Tugas statistik tentang regresi dan korelasi.
Data DKI Jakarta
|
IPM
|
Tingkat Kemiskinan
|
Angka Pengangguran
|
Ekspor
|
PDRB
|
|
74.80
|
13.88
|
13.10
|
5.63
|
23.86
|
|
75.10
|
16.04
|
12.58
|
5.71
|
2.50
|
|
75.40
|
18.20
|
12.06
|
6.10
|
26.36
|
|
75.80
|
20.36
|
10.25
|
7.15
|
27.85
|
|
76.10
|
22.52
|
11.89
|
8.56
|
29.52
|
|
76.30
|
24.68
|
10.93
|
10.07
|
31.28
|
|
76.60
|
26.68
|
10.01
|
11.41
|
33.29
|
|
77.10
|
29.02
|
9.39
|
13.70
|
35.37
|
|
77.30
|
31.69
|
8.96
|
11.65
|
37.14
|
|
77.60
|
33.11
|
7.70
|
15.77
|
39.56
|
|
Descriptive
Statistics
|
|||
|
|
Mean
|
Std.
Deviation
|
N
|
|
Y
|
28.6730
|
10.42495
|
10
|
|
X1
|
76.2100
|
.95038
|
10
|
|
X2
|
23.6180
|
6.56904
|
10
|
|
X3
|
10.6870
|
1.73313
|
10
|
|
X4
|
9.5750
|
3.54023
|
10
|
|
Variables
Entered/Removeda
|
|||
|
Model
|
Variables
Entered
|
Variables
Removed
|
Method
|
|
1
|
X4, X3,
X2, X1b
|
.
|
Enter
|
|
a.
Dependent Variable: Y
|
|||
|
b. All
requested variables entered.
|
|||
|
Correlations
|
||||||
|
|
Y
|
X1
|
X2
|
X3
|
X4
|
|
|
Pearson
Correlation
|
Y
|
1.000
|
.789
|
.786
|
-.746
|
.758
|
|
X1
|
.789
|
1.000
|
.998
|
-.944
|
.960
|
|
|
X2
|
.786
|
.998
|
1.000
|
-.940
|
.953
|
|
|
X3
|
-.746
|
-.944
|
-.940
|
1.000
|
-.911
|
|
|
X4
|
.758
|
.960
|
.953
|
-.911
|
1.000
|
|
|
Sig.
(1-tailed)
|
Y
|
.
|
.003
|
.004
|
.007
|
.006
|
|
X1
|
.003
|
.
|
.000
|
.000
|
.000
|
|
|
X2
|
.004
|
.000
|
.
|
.000
|
.000
|
|
|
X3
|
.007
|
.000
|
.000
|
.
|
.000
|
|
|
X4
|
.006
|
.000
|
.000
|
.000
|
.
|
|
|
N
|
Y
|
10
|
10
|
10
|
10
|
10
|
|
X1
|
10
|
10
|
10
|
10
|
10
|
|
|
X2
|
10
|
10
|
10
|
10
|
10
|
|
|
X3
|
10
|
10
|
10
|
10
|
10
|
|
|
X4
|
10
|
10
|
10
|
10
|
10
|
|
|
Model
Summaryb
|
||||||||||
|
Model
|
R
|
R Square
|
Adjusted
R Square
|
Std.
Error of the Estimate
|
Change
Statistics
|
Durbin-Watson
|
||||
|
R Square
Change
|
F Change
|
df1
|
df2
|
Sig. F
Change
|
||||||
|
1
|
.789a
|
.622
|
.320
|
8.59643
|
.622
|
2.059
|
4
|
5
|
.224
|
2.820
|
|
a. Predictors:
(Constant), X4, X3, X2, X1
|
||||||||||
|
b.
Dependent Variable: Y
|
||||||||||
|
ANOVAa
|
||||||
|
Model
|
Sum of
Squares
|
Df
|
Mean
Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
608.623
|
4
|
152.156
|
2.059
|
.224b
|
|
Residual
|
369.493
|
5
|
73.899
|
|
|
|
|
Total
|
978.115
|
9
|
|
|
|
|
|
a.
Dependent Variable: Y
|
||||||
|
b.
Predictors: (Constant), X4, X3, X2, X1
|
||||||
|
Coefficientsa
|
|||||||||||||
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
95.0% Confidence Interval for B
|
Correlations
|
Collinearity Statistics
|
||||||
|
B
|
Std. Error
|
Beta
|
Lower Bound
|
Upper Bound
|
Zero-order
|
Partial
|
Part
|
Tolerance
|
VIF
|
||||
|
1
|
(Constant)
|
-914.549
|
4130.800
|
|
-.221
|
.834
|
-11533.108
|
9704.011
|
|
|
|
|
|
|
X1
|
12.553
|
56.378
|
1.144
|
.223
|
.833
|
-132.372
|
157.478
|
.789
|
.099
|
.061
|
.003
|
349.643
|
|
|
X2
|
-.547
|
7.327
|
-.345
|
-.075
|
.943
|
-19.381
|
18.286
|
.786
|
-.033
|
-.021
|
.004
|
282.101
|
|
|
X3
|
-.013
|
5.074
|
-.002
|
-.003
|
.998
|
-13.055
|
13.029
|
-.746
|
-.001
|
-.001
|
.106
|
9.417
|
|
|
X4
|
-.043
|
3.030
|
-.014
|
-.014
|
.989
|
-7.831
|
7.745
|
.758
|
-.006
|
-.004
|
.071
|
14.011
|
|
|
a. Dependent Variable: Y
|
|||||||||||||
|
Coefficient
Correlationsa
|
||||||
|
Model
|
X4
|
X3
|
X2
|
X1
|
||
|
1
|
Correlations
|
X4
|
1.000
|
.011
|
.286
|
-.447
|
|
X3
|
.011
|
1.000
|
-.125
|
.265
|
||
|
X2
|
.286
|
-.125
|
1.000
|
-.971
|
||
|
X1
|
-.447
|
.265
|
-.971
|
1.000
|
||
|
Covariances
|
X4
|
9.179
|
.176
|
6.344
|
-76.296
|
|
|
X3
|
.176
|
25.741
|
-4.641
|
75.716
|
||
|
X2
|
6.344
|
-4.641
|
53.678
|
-400.978
|
||
|
X1
|
-76.296
|
75.716
|
-400.978
|
3178.513
|
||
|
a.
Dependent Variable: Y
|
||||||
|
Collinearity
Diagnosticsa
|
||||||||
|
Model
|
Dimension
|
Eigenvalue
|
Condition
Index
|
Variance
Proportions
|
||||
|
(Constant)
|
X1
|
X2
|
X3
|
X4
|
||||
|
1
|
1
|
4.841
|
1.000
|
.00
|
.00
|
.00
|
.00
|
.00
|
|
2
|
.153
|
5.618
|
.00
|
.00
|
.00
|
.01
|
.02
|
|
|
3
|
.004
|
33.619
|
.00
|
.00
|
.03
|
.04
|
.78
|
|
|
4
|
.001
|
68.236
|
.00
|
.00
|
.04
|
.87
|
.00
|
|
|
5
|
2.078E-007
|
4826.198
|
1.00
|
1.00
|
.94
|
.07
|
.20
|
|
|
a. Dependent
Variable: Y
|
||||||||
|
Residuals
Statisticsa
|
|||||
|
|
Minimum
|
Maximum
|
Mean
|
Std.
Deviation
|
N
|
|
Predicted
Value
|
16.4364
|
40.7049
|
28.6730
|
8.22343
|
10
|
|
Residual
|
-16.52419
|
7.42362
|
.00000
|
6.40740
|
10
|
|
Std.
Predicted Value
|
-1.488
|
1.463
|
.000
|
1.000
|
10
|
|
Std.
Residual
|
-1.922
|
.864
|
.000
|
.745
|
10
|
|
a.
Dependent Variable: Y
|
|||||
Tugas
Statistik
Dari hasil
studi pustaka dan laporan diperoleh hasil berikut
IPM Tingkat Kemiskinan Angka Pengangguran Ekspor PDRB
(X1) (X2) (X3) (X4) (Y)
Pertanyaan
:
a. Tentukan
besarnya a, b1, b2, b3, dan b4
Kemudian
masukan ke dalam persamaan Y = a+b1X1+b2X2+b3X3+b4X4
b. Variable
apa yang berpengaruh dominan terhadap PDRB
c. Apakah
variabel-variabel tersebut berpengaruh dominan baik secara simultan maupun
parsial
Jawaban
:
a.
a
= -914,549
b1
= 12,553
b2
= -0,547
b3
= -0,013
b4
= -0,043
Y
= -914,549 + 12,553X1 + -0,547X2 + -0,013X3 + -0,043X4
a
= -914,549, artinya nilai PDRB tidak ada karena terkena pengaruh dari IPM,
tingkat kemiskinan, angka pengangguran, dan ekspor.
b.
Indeks
Pembangunan Manusia
X1
--> b1 > b2,b3,b4
Karena
Indeks Pembangunan Manusia karena IPM mempunyai nilai yang lebih besar daripada
tingkat kemiskinan, angka pengangguran, dan ekspor.
c.
- simultan
Fhitung Ftabel
2,059 < 5,1922
Fhitung lebih kecil dari Ftabel sehingga
Ho diterima, Hi ditolak.
-parsial
thitung ttabel
X1
thitung < ttabel
0,233 < 2,015
thitung lebih kecil ttabel sehingga Ho
diterima, Hi ditolak.
X2
thitung < ttabel
-0,075 < 2,015
thitung lebih kecil ttabel sehingga Ho
diterima, Hi ditolak.
X3
thitung < ttabel
-0,003 < 2,015
thitung lebih kecil ttabel sehingga Ho
diterima, Hi ditolak.
X4
thitung < ttabel
-0,014 < 2,015
thitung lebih kecil ttabel sehingga Ho
diterima, Hi ditolak.
r = 0,789, artinya, ada korelasi sangat kuat antara
IPM, tingkat kemiskinan, angka pengangguran dan ekspor terhadap PDRB.
R2 = 0,622, artinya, kontribusi IPM,
tingkat kemiskinan, angka pengangguran, dan ekspor terhadap persamaan regresi
sebesar 62%, sedangkan 38% kontribusi dari PDRB.
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