Contoh Soal Statistik Regresi Korelasi U
SOAL:
Diketahui: Data Sebagai Berikut…
NO
1
2
3
4
5
6
7
8
9
10
Tinggi Badan ( cm ) X
168
173
162
157
160
165
163
170
168
164
Berat Badan ( KG ) Y
63
81
54
49
52
62
56
78
64
61
Ditanya:
-Tentukan Nilai Koefisien Korelasi dan Regresi
-Apakah Nilai Koefisien Signifikan atau Tidak
Jawab:
-Nilai Koefisien Korelasi dan Regresin Menggunakan SPSS
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT Y
/METHOD=ENTER X.
-
Regression
Notes
Output Created
15-Mar-2014 22:56:04
Comments
Input
Active Dataset
DataSet1
Filter
Weight
Split File
N of Rows in Working Data
10
File
Missing Value Handling
Definition of Missing
User-defined missing values are treated
as missing.
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 1
Cases Used
Statistics are based on cases with no
missing values for any variable used.
Syntax
REGRESSION
/DESCRIPTIVES MEAN STDDEV
CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI R
ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT Y
/METHOD=ENTER X.
Resources
Processor Time
00:00:00.156
Elapsed Time
00:00:00.100
Memory Required
1372 bytes
Additional Memory Required
0 bytes
for Residual Plots
[DataSet1]
Descriptive Statistics
Mean
Std. Deviation
N
Y
62.00
10.499
10
X
165.00
4.830
10
Correlations
Y
Pearson Correlation
Sig. (1-tailed)
N
X
Y
1.000
.946
X
.946
1.000
Y
.
.000
X
.000
.
Y
10
10
X
10
10
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 2
Variables Entered/Removed
b
Variables
Model
Variables Entered
1
X
Removed
a
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: Y
Model Summary
Model
R
Std. Error of the
Square
Estimate
R Square
a
1
Adjusted R
.946
.896
.883
Change Statistics
R Square Change
3.594
F Change
.896
df1
68.814
df2
1
Sig. F Change
8
.000
a. Predictors: (Constant), X
b
ANOVA
Model
1
Sum of Squares
df
Mean Square
Regression
888.686
1
888.686
Residual
103.314
8
12.914
Total
992.000
9
F
Sig.
a
68.814
.000
a. Predictors: (Constant), X
b. Dependent Variable: Y
Coefficients
a
Standardized
Unstandardized Coefficients
Model
1
B
(Constant)
X
a.
Std. Error
-277.429
40.933
2.057
.248
Coefficients
Beta
95% Confidence Interval for B
t
.946
Sig.
Lower Bound
Upper Bound
-6.778
.000
-371.821
-183.036
8.295
.000
1.485
2.629
Dependent Variable: Y
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 3
CORRELATIONS
/VARIABLES=X Y
/PRINT=TWOTAIL NOSIG
/MISSING=PAIRWISE.
-
Correlations
Notes
Output Created
16-Mar-2014 01:00:09
Comments
Input
Active Dataset
DataSet1
Filter
Weight
Split File
N of Rows in Working Data
10
File
Missing Value Handling
Definition of Missing
User-defined missing values are
treated as missing.
Cases Used
Statistics for each pair of variables are
based on all the cases with valid data
for that pair.
Syntax
CORRELATIONS
/VARIABLES=X Y
/PRINT=TWOTAIL NOSIG
/MISSING=PAIRWISE.
Resources
Processor Time
00:00:00.032
Elapsed Time
00:00:00.023
[DataSet1]
Correlations
X
X
Pearson Correlation
Y
1
Sig. (2-tailed)
N
Y
Pearson Correlation
Sig. (2-tailed)
N
**
.946
.000
10
10
**
1
.946
.000
10
10
**. Correlation is significant at the 0.01 level (2-tailed).
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 4
Untuk Penghitungan Manual Sebagai Berikut:
-
Nilai Koefisien Korelasi
NO
Xi
Yi
Xi²
Yi²
Xi.Yi
1
168
63
28224 3969 10584
2
173
81
29929 6561 14013
3
162
54
26244 2916
8748
4
157
49
24649 2401
7693
5
160
52
25600 2704
8320
6
165
62
27225 3844 10230
7
163
56
26569 3136
9128
8
170
78
28900 6084 13260
9
168
64
28224 4096 10752
10
164
61
26896 3721 10004
Jumlah 1650 620 272460 39432 102732
Ket: x adalah Tinggi Badan
Y adalah Berat Badan
Berdasarkan Tingkat Hubungan Nilai r
Maka: “Terdapat Hubungan Korelasi Yang Sangat Kuat Antara Tinggi Badan dan Berat Badan
Dengan Arah Positif”
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 5
-
Hipotesis Statistik
Ho: ρxy = 0 (Tidak terdapat hubungan antara tinggi badan dan berat badan)
H1: ρxy ≠ 0 (Terdapat hubungan antara tinggi badan dan berat badan)
Dari tabel t dengan α = 0,05
Diperoleh ttab = t0.025;df=8 = 2,306
Kriteria uji: Karena
( ) α = 0,025 dan df = n-2
df = 10 – 2 = 8
= 8,295> ttab = 2,306 maka Ho ditolak
Kesimpulan: “Bahwa Berat Badan Berpengaruh Signifikan Terhadap Berat Badan”.
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 6
Diketahui: Data Sebagai Berikut…
NO
1
2
3
4
5
6
7
8
9
10
Tinggi Badan ( cm ) X
168
173
162
157
160
165
163
170
168
164
Berat Badan ( KG ) Y
63
81
54
49
52
62
56
78
64
61
Ditanya:
-Tentukan Nilai Koefisien Korelasi dan Regresi
-Apakah Nilai Koefisien Signifikan atau Tidak
Jawab:
-Nilai Koefisien Korelasi dan Regresin Menggunakan SPSS
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI R ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT Y
/METHOD=ENTER X.
-
Regression
Notes
Output Created
15-Mar-2014 22:56:04
Comments
Input
Active Dataset
DataSet1
Filter
Weight
Split File
N of Rows in Working Data
10
File
Missing Value Handling
Definition of Missing
User-defined missing values are treated
as missing.
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 1
Cases Used
Statistics are based on cases with no
missing values for any variable used.
Syntax
REGRESSION
/DESCRIPTIVES MEAN STDDEV
CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI R
ANOVA CHANGE
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT Y
/METHOD=ENTER X.
Resources
Processor Time
00:00:00.156
Elapsed Time
00:00:00.100
Memory Required
1372 bytes
Additional Memory Required
0 bytes
for Residual Plots
[DataSet1]
Descriptive Statistics
Mean
Std. Deviation
N
Y
62.00
10.499
10
X
165.00
4.830
10
Correlations
Y
Pearson Correlation
Sig. (1-tailed)
N
X
Y
1.000
.946
X
.946
1.000
Y
.
.000
X
.000
.
Y
10
10
X
10
10
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 2
Variables Entered/Removed
b
Variables
Model
Variables Entered
1
X
Removed
a
Method
. Enter
a. All requested variables entered.
b. Dependent Variable: Y
Model Summary
Model
R
Std. Error of the
Square
Estimate
R Square
a
1
Adjusted R
.946
.896
.883
Change Statistics
R Square Change
3.594
F Change
.896
df1
68.814
df2
1
Sig. F Change
8
.000
a. Predictors: (Constant), X
b
ANOVA
Model
1
Sum of Squares
df
Mean Square
Regression
888.686
1
888.686
Residual
103.314
8
12.914
Total
992.000
9
F
Sig.
a
68.814
.000
a. Predictors: (Constant), X
b. Dependent Variable: Y
Coefficients
a
Standardized
Unstandardized Coefficients
Model
1
B
(Constant)
X
a.
Std. Error
-277.429
40.933
2.057
.248
Coefficients
Beta
95% Confidence Interval for B
t
.946
Sig.
Lower Bound
Upper Bound
-6.778
.000
-371.821
-183.036
8.295
.000
1.485
2.629
Dependent Variable: Y
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 3
CORRELATIONS
/VARIABLES=X Y
/PRINT=TWOTAIL NOSIG
/MISSING=PAIRWISE.
-
Correlations
Notes
Output Created
16-Mar-2014 01:00:09
Comments
Input
Active Dataset
DataSet1
Filter
Weight
Split File
N of Rows in Working Data
10
File
Missing Value Handling
Definition of Missing
User-defined missing values are
treated as missing.
Cases Used
Statistics for each pair of variables are
based on all the cases with valid data
for that pair.
Syntax
CORRELATIONS
/VARIABLES=X Y
/PRINT=TWOTAIL NOSIG
/MISSING=PAIRWISE.
Resources
Processor Time
00:00:00.032
Elapsed Time
00:00:00.023
[DataSet1]
Correlations
X
X
Pearson Correlation
Y
1
Sig. (2-tailed)
N
Y
Pearson Correlation
Sig. (2-tailed)
N
**
.946
.000
10
10
**
1
.946
.000
10
10
**. Correlation is significant at the 0.01 level (2-tailed).
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 4
Untuk Penghitungan Manual Sebagai Berikut:
-
Nilai Koefisien Korelasi
NO
Xi
Yi
Xi²
Yi²
Xi.Yi
1
168
63
28224 3969 10584
2
173
81
29929 6561 14013
3
162
54
26244 2916
8748
4
157
49
24649 2401
7693
5
160
52
25600 2704
8320
6
165
62
27225 3844 10230
7
163
56
26569 3136
9128
8
170
78
28900 6084 13260
9
168
64
28224 4096 10752
10
164
61
26896 3721 10004
Jumlah 1650 620 272460 39432 102732
Ket: x adalah Tinggi Badan
Y adalah Berat Badan
Berdasarkan Tingkat Hubungan Nilai r
Maka: “Terdapat Hubungan Korelasi Yang Sangat Kuat Antara Tinggi Badan dan Berat Badan
Dengan Arah Positif”
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 5
-
Hipotesis Statistik
Ho: ρxy = 0 (Tidak terdapat hubungan antara tinggi badan dan berat badan)
H1: ρxy ≠ 0 (Terdapat hubungan antara tinggi badan dan berat badan)
Dari tabel t dengan α = 0,05
Diperoleh ttab = t0.025;df=8 = 2,306
Kriteria uji: Karena
( ) α = 0,025 dan df = n-2
df = 10 – 2 = 8
= 8,295> ttab = 2,306 maka Ho ditolak
Kesimpulan: “Bahwa Berat Badan Berpengaruh Signifikan Terhadap Berat Badan”.
FRANDIKA SEPTA (TUGAS REGRESI DAN KORELASI MENGGUNAKAN SPSS)
[email protected] || http://www.frandika-septa.blogspot.com
Page 6