Menghitung Regresi Linier Berganda 3 Prediktor
Menghitung Regresi Linier Berganda 3 Prediktor
Disusun Oleh :
Laila Majda 202101041337
MAHASISWA SEMESTER II
MAGISTER TEKNOLOGI PENDIDIKAN
SEKOLAH
PASCASARJANA UIKA BOGOR
TAHUN 2021
LATIHAN SOAL Halaman 270
Uji hipotesis pengaruh X1 , X2 , X3
terhadap Y baik secara Bersama-sama maupun parsial dari data berikut :
|
X12 |
X2 |
X3 |
Y |
|
4 |
5 |
8 |
7 |
|
7 |
6 |
7 |
9 |
|
7 |
8 |
9 |
12 |
|
6 |
12 |
10 |
8 |
|
9 |
11 |
13 |
15 |
|
9 |
14 |
17 |
16 |
|
5 |
6 |
9 |
12 |
|
8 |
10 |
12 |
13 |
1.
Tentukan R1 , R2 , R3
, Y
2.
Tentukan Persamaan Garis Regresinya
Jawaban Soal
Tabel 1.1 Tabel
Penolong
|
Resp |
X1 |
X2 |
X3 |
Y |
X12 |
X22 |
X32 |
Y2 |
X1Y |
X2 Y |
X3Y |
X1 X2 |
X1 X3 |
X2 X3 |
|
1 |
4 |
5 |
8 |
7 |
16 |
25 |
64 |
49 |
28 |
35 |
56 |
20 |
32 |
40 |
|
2 |
7 |
6 |
7 |
9 |
49 |
36 |
49 |
81 |
63 |
54 |
63 |
42 |
49 |
42 |
|
3 |
7 |
8 |
9 |
12 |
49 |
64 |
81 |
144 |
84 |
96 |
108 |
56 |
63 |
72 |
|
4 |
6 |
12 |
10 |
8 |
36 |
144 |
100 |
64 |
48 |
96 |
80 |
72 |
60 |
120 |
|
5 |
9 |
11 |
13 |
15 |
81 |
121 |
169 |
225 |
135 |
165 |
195 |
99 |
117 |
143 |
|
6 |
9 |
14 |
17 |
16 |
81 |
196 |
289 |
256 |
144 |
224 |
272 |
126 |
153 |
238 |
|
7 |
5 |
6 |
9 |
12 |
25 |
36 |
81 |
144 |
60 |
72 |
108 |
30 |
45 |
54 |
|
8 |
8 |
10 |
12 |
13 |
64 |
100 |
144 |
169 |
104 |
130 |
156 |
80 |
96 |
120 |
|
∑ |
55 |
72 |
85 |
92 |
401 |
722 |
977 |
1132 |
666 |
872 |
1038 |
525 |
615 |
829 |
1.
Langkah – Langkah menentukan R1
, R2 , R3 , Y.
a.
Dari table 1.1 diperoleh data sebagai
berikut :
∑ X1 = 55 ∑
X12 = 401 ∑ X1Y = 666 ∑ X1 X2 = 525
∑ X2 = 72 ∑ X22 = 722 ∑ X2Y = 872 ∑ X1 X3 = 615
∑ X3 = 85 ∑
X32 = 977 ∑ X3Y = 1038 ∑ X2 X3 = 829
∑ Y
= 92 ∑ Y2 = 1132
b. Menentukan
skor deviasi diperoleh hasil sebagai berikut :
1)
∑ X1 2 = ∑ X1 2
- ( ∑ X1 ) 2
n
= 401 – ( 55)2
8
= 401 – 378,125
= 22,87
2)
∑ X2 2 = ∑ X2 2
- ( ∑ X2 ) 2
n
= 722 – ( 72)2
8
= 722 – 648
= 74
3)
∑ X3 2 = ∑ X3 2
- ( ∑ X3 ) 2
n
= 977 – ( 85)2
8
= 977 – 903,25
= 73,75
4)
∑ y2
= ∑ y 2 - ( ∑ y) 2
n
= 1132 – ( 92)2
8
= 1132 – 1058
= 74
5)
∑ X1 y = ∑ X1 Y
- ( ∑ X1) ( ∑ Y)
n
= 666 – ( 55) ( 92)
8
= 666 – 5060
8
= 666 – 632,5
= 33,5
6)
∑ X2 y = ∑ X2 Y
- ( ∑ X2) ( ∑ Y)
n
= 872 – ( 72) ( 92)
8
= 872 – 6624
8
= 872 – 828
= 44
7)
∑ X3 y = ∑ X3 Y
- ( ∑ X3) ( ∑ Y)
n
= 1038 – ( 85) ( 92)
8
= 1038 – 7820
8
= 1038 – 977,5
= 60,5
8)
∑ X1 X2 = ∑ X1 X2 - ( ∑ X1) ( ∑ X2)
n
= 525 – ( 55) ( 72)
8
= 525 – 3960
8
= 525 – 495
= 30
9)
∑ X1 X3 = ∑ X1 X3 - ( ∑ X1) ( ∑ X3)
n
= 615– ( 55) ( 85)
8
= 615 – 4675
8
= 615 – 584,375
= 30,63
10)
∑ X2 X3 = ∑ X2 X3 - ( ∑ X2) ( ∑ X3)
n
= 829 – ( 72) ( 85)
8
= 829 – 6120
8
= 829 – 765
= 64
c.
Menentukan R1 , R2 , R3
, Y dengan cara menyelesaikan persamaan berikut.
Tabel
1.2 Tabel
hasil skor deviasi
|
∑ X1 2 |
∑ X2 2 |
∑ X3 2 |
∑ y2 |
∑ X1 y |
∑ X2 y |
∑ X3 y |
∑ X1 X2 |
∑ X1 X3 |
∑ X2X3 |
|
22,87 |
74 |
73,75 |
74 |
33,5 |
44 |
60,5 |
30 |
30,63 |
64 |
Persamaan regresi untuk tiga
predictor adalah :
d.
Untuk mencari koefisien regresi a,
b1, b2, b3 digunakan persamaan simultan
sebagai berikut :
1. ∑
x1
y =
b1 S x 12 + b2
S x 1
x 2 + b3 S
x 1 x 3
2. ∑
x2
y =
b1 S x 1 x 2
+ b2 x
2
2 + b3 S
x 2 x 3
3. ∑
x3
y =
b1 S x 1 x 3 + b2 S x 2 x 3 +
b3 ∑ X3 2
a = Y - b1
X1 + b2 X2 + b3
X3
e.
Hasil perhitungan dengan metode skor
deviasi dimasukkan ke persamaan 1, 2,dan 3
1.
33,5 =
22,87 b1 + 30 b2
+
30,63
b3
2.
44 = 30 b1 + 74 b2
+ 64
b3
3.
60,5 =
30,63 b1 + 64 b2 + 73,75 b3
22,8
30 30,63 =
33,5
30
74 64 = 44
30,63 64 73,75 = 60,5
1
1,312 1,339 = 1,46
1
2,467 2,13 = 1,46
1
2,08 2,40 = 1,97
1
1,312 1,339 = 1,46
0
1,148 0,791 = 0
0
0,768 1,061 = 0,51
1
1,312 1,339 = 1,46
0
1 0,689 = 0
0
1 1,381 =
0,664
b3 =
0,959
b
2 + 0,689 b3 = 0
b 2 = - 0,689 ( 0,959)
b
2 = - 0,66
b1 + 1,312b2 + 1,339 b3 = 1,46
b1 = 1,46 – 1,312 (- 0,66) – 1,339 (0,959)
b1 = 1,46 + 0,865 – 1,284
|
b1
= 1,036 |
||
1
1,312 1,339 = 1,46
0
1 0,689 = 0
0
0 0,692 =
0,664
1
1,312 1,339 = 1,46
0
1 0,689 = 0
0
0 1 = 0,959
f.
Menghitung Koefisien Determinasi
R2 y.123 = b1.
∑ X1 y + b2
. ∑ X2 y + b3
∑ X3 y
∑ y2
= (1,036)(33,5) + (- 0,66)(44) + (0,959)(60,5)
74
=
34,706 + (- 29,04 ) + 58,0195
74
= 63,0555
74
=
0,852
g. Menghitung koefesien korelasi
Ry.123 =
ÖR2y.123
= Ö0,852
= 0,923
3.
Menentukan Persamaan Garis Regresinya (Y = a +b1X1
+ b2X2 + b3X3)
Tabel 2.1 Tabel
Penolong Untuk Menghitung
Persamaan Regresi Dan Korelasi Tiga Prediktor
|
Resp |
X1 |
X2 |
X3 |
Y |
X12 |
X22 |
X32 |
Y2 |
X1Y |
X2 Y |
X3Y |
X1 X2 |
X1 X3 |
X2 X3 |
|
1 |
4 |
5 |
8 |
7 |
16 |
25 |
64 |
49 |
28 |
35 |
56 |
20 |
32 |
40 |
|
2 |
7 |
6 |
7 |
9 |
49 |
36 |
49 |
81 |
63 |
54 |
63 |
42 |
49 |
42 |
|
3 |
7 |
8 |
9 |
12 |
49 |
64 |
81 |
144 |
84 |
96 |
108 |
56 |
63 |
72 |
|
4 |
6 |
12 |
10 |
8 |
36 |
144 |
100 |
64 |
48 |
96 |
80 |
72 |
60 |
120 |
|
5 |
9 |
11 |
13 |
15 |
81 |
121 |
169 |
225 |
135 |
165 |
195 |
99 |
117 |
143 |
|
6 |
9 |
14 |
17 |
16 |
81 |
196 |
289 |
256 |
144 |
224 |
272 |
126 |
153 |
238 |
|
7 |
5 |
6 |
9 |
12 |
25 |
36 |
81 |
144 |
60 |
72 |
108 |
30 |
45 |
54 |
|
8 |
8 |
10 |
12 |
13 |
64 |
100 |
144 |
169 |
104 |
130 |
156 |
80 |
96 |
120 |
|
∑ |
55 |
72 |
85 |
92 |
|
722 |
977 |
1132 |
666 |
872 |
1038 |
525 |
615 |
829 |
|
n = |
8 |
|
||||||||||||
|
Rata-rata Ȳ = |
11,5 |
|
||||||||||||
|
Rata-rata X̄ 1 = |
6,875 |
|
||||||||||||
|
Rata-rata X̄ 2 = |
9 |
|
||||||||||||
|
Rata-rata X̄ 3= |
10,626 |
|
||||||||||||
Dimana Nilai :
b1 = 1,036
b 2 = - 0,66
b3 = 0,959
a. Menentukan nilai a
a =
Ȳ
– b1 X̄1 – b2 X̄2 – b3 X̄3
=
11,5 – (1,036) (6,875) – (- 0,66) (9) – (0,959) (
10,626 )
=
11,5 – 7,1225 – (-5,94) – 10,19
= 0,127
b. Menentukan
persamaan garis regresi
Di peroleh persamaan
regresi :
Ŷ = a + b1X1
+ b2X2 + b3X3
Ŷ = 0,127 + 1,036 X1
– 9 X2 + 10,626 X3
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