NIM : 201532298
SESI 10
Soal 2
Lakukan prediksi CHOL
dengan variable independen 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
|
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
|
Model 1. CHOL= β0 + β1 TRIG
Model Summary
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the
Estimate
|
1
|
.203a
|
.041
|
.019
|
25.273
|
a. Predictors: (Constant), Trigliserida
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
Regression
Residual
Total
|
1181.676
|
1
|
1181.676
|
1.850
|
.181a
|
27464.768
|
43
|
638.716
|
|||
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)
Trigliserida
|
203.123
|
17.156
|
11.840
|
.000
|
|
.127
|
.093
|
.203
|
1.360
|
.181
|
a. Dependent Variable: Cholesterol
Coefficient
Standard
Error Parcial
F
β0
= 203.123
β1
= 0.127
Sβ1 = 0.093
1.850
Estimasi model 1: CHOL = 203.123 + 0.127 TRIG
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
1
|
1181.676
|
1181.676
|
1.850
|
0.041
|
Residual
|
43
|
27464.768
|
638.716
|
||
Total
|
44
|
28646.444
|
Model 2. CHOL= β0 + β1 UM
Model Summary
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the
Estimate
|
1
|
.151a
|
.023
|
.000
|
25.514
|
a. Predictors: (Constant), Umur
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
Regression
Residual
Total
|
655.625
|
1
|
655.625
|
1.007
|
.321a
|
27990.819
|
43
|
650.949
|
|||
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)
Umur
|
204.048
|
22.093
|
9.236
|
.000
|
|
.445
|
.444
|
.151
|
1.004
|
.321
|
a. Dependent Variable: Cholesterol
Coefficient
|
Standard Error
|
Parcial F
|
β0 = 204.048
β1 = 0.445
|
Sβ1 = 0.444
|
1.007
|
Estimasi model 2: CHOL = 204.048 + 0.445 UM
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
1
|
655.625
|
655.625
|
1.007
|
0.023
|
Residual
|
43
|
27990.819
|
650.949
|
||
Total
|
44
|
28646.444
|
Model 3. CHOL= β0 + β1 UMSQ
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
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
Regression
Residual
Total
|
396.227
|
1
|
396.227
|
.603
|
.442a
|
28250.217
|
43
|
656.982
|
|||
28646.444
|
44
|
a. Predictors: (Constant), Umur Kuadrat
b. Dependent Variable: Cholesterol
Coefficientsa
Model
|
Unstandardized Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|||
1
(Constant)
Umur Kuadrat
|
217.420
|
11.555
|
18.816
|
.000
|
|
.003
|
.004
|
.118
|
.777
|
.442
|
a. Dependent Variable: Cholesterol
Coefficient
Standard
Error Parcial
F
β0
= 217.420
β1
= 0.003
Sβ1 = 0.004
0.603
Estimasi model 3: CHOL = 217.420 + 0.003 UM
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
1
|
396.227
|
396.227
|
0.603
|
0.014
|
Residual
|
43
|
28250.217
|
656.982
|
||
Total
|
44
|
28646.444
|
Model 4. CHOL= β0 + β1 TRIG + β2 UM
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
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
Regression
Residual
Total
|
1437.719
|
2
|
718.860
|
1.110
|
.339a
|
27208.725
|
42
|
647.827
|
|||
28646.444
|
44
|
a. Predictors: (Constant), Umur, Trigliserida
b. Dependent Variable: Cholesterol
Coefficientsa
Model
|
Unstandardized Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|||
1
(Constant)
Trigliserida
Umur
|
192.155
|
24.554
|
7.826
|
.000
|
|
.108
|
.098
|
.173
|
1.099
|
.278
|
|
.292
|
.464
|
.099
|
.629
|
.533
|
a. Dependent Variable: Cholesterol
Coefficient
Standard
Error Parcial
F
β0
= 192.155
β1
= 0.108
Sβ1 = 0.098
1.099
β2
= 0.292
Sβ2 = 0.464
0.629
Estimasi model 4: CHOL = 192.155 + 0.108 TRIG +
0.292 UM
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
2
|
1437.719
|
718.860
|
1.110
|
0.050
|
Residual
|
42
|
27208.725
|
647.827
|
||
Total
|
44
|
28646.444
|
Model 5. CHOL= β0 + β1 TRIG + β2 UMSQ
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
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1
Regression
Residual
Total
|
1292.618
|
2
|
646.309
|
.992
|
.379a
|
27353.826
|
42
|
651.282
|
|||
28646.444
|
44
|
a. Predictors: (Constant), Umur Kuadrat,
Trigliserida
b. Dependent Variable: Cholesterol
Coefficientsa
Model
|
Unstandardized Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|||
1
(Constant)
Trigliserida
Umur Kuadrat
|
200.525
|
18.433
|
10.879
|
.000
|
|
.115
|
.098
|
.185
|
1.173
|
.247
|
|
.002
|
.005
|
.065
|
.413
|
.682
|
a. Dependent Variable: Cholesterol
Coefficient
Standard
Error Parcial
F
β0
= 200.525
β1
= 0.115
Sβ1 = 0.098
1.173
β2
= 0.002
Sβ2 = 0.005
0.413
Estimasi model 5: CHOL = 200.525 + 0.115 TRIG +
0.002 UMSQ
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
2
|
1292.618
|
646.309
|
0.992
|
0.045
|
Residual
|
42
|
27353.826
|
651.282
|
||
Total
|
44
|
28646.444
|
Model 6. CHOL= β0 + β1 TRIG + β2 UM + β3 UMSQ
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
ANOVAb
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
1 Regression
Residual
Total
|
4086.344
|
3
|
1362.115
|
2.274
|
.094a
|
24560.100
|
41
|
599.027
|
|||
28646.444
|
44
|
a. Predictors: (Constant), Umur Kuadrat,
Trigliserida, Umur b. Dependent Variable: Cholesterol
Coefficientsa
Model
|
Unstandardized Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|||
1
(Constant)
Trigliserida
Umur
Umur Kuadrat
|
-21.969
|
104.532
|
-.210
|
.835
|
|
.079
|
.095
|
.126
|
.825
|
.414
|
|
9.220
|
4.269
|
3.132
|
2.160
|
.037
|
|
-.088
|
.042
|
-3.035
|
-2.103
|
.042
|
a. Dependent Variable: Cholesterol
Coefficient
Standard
Error
Parcial
F
β0 = -21.969
β1 = 0.079
Sβ1 = 0.095
0.825
β2 = 9.220
Sβ2 = 4.269
2.160
β3 = -0.088
Sβ2 = 0.042
-2.103
Estimasi model 6: CHOL =
-21.969 + 0.079 TRIG + 9.220 UM - 0.088 UMSQ
ANOVA Tabel
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
Regression
|
3
|
4086.344
|
1362.115
|
2.274
|
0.143
|
Residual
|
41
|
24560.100
|
599.027
|
||
Total
|
44
|
28646.444
|
Dari ke enam model
estimasi diatas kita bisa menduga model estimasi no 6 dengan independen
variabel TRI, UM dan UM2 adalah yang terbaik bila dilihat dari besaran r2 yaitu 0.143, walaupun nilai r2 nya tidak terlalu besar.
Uji parsial F
ANOVA Tabel untuk TDS
dengan IMT, UM, UMSQ
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
X1
Regression X2|X1
X3|X1, X2
|
1
1
1
|
1181.676
256.043
2648.625
|
1181.676
256.043
2648.625
|
1.973
0.427
4.422*
|
0.143
|
Residual
|
41
|
24560.100
|
599.027
|
||
Total
|
44
|
28646.444
|
*p<0.05
F (X3|X1, X2)=4.422 > F1,41,0.05 =4.08,
H0 ditolak. Berarti, penambahan independen variabel
X3
bermakna dalam meningkatkan prediksi Y.
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
|
0.041
|
2
|
Y = 204.048 + 0.445 UM
(.444)
|
1.007
|
0.023
|
3
|
Y = 217.420 + 0.003 UMSQ
(.004)*
|
0.603
|
0.014
|
4
|
Y = 192.155 + 0.108 TRIG + 0.292 UM
(.098)
(.464)
|
1.110
|
0.050
|
5
|
Y = 200.525 + 0.115 TRIG + 0.002 UMSQ
(.098)
(.005)*
|
0.992
|
0.045
|
6
|
Y = -21.969 + 0.079 TRIG + 9.220 UM - 0.088
UMSQ
(.095)
(4.269)
(.042)*
|
2.274
|
0.143
|
*Bermakna (p<0.05)
Dari ke enam model
estimasi terlihat bahwa variable Trigliserida secara konsisten sangat
berpengaruh terhadap Cholesterol (p<0.05). Pada model estimasi 6 tampak
nilai r2 sebesar 0.143 dan bila dibanding dengan model
estimasi 1 sampai 5 penambahan nilai r2 relative kecil masing-
masing .041, .023, .014, .050, dan .045 atau .102, .012, .003, .093, dan .098,
ini sagat tidak
berarti.
Dengan demikian kita
bisa berkesimpulan variable UMSQ sangat bermakna pengaruhnya terhadap CHOL.
Sebaliknya penambahan variable TRIG dan UM tidak berperan dalam menjelaskan
variasi CHOL dan kita tidak perlu menambahkan kedua variable tersebut kedalam
model. Model akhir yaitu: Y = 217.420 + 0.003 UMSQ.
Soal 3
Andaikan kita memiliki data informasi sebagai
berikut: Model estimasi 1: Y = -122.345 + 6.227X
Model estimasi 2: Y = 32.901 – 3.051X + 0.1176X2
Model estimasi 3: Y = 114.621 – 10.620X +
0.3247X2 + 0.00173X3
Tabel anova
Sumber
|
df
|
SS
|
MS
|
F*
|
r2*
|
X
|
1
|
174473.96
|
174473.96
|
429.17
|
0.968
|
Regresi X2|X
|
1
|
10515.44
|
10515.44
|
25.9
|
|
X3|X, X2
|
1
|
415.19
|
415.19
|
1.02
|
|
Residual
|
15
|
6098.08
|
406.54*
|
||
Total
|
18
|
190502.93
|
*MS residual: SS
residual ÷ df residual = 6098.08 ÷ 15 = 406.54
*F = MS(X atau X2|X atau X3|X, X2) ÷ MS residual
*r2 = (SS total - SS residual) ÷ SS total
Kesimpulan: berdasarkan F (X)=429.17 > F1,15,0.05=4.54 dan F (X2|X)=429.17 > F1,15,0.05=4.54, H0 ditolak. Berarti penambahan independen variabel X dan X2 bermakna dalam meningkatkan prediksi Y, sedangkan X3 tidak.
Model terbaik: model estimasi 2 yaitu Y = 32.901 – 3.051X + 0.1176X2
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