TUGAS ANALISIS REGRESI
TEMU KE 9 HALAMAN 153
- Hitung SS for Regression (X3ІX1,X2);
- Hitung SS for Residual;
- Hitung Means SS for Regression (X3ІX1,X2);
- Hitung Means SS for Residual;
- Hitung nilai F parsial;
- Hitung nilai r2;
- Buktikan bahwa penambahan X3 berperan dalam memprediksi Y.
UM
|
CHOL
|
TRIG
|
UMSQ
|
UM
|
CHOL
|
TRIG
|
UMSQ
|
UM
|
CHOL
|
TRIG
|
UMSQ
|
40
|
218
|
194
|
1600
|
37
|
212
|
140
|
1369
|
55
|
319
|
191
|
3025
|
46
|
265
|
188
|
2116
|
40
|
244
|
132
|
1600
|
58
|
212
|
216
|
3364
|
69
|
197
|
134
|
4761
|
32
|
217
|
140
|
1024
|
41
|
209
|
154
|
1681
|
44
|
188
|
155
|
1936
|
56
|
227
|
279
|
3136
|
60
|
224
|
198
|
3600
|
41
|
217
|
191
|
1681
|
49
|
218
|
101
|
2401
|
50
|
184
|
129
|
2500
|
56
|
240
|
207
|
3136
|
50
|
241
|
213
|
2500
|
48
|
222
|
115
|
2304
|
48
|
222
|
155
|
2304
|
46
|
234
|
168
|
2116
|
49
|
229
|
148
|
2401
|
49
|
244
|
235
|
2401
|
52
|
231
|
242
|
2704
|
39
|
204
|
164
|
1521
|
41
|
190
|
167
|
1681
|
51
|
297
|
142
|
2601
|
40
|
211
|
104
|
1600
|
38
|
209
|
186
|
1444
|
46
|
230
|
240
|
2116
|
47
|
230
|
218
|
2209
|
36
|
208
|
179
|
1296
|
60
|
258
|
173
|
3600
|
67
|
230
|
239
|
4489
|
39
|
214
|
129
|
1521
|
47
|
243
|
175
|
2209
|
57
|
222
|
183
|
3249
|
59
|
238
|
220
|
3481
|
58
|
236
|
199
|
3364
|
50
|
213
|
190
|
2500
|
56
|
219
|
155
|
3136
|
66
|
193
|
201
|
4356
|
43
|
238
|
259
|
1849
|
44
|
241
|
201
|
1936
|
52
|
193
|
193
|
2704
|
55
|
234
|
156
|
3025
|
Model 1. CHOL=βo+β1TRIG
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
| ||||||
Coefficient Standard Error Partial F
βo= 203,123
β1= 0,127 Sβ1= 0,093 1,865
Estimasi model 1: CHOL= 203,123+0,127 TRIG
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
1181,676
|
1
|
1181,676
|
1,850
|
,181b
|
Residual
|
27464,768
|
43
|
638,716
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), TRIGLISERIDA
| ||||||
Model 2. CHOL= βo+β1UM
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
| ||||||
Coefficient Standard Error Partial F
βo= 204,048
β1= 0,445 Sβ1= 0,444 1,007
Estimasi Model 2: CHOL= 204,048+ 0,445 UM
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
655,625
|
1
|
655,625
|
1,007
|
,321b
|
Residual
|
27990,819
|
43
|
650,949
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), UMUR
| ||||||
Model 3.CHOL = βo+β1UMSQ
Coefficientsa
| ||||||
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
| ||
B
|
Std. Error
|
Beta
| ||||
1
|
(Constant)
|
217,420
|
11,555
|
18,816
|
,000
| |
UMUR JUADRAT
|
,003
|
,004
|
,118
|
,777
|
,442
| |
a. Dependent Variable: CHOLESTEROL
| ||||||
Coefficient Standard Error Partial F
βo= 217,420
β1= 0,003 Sβ1= 0,004 0,5625
Estimasi Model 3: CHOL= 217,420+ 0,003 UMSQ
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
396,227
|
1
|
396,227
|
,603
|
,442b
|
Residual
|
28250,217
|
43
|
656,982
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), UMUR JUADRAT
| ||||||
Model 4.: CHOL = βo+β1TRIG + β2 UM
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
| ||||||
Coefficient Standard Error Partial F
βo= 192,155
β1= 0,108 Sβ1= 0,098 1,1214
β2= 0,292 Sβ2= 0,464 0,3969
Estimasi Model 4: CHOL = 192,155+0,108 TRIG + 0,292 UM
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
1437,719
|
2
|
718,860
|
1,110
|
,339b
|
Residual
|
27208,725
|
42
|
647,827
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), UMUR, TRIGLISERIDA
| ||||||
Model 5. : CHOL = βo+β1TRIG + β2 UMSQ
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 JUADRAT
|
,002
|
,005
|
,065
|
,413
|
,682
| |
a. Dependent Variable: CHOLESTEROL
| ||||||
Coefficient Standard Error Partial F
βo= 200,525
β1= 0,115 Sβ1= 0,098 1,3689
β2= 0,002 Sβ2= 0,005 0,16
Estimasi Model 5: CHOL = 200,525 +0,115 TRIG + 0,002 UMSQ
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
1292,618
|
2
|
646,309
|
,992
|
,379b
|
Residual
|
27353,826
|
42
|
651,282
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), UMUR JUADRAT, TRIGLISERIDA
| ||||||
Model 6. : CHOL = βo+β1TRIG + β2 UM + β3 UMSQ
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 JUADRAT
|
-,088
|
,042
|
-3,035
|
-2,103
|
,042
| |
a. Dependent Variable: CHOLESTEROL
| ||||||
Coefficient Standard Error Partial F
βo= -21,969
β1= 0,079 Sβ1= 0,095 0,6889
β2= 9,220 Sβ2= 4,269 4,6656
β3 = -0,088 Sβ3 = 0,042 4,42
Estimasi Model 6: CHOL = -21,969 + 0,079 TRIG + 9,220 UM – 0,088 UMSQ
ANOVAa
| ||||||
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
| |
1
|
Regression
|
4086,344
|
3
|
1362,115
|
2,274
|
,094b
|
Residual
|
24560,100
|
41
|
599,027
| |||
Total
|
28646,444
|
44
| ||||
a. Dependent Variable: CHOLESTEROL
| ||||||
b. Predictors: (Constant), UMUR JUADRAT, TRIGLISERIDA, UMUR
| ||||||
Dari ke enam model estimasi di atas kita bisa menduga model estimasi No. 6 dengan independen variable Trig, UM dan (UM)2 adalah yang terbaik bila di lihat dari besaran r2 yaitu 0.05. Namun sebaiknya kita perhatikam uraian di bawah ini.
Kita dapat memperinci nilai-nilai Sum Square of Regression dalam tabel ANOVA sebagai berikut :
Sumber
|
df
|
SS
|
MS
|
F
|
R2
|
Regresi
X1
X2 I X1
X3 I X1,X2
|
1
1
1
|
1181,676
256.043
2648.625
|
1181.676
256.043
2648.625
|
1.972
0.395
4.42
|
0.05
|
Residual
|
41
|
24560.100
|
599.027
| ||
Total
|
44
|
28646.444
|
*p<0.05
Berikut ringkasan table analisis yang dapat membantu kita dalam pemilihan model estimasi yang terbaik.
No.
|
Model Estimasi
|
F
|
r2
|
1.
|
Y = 203,123+0,127 TRIG (0,093)*
|
1,865
|
0.181
|
2.
|
Y = 204,048+ 0,445 UM (0,444)*
|
1,007
|
0,321
|
3.
|
Y = 217,420+ 0,003 UMSQ (0,004)*
|
0,5625
|
0,442
|
4.
|
Y = 192,155+0,108 TRIG + 0,292 UM
(0,098)* (0,464)
|
1,110
|
0,339
|
5.
|
Y = 200,525 +0,115 TRIG + 0,002 UMSQ
(0,098)* (0,005)
|
0,992
|
0,379
|
6.
|
Y = -21,969 + 0,079 TRIG + 9,220 UM – 0,088 UMSQ
(0,095)* (4,269) (0,042)
|
2,274
|
0,094
|
Angka dalam tanda kurung adalah Standar Error dari parameter
*bermakna (p<0.05)
Dari ke enam model estimasi terlihat bahwa variable TRIG secara konsisten sangat berpengaruh terhadap CHOL (p<0.05). Pada model estimasi 1 tampak nilai r2 sebesar 0.181 dan bila disbanding dengan model estimasi 4 dan 5 penambahan nilai r2 relatif kecil masing-masing 0.158, 0.198 ini sangat tidak berarti.
Dengan demikian kita bisa berkesimpulan variable TRIG sangat bermakna pengaruhnya terhadap CHOL. Sebaliknya penambahan variable UM dan UMSQ tidak berperan dalam menjelaskan variasi CHOL dan kita tidak perlu menambahkan kedua variable tersebut ke dalam model. Model akhir yaitu : Y = 203,123+0,127 TRIG.
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