Lakukan prediksi CHOL dengan variabel independent
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
Mean SS for Residual ;
e. Hitung
nilai F parsial ;
f. Hitung
nilai r2
g. Buktikan
bahwa penambahan X3 berperan dalam memprediksi Y.
Jawab :
- · HASIL SPSS MODEL 1
|
Variables Entered/Removedb
|
|||
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
Trigliserida a
|
.
|
Enter
|
|
a. All requested variables entered.
|
|
||
|
b. Dependent Variable: Cholesterol
|
|
||
|
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
|
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
|
|
|
|
|||
Model
1. CHOL ß0 + ß1 TRIG
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = 203.123
|
|
|
|
ß1 = 0.127
|
Sß1 = 0.093
|
1.850
|
Estimasi
Model 1 : CHOL = 203.123 + 0.217 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
|
|
|
|
- · HASIL SPSS MODEL 2
|
Variables Entered/Removedb
|
|||
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
Umur a
|
.
|
Enter
|
|
a. All requested variables entered.
|
|
||
|
b. Dependent Variable: Cholesterol
|
|
||
|
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
|
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
|
|
|
|
|||
Model
2. CHOL ß0 + ß1 UM
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = 204.048
|
|
|
|
ß1 = 0.445
|
Sß1 = 0.444
|
1.007
|
Estimasi
Model 2 : CHOL 204.048 + 0.445 UM
ANOVA Tabel
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
655.625
|
655.625
|
1.007
|
.023
|
|
Residual
|
24
|
27990.819
|
650.949
|
||
|
Total
|
25
|
28646.444
|
|
|
|
- · HASIL SPSS MODEL 3
|
Variables Entered/Removedb
|
|||
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
Umur Kuadrata
|
.
|
Enter
|
|
a. All requested variables entered.
|
|
||
|
b. Dependent Variable: Cholesterol
|
|
||
|
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
|
396.227
|
1
|
396.227
|
.603
|
.442a
|
|
Residual
|
28250.217
|
43
|
656.982
|
|
|
|
|
Total
|
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)
|
217.420
|
11.555
|
|
18.816
|
.000
|
|
Umur Kuadrat
|
.003
|
.004
|
.118
|
.777
|
.442
|
|
|
a. Dependent Variable: Cholesterol
|
|
|
|
|||
Model
3. CHOL ß0 + ß1 (UM)2
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = 217.420
|
|
|
|
ß1 = 0.003
|
Sß1 = 0.004
|
0.603
|
Estimasi
Model 3 : CHOL 217.420 + 0.003 (UM)2
ANOVA Tabel
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
1
|
396.227
|
396.227
|
.603
|
.014
|
|
Residual
|
43
|
28250.217
|
656.982
|
||
|
Total
|
44
|
28646.444
|
|
|
|
- · HASIL SPSS MODEL 4
|
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
|
1437.719
|
2
|
718.860
|
1.110
|
.339a
|
|
Residual
|
27208.725
|
42
|
647.827
|
|
|
|
|
Total
|
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)
|
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
4. CHOL ß0 + ß1 TRIG
+ ß2 UM
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = 192.155
|
|
|
|
ß1 = 0.108
|
Sß1 = 0.098
|
1.110
|
|
ß2 = 0.292
|
Sß2 = 0.464
|
|
Estimasi
Model 4 : CHOL 192.155 + 0.108 TRIG + 0.292 UM
ANOVA Tabel
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
2
|
1437.719
|
718.860
|
1.110
|
.050
|
|
Residual
|
42
|
27208.725
|
647.827
|
||
|
Total
|
44
|
28646.444
|
|
|
|
- · HASIL SPSS MODEL 5
|
Variables Entered/Removedb
|
|||
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
Umur Kuadrat, Trigliserida a
|
.
|
Enter
|
|
a. All requested variables entered.
|
|
||
|
b. Dependent Variable: Cholesterol
|
|
||
|
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
|
1292.618
|
2
|
646.309
|
.992
|
.379a
|
|
Residual
|
27353.826
|
42
|
651.282
|
|
|
|
|
Total
|
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)
|
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
5. CHOL ß0 + ß1 (UM)2
+ ß2 TG
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = 200.525
|
|
|
|
ß1 = 0.115
|
Sß1 = 0.098
|
0.992
|
|
ß2 = 0.002
|
Sß2 = 0.005
|
|
Estimasi
Model 5 : 200.525 + 0.115 TRIG + 0.002 UMSQ
ANOVA Tabel
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
2
|
1292.618
|
646.309
|
.992
|
.045
|
|
Residual
|
42
|
27353.826
|
651.282
|
||
|
Total
|
44
|
28646.444
|
|
|
|
- · HASIL SPSS MODEL 6
|
Variables Entered/Removedb
|
|||
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
Umur Kuadrat, Trigliserida , Umur a
|
.
|
Enter
|
|
a. All requested variables entered.
|
|
||
|
b. Dependent Variable: Cholesterol
|
|
||
|
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
|
4086.344
|
3
|
1362.115
|
2.274
|
.094a
|
|
Residual
|
24560.100
|
41
|
599.027
|
|
|
|
|
Total
|
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)
|
-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
|
|
|
|
|||
Model
6. CHOL ß0 + ß1 TRIG
+ ß2 UM + ß3 UMSQ
|
Coefficient
|
Standart Error
|
Partial F
|
|
ß0 = -21969
|
|
|
|
ß1 = .079
|
Sß1 = 0.095
|
2.274
|
|
ß2 = 9.220
|
Sß2 = 4.269
|
|
|
ß3 = -.088
|
Sß3 = 0.042
|
|
Estimasi
Model 6 : -21.969 + 0.079 TRIG + 9.220 UM – 0.088 UMSQ
ANOVA Tabel
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
|
3
|
4086.344
|
1362.115
|
2.274
|
0.143
|
|
Residual
|
41
|
24560.100
|
599.027
|
||
|
Total
|
44
|
28646.444
|
|
|
|
ANOVA
Tabel untuk CHOL dengan TRIG, UM, UMSQ
|
Sumber
|
df
|
SS
|
MS
|
F
|
r2
|
|
Regresi
X1
X2|X1
X3|X1,X2
|
1
1
1
|
1181.676
256.043
2648.625
|
1181.676
256.043
2648.625
|
1.972
0.427
4.421*
|
0.143
|
|
Residual
|
41
|
24560.100
|
599.027
|
||
|
Total
|
41
|
28646.444
|
|
|
|
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
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