Selasa, 22 November 2016

ANALISIS REGRESI PART 8


HALAMAN 153 


Latihan 1.
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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