|
154
|
|
60
|
224
|
198
|
|
50
|
184
|
129
|
|
48
|
222
|
115
|
|
49
|
229
|
148
|
|
39
|
204
|
164
|
|
40
|
211
|
104
|
|
47
|
230
|
218
|
|
67
|
230
|
239
|
|
57
|
222
|
183
|
|
50
|
213
|
190
|
|
43
|
238
|
259
|
|
55
|
234
|
156
|
1. Lakukan
prediksi CHOL dengan variabel independen TRIG, UMUR dan UMUR2
Model 1 : CHOL = β₀
+ β₁TRIG
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 203.123
|
|
1.850
|
|
β₁
= 0.127
|
.093
|
|
Estimasi model 1 : CHOL = 203.123 + 0.127 TRIG
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
1181.676
|
1181.676
|
1.850
|
.041
|
|
Residual
|
43
|
27464.768
|
638.716
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Model 2 : CHOL = β₀
+ β₂UM+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 204.048
|
|
1.007
|
|
β₁
= 0.445
|
.0444
|
|
Estimasi model : CHOL = 204.048 + 0.445 UM
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
655.625
|
655.625
|
1.007
|
.023
|
|
Residual
|
43
|
27990.819
|
650.949
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Model 3: CHOL = β₀
+ β₃(UM)²+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 217.420
|
|
0.603
|
|
β₁
= .003
|
.004
|
|
Estimasi model : CHOL = 217.420+ .003 (UM)²
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
396.227
|
396.277
|
0.603
|
.014
|
|
Residual
|
43
|
28250.217
|
656.982
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Model 4: CHOL = β₀
+ β₁ TRIG + β₂UM+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 192.155
|
|
1.110
|
|
β₁
= 0.108
|
.098
|
|
|
β₂
= 0.292
|
.464
|
|
Estimasi model : CHOL = 192.155+ 0.108+0.292UM
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
1437.719
|
718.860
|
1.110
|
.050
|
|
Residual
|
43
|
27208.725
|
647.827
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Model 5: CHOL = β₀
+ β₁TRIG+β₃(UM)²+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 200.525
|
|
.992
|
|
β₁
= .115
|
.098
|
|
|
β₃
= .002
|
.005
|
|
Estimasi model : CHOL = 200.525+.115+.002 (UM)²
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
2
|
1292.618
|
644.309
|
.992
|
.045
|
|
Residual
|
42
|
27353.826
|
651.282
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Model 6: CHOL = β₀
+ β₁TRIG+β₂ UM+β₃(UM)²+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -21.969
|
|
2.274
|
|
β₁
= .079
|
.095
|
|
|
β₂
= 9.220
|
4.269
|
|
|
β₃
= -.088
|
.042
|
|
Estimasi model : CHOL = -21.969+.079+9.220 - .088
(UM)²
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
3
|
4086.344
|
1362.115
|
2.274
|
.143
|
|
Residual
|
41
|
24560.100
|
599.027
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
Kita lakukan uji
parsial F
ANOVA tabel
untuk CHOL dengan TRIG, UM, UMSQ
|
Sumber
|
df
|
SS
|
MS
|
F
|
r²
|
|
X1
Regresi X2|X3
X3|X1,X2
|
1
1
1
|
1181.676
256.043
2648.625
|
1181.676
256.043
2648.625
|
1.972
0.427
4.421*
|
0.142
|
|
Residual
|
41
|
24560.100
|
599.027
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
*P<0,05
Berikut
ringkasan tabel analisis yang dapat membantu kita dalam pemilihan model
estimasi yang terbaik.
|
No
|
Model
Estimasi
|
F
|
r²
|
|
1
|
Y
= 203.123 + 0.127 TRIG
(.093)
|
1.850
|
.041
|
|
2
|
Y =
204.048 + 0.445 UM
(.0444)
|
1.007
|
.023
|
|
3
|
Y =
217.420+ .003 (UM)²
(.004)*
|
.603
|
.014
|
|
4
|
Y =
192.155+ 0.108+0.292UM
(.098) (.464)
|
1.110
|
.050
|
|
5
|
Y
= 200.525+.115+.002 (UM)²
(.098) (.005)
|
.992
|
.045
|
|
6
|
Y = -21.969+.079+9.220 - .088 (UM)²
(.095) (4.269)*
(.042)*
|
2.274
|
.143
|
*bermakna
p<0,05
Uji F= (1181.676/1)/
(256,043+2648,625+24560.100/41)= 1,764
(F tabel = 4,08) Hasil data
p>0,05=tidak signifikan
Dari ke enam
model estimasi terlihat bahwa variable trigliserida secara konsisten tidak
berpengaruh terhadap cholesterol (p<0,05). pada model estimasi 1 tampak
nilai r² sebesar 0,041 dan bila dibandingkan dengan model estimasi 4,5 yang
nilai naik atau turunnya tidak signifikan dengan jumlah yang tidak berarti.
namun kenaikan cukup signifikan bisa dilihat di model ke 6 dari 0,041 di model
1 naik sampai 2,274 di model ke-6.
Dengan
demikian kita bisa berkesimpulan variable trigliserida tidak memiliki pengaruh
berarti pada peningkatan kadar cholesterol, namun pada model ke enam dimana
penambahan variable um dan umsq mampu menjelaskan variasi cholesterol dan perlu
ditambahkan ke dalam model. model akhir yaitu :
Y=-21,969
+ 0,079 TRIG + 9,220 UM + -0,088 UMSQ
.
LATIHAN 2 HAL 154
|
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
|
185
|
|
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
|
2.
Lakukan prediksi BB
dengan variabel independen TB, BTL, dan AK
Model 1 : BB= β₀
+ β₁TB
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -2.492
|
|
2.327
|
|
β₁
= .441
|
.289
|
|
Estimasi model 1 : BB = -2.492 + .441 TB
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
326.204
|
326.204
|
2.327
|
.143
|
|
Residual
|
14
|
1962.751
|
140.196
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Model 2 : BB = β₀
+ β₂BTL+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -4.303
|
|
117.411
|
|
β₁
= 1.554
|
.143
|
|
Estimasi model : BB= -4.303+ 1.554 BTL
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
2045.099
|
2045.099
|
117.411
|
.893
|
|
Residual
|
14
|
243.855
|
17.418
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Model 3: BB= β₀
+ β₃AK+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= 52.517
|
|
8.620
|
|
β₁
= .013
|
.004
|
|
Estimasi model : BB = 52.517 + .013 AKL
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
872.301
|
872.301
|
8.620
|
.381
|
|
Residual
|
14
|
1216.653
|
101.190
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Model 4: BB= β₀
+ β₁ TB + β₂BTL+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -27.527
|
|
165.499
|
|
β₁
= .155
|
.101
|
|
|
β₂
= 1.496
|
.142
|
|
Estimasi model : BB= -27.527+ .155+.1496BTL
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
2
|
2082.309
|
1041.154
|
165.499
|
.910
|
|
Residual
|
13
|
206.645
|
15.896
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Model 5: BB = β₀
+ β₁TB+β₃AK+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -31.333
|
|
8.185
|
|
β₁
= .492
|
.216
|
|
|
β₃
= .014
|
.004
|
|
Estimasi model : BB = -31.333+.492+.014 AK
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
2
|
1275.821
|
637.911
|
8.185
|
.557
|
|
Residual
|
13
|
1013.133
|
77.933
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Model 6: BB= β₀
+ β₁TB+β₂ BTL+β₃AK+E
|
Coefficient
|
Standar Error
|
Partial F
|
|
β₀
= -33.412
|
|
61.141
|
|
β₁
= .210
|
.090
|
|
|
β₂
= 1.291
|
.150
|
|
|
β₃
= .004
|
.002
|
|
Estimasi model : BB = -33.412+.210+1.291 + .004
ANOVA TABEL
|
Sumber
|
Df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
3
|
2148.400
|
716.133
|
61.141
|
.939
|
|
Residual
|
12
|
140.554
|
11.713
|
|
|
|
Total
|
15
|
2288.954
|
|
|
|
Kita lakukan uji
parsial F
ANOVA tabel
untuk CHOL dengan TRIG, UM, UMSQ
|
Sumber
|
df
|
SS
|
MS
|
F
|
r²
|
|
X1
Regresi X2|X3
X3|X1,X2
|
1
1
1
|
326.204
1756.105
66.091
|
326.204
1756.105
66.091
|
29.195
157.17
5.915
|
0.142
|
|
Residual
|
41
|
140.554
|
11.173
|
|
|
|
Total
|
44
|
2288.954
|
|
|
|
*P<0.05
Ringkasan Table analisis yang bisa
memantu memilih model estimasi terbaik :
|
No.
|
Model Estimasi
|
F
|
r²
|
|
1
|
Y= -2,492 + 0,441 TB
(.289)
|
2.327
|
0,014
|
|
2
|
Y= -4,303 + 1,554 BTL
(.143)
|
117.411
|
0,893
|
|
3
|
Y=52,217 + 0,013 AK
(.004)*
|
8.620
|
0,381
|
|
4
|
Y=-27,527 + 0,155 TB + 1,496 BTL
(.101) (.142)
|
65.499
|
0,909
|
|
5
|
Y= -31,333 + 0,492 TB + 0,014 AK
(.216) (.004)
|
8.185
|
0,557
|
|
6
|
Y= -33,412 + 0,210 TB + 1,291 BTL + 0,004 AK
(.090) (.150) (.002)
|
61.141
|
0,938
|
*bermakna p<0,05
Uji F= (326,204/1)/
(1756,105+66,091+140,554/14)= 2,326
(F tabel = 4,60) Hasil data
p>0,05=tidak signifikan
Dari keenam
model estimasi terlihat bahwa variable tinggi badan secara konsisten tidak
berpengaruh terhadap berat badan (p<0,05). pada model estimasi 1 tampak
nilai r² sebesar 0,014 dan bila dibandingkan dengan model estimasi lainnya
(2,3,4,5,6) mengalami kenailam yang signifikan dengan jumlah yang cukup
berarti, Hingga di model ke 6 mencapai 0,938 dari 0,014 di model 1.
dengan
demikian kita bisa berkesimpulan variable tinggi badan tidak memiliki pengaruh
berarti pada peningkatan berat badan, namun pada model ke enam dimana
penambahan variable berat tanpa lemak dan asupan kalori mampu menjelaskan
variasi berat badan dan perlu ditambahkan ke dalam model. model akhir yaitu
:
Y= -33,412 + 0,210 TB + 1,291 BTL + 0,004AK
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