Latihan hal. 153-154
1. Lakukan
prediksi CHOL dengan variabel independen TRIG, UM, dan UM kuadrat
a. Hitung
SS for Regression
b. Hitung
SS for Residual
c. Hitung
Means SS for Regression
d. Hitung
Means SS for Residual
e. Hitung
nilai F parsial
f. Hitung
nilai r²
g. Buktikan
bahwa penambahan
berperan dalam
memprediksi Y
JAWABAN :
Estimasi
model 1 : CHOL = 203,123 + 0,127 TRIG
|
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
|
||||||
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 203,123
β₁ = 0,127
|
Sβ₁ = 0,093
|
1,850
|
0,041
|
Estimasi
model 2 : CHOL = 204,048 + 0,445 UM
|
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
|
||||||
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 204,048
β₁ = 0,445
|
Sβ₁ = 0,444
|
1,007
|
0,023
|
Estimasi
model 3 : CHOL = 217,420 + 0,003 UMSQ
|
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
|
||||||
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 217, 420
β₁ = 0,03
|
Sβ₁ = 0,004
|
0,603
|
0,014
|
Estimasi
model 4 CHOL = 192,155 + 0,108 TRIG + 0,292 UM
|
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
|
||||||
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 192,155
β₁ = 0,108
β₂ = 0,292
|
Sβ₁ = 0,098
Sβ₂ = 0,464
|
1,110
0,629
|
0,050
|
Estimasi
model 5 : CHOL = 200,525 + 0,115 TRIG + 0,002 UMSQ
|
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
|
||||||
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 200,525
β₁ = 0,115
β₂ = 0,002
|
Sβ₁ = 0,098
Sβ₂ = 0,005
|
0,992
0,4
|
0,045
|
Estimasi
model 6 : CHOL = -21,969 + 0,079 TRIG + 9,220 UM + -0,088 UMSQ
|
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
|
|
Hasilnya :
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = -21,969
β₁ = 0,079
β₂ = 9,220
β₃ = 0,088
|
Sβ₁ = 0,095
Sβ₂ = 4,269
Sβ₃ = 0,042
|
2,274
2,159
2,095
|
0,142
|
Ringkasan table
ANOVA untuk CHOL, TRIG, UM dan UMSQ
|
Sumber
|
df
|
SS
|
MS
|
F
|
r²
|
|
X₁
Regresi 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*
|
0,142
|
|
Residual
|
41
|
24560.100
|
599.027
|
|
|
|
Total
|
44
|
28646.444
|
|
|
|
*p<0,05
Ringkasan
Table analisis yang bisa memantu memilih model estimasi terbaik :
|
No.
|
Model Estimasi
|
F
|
r²
|
|
1
|
Y=203,123 +
0,127 TRIG
(0,093)
|
1,850
|
0,041
|
|
2
|
Y= 204,048 +
0,445 UM
(0,444)
|
1.007
|
0,023
|
|
3
|
Y=217,420 +
0,003 UMSQ
(0,004)*
|
0,603
|
0,014
|
|
4
|
Y=192,155 +
0,108 TRIG + 0,292 UM
(0,098) (0,464)
|
1,110
|
0,050
|
|
5
|
Y= 200,525 +
0,115 TRIG + 0,002 UMSQ
(0,098) (0,005)
|
0,992
|
0,045
|
|
6
|
Y=-21,969 +
0,079 TRIG + 9,220 UM + -0,088 UMSQ
(0,095) (4,269)*
(0,042) *
|
2,274
|
2,274
|
*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-6 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-6 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
2. Lakukan
prediksi BB dengan variabel independen TB, BTL, dan AK
a. Hitung
SS for Regression
b. Hitung
SS for Residual
c. Hitung
Means SS for Regression
d. Hitung
Means SS for Residual
e. Hitung
nilai F parsial
f. Hitung
nilai r²
g. Buktikan
bahwa penambahan
berperan dalam
memprediksi Y
JAWABAN
Estimasi
model 1 : BB = -2,492 + 0,441 TB
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
Df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
326.204
|
1
|
326.204
|
2.327
|
.149a
|
|
Residual
|
1962.751
|
14
|
140.196
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Tinggi badan
|
||||||
|
Coefficientsa
|
||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
|
B
|
Std. Error
|
Beta
|
||||
|
1
|
(Constant)
|
-2.492
|
48.880
|
|
-.051
|
.960
|
|
Tinggi
badan
|
.441
|
.289
|
.378
|
1.525
|
.149
|
|
|
a. Dependent
Variable: Berat badan
Hasilnya :
|
||||||
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = -2,492
β₁ = 0,441
|
Sβ₁ = 48,880
|
2.327
|
0,014
|
Estimasi
model 2 : BB = -4,303 + 1,554 BTL
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
2045.099
|
1
|
2045.099
|
117.411
|
.000a
|
|
Residual
|
243.855
|
14
|
17.418
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Berat badan tanpa lemak
|
||||||
|
b. Dependent
Variable: Berat badan
|
||||||
|
Coefficientsa
|
||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
|
B
|
Std. Error
|
Beta
|
||||
|
1
|
(Constant)
|
-4.303
|
7.112
|
|
-.605
|
.555
|
|
Berat
badan tanpa lemak
|
1.554
|
.143
|
.945
|
10.836
|
.000
|
|
|
a.
Dependent Variable: Berat badan
|
||||||
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = -4,303
β₁ = 1,554
|
Sβ₁ = 0,143
|
117,411
|
0,893
|
Estimasi
model 3 : BB = 52,217 + 0,013 AK
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
872.301
|
1
|
872.301
|
8.620
|
.011a
|
|
Residual
|
1416.653
|
14
|
101.190
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Asupan kalori
|
||||||
|
b.
Dependent Variable: Berat badan
|
||||||
|
Coefficientsa
|
||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
|
B
|
Std. Error
|
Beta
|
||||
|
1
|
(Constant)
|
52.517
|
7.074
|
|
7.423
|
.000
|
|
Asupan
kalori
|
.013
|
.004
|
.617
|
2.936
|
.011
|
|
|
a.
Dependent Variable: Berat badan
|
||||||
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = 52,517
β₁ = 0,013
|
Sβ₁ = 0,004
|
8,620
|
0,381
|
Estimasi
model 4 : BB = -27,527 + 0,155 TB + 1,496 BTL
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
2082.309
|
2
|
1041.154
|
65.499
|
.000a
|
|
Residual
|
206.645
|
13
|
15.896
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Berat badan tanpa lemak, Tinggi badan
|
||||||
|
b.
Dependent Variable: Berat badan
|
||||||
|
Coefficientsa
|
||||||||||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||||||||||
|
B
|
Std. Error
|
Beta
|
||||||||||||
|
1
|
(Constant)
|
-27.527
|
16.631
|
|
-1.655
|
.122
|
||||||||
|
Tinggi
badan
|
.155
|
.101
|
.132
|
1.530
|
.150
|
|||||||||
|
Berat
badan tanpa lemak
|
1.496
|
.142
|
.910
|
10.511
|
.000
|
|||||||||
|
a. Dependent
Variable: Berat badan
|
||||||||||||||
Estimasi
model 5 : BB = -31,333 + 0,492 TB + 0,014 AK
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
Df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
1275.821
|
2
|
637.911
|
8.185
|
.005a
|
|
Residual
|
1013.133
|
13
|
77.933
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Asupan kalori, Tinggi badan
|
||||||
|
b.
Dependent Variable: Berat badan
|
||||||
|
Coefficientsa
|
||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
|
B
|
Std. Error
|
Beta
|
||||
|
1
|
(Constant)
|
-31.333
|
37.369
|
|
-.838
|
.417
|
|
Tinggi
badan
|
.492
|
.216
|
.421
|
2.275
|
.040
|
|
|
Asupan
kalori
|
.014
|
.004
|
.646
|
3.491
|
.004
|
|
|
a.
Dependent Variable: Berat badan
|
||||||
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = -31,333
β₁ = 0,492
β₂ = 0,014
|
Sβ₁ = 0,216
Sβ₂ = 0,004
|
8,185
3,5
|
0,557
|
Estimasi
model 6 : BB = -33,412 + 0,210 TB + 1,291 BTL + 0,004 AK
|
ANOVAb
|
||||||
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
2148.400
|
3
|
716.133
|
61.141
|
.000a
|
|
Residual
|
140.554
|
12
|
11.713
|
|
|
|
|
Total
|
2288.954
|
15
|
|
|
|
|
|
a.
Predictors: (Constant), Asupan kalori, Tinggi badan, Berat badan tanpa lemak
|
||||||
|
b.
Dependent Variable: Berat badan
|
||||||
|
Coefficientsa
|
||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
||
|
B
|
Std. Error
|
Beta
|
||||
|
1
|
(Constant)
|
-33.412
|
14.489
|
|
-2.306
|
.040
|
|
Tinggi
badan
|
.210
|
.090
|
.180
|
2.339
|
.037
|
|
|
Berat
badan tanpa lemak
|
1.291
|
.150
|
.785
|
8.631
|
.000
|
|
|
Asupan
kalori
|
.004
|
.002
|
.209
|
2.375
|
.035
|
|
|
a.
Dependent Variable: Berat badan
|
||||||
|
coefficients
|
Standar Error
|
Partial F
|
r²
|
|
β₀ = -33,412
β₁ = 0,210
β₂ = 1,291
β₃= 0,004
|
Sβ₁ = 0,090
Sβ₂ = 0,150
Sβ₃= 0,002
|
2,333
8,606
2
|
0,938
|
Ringkasan table
ANOVA untuk CHOL, TRIG, UM dan UMSQ
|
Sumber
|
df
|
SS
|
MS
|
F
|
r²
|
|
X₁
Regresi X₂ │X₁
X₃│X₁, X₂
|
1
1
1
|
326.204
1756,105
66,091
|
326.204
1756,105
66,091
|
2.327
63,172
58,814
|
0,142
|
|
Residual
|
14
|
140.554
|
11.713
|
|
|
|
Total
|
15
|
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
(0, .289)
|
2.327
|
0,014
|
|
2
|
Y= -4,303 + 1,554 BTL
(0, .143)
|
117.411
|
0,893
|
|
3
|
Y=52,217 + 0,013
AK
(0, .004)*
|
8.620
|
0,381
|
|
4
|
Y=-27,527 +
0,155 TB + 1,496 BTL
(0, .101) (0, .142)
|
65.499
|
0,909
|
|
5
|
Y= -31,333 + 0,492 TB + 0,014 AK
(0,
.216) (0, .004)
|
8.185
|
0,557
|
|
6
|
Y= -33,412 +
0,210 TB + 1,291 BTL + 0,004 AK
(0,
.090) (0, .150) (0,
.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 ke-6 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-6 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 +
0,004 AK
