Selasa, 17 Januari 2017

TUGAS ANALISIS REGRESI TEMU 13

NAMA : YESINTA VILIANTI
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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