14 regresi linier_sederhana
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REGRESI LINIER SEDERHANA
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REGRESI
• Diperkenalkan oleh Francis Galton
• Menghubungkan antara satu variabel (yang selanjutnya disebut variabel terikat/dependent variable) dengan satu atau lebih variabel (yang selanjutnya disebut variabel penjelas/explanatory variable)
• “Regression analysis is concerned with the study of dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables, with a view to estimating and/or predicting the (population) mean or average value of the former in terms of the known or fixed (in repeated sampling) values of the latter.” (Gujarati)
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CONTOH KASUS DI BID.BISNIS
• Apakah biaya promosi (signifikan) berpengaruh terhadap tingkat penjualan suatu produk?
• Apakah harga BBM berpengaruh terhadap harga pokok produksi?
• Apakah gaji karyawan berpengaruh terhadap kinerja karyawan?
• Apakah motivasi kerja berpengaruh terhadap keuntungan perusahaan?
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PERSAMAAN REGRESI POPULASI
iii uXY 21
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TOPIK BAHASAN DLM.REGRESI
• Penaksiran parameter
• Signifikansi pengaruh-pengaruh
• Kebaikan suai (Goodness of Fit)
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PERSAMAAN REGRESI SAMPEL
iii uXY ˆˆˆ21
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KOEFISIEN REGRESI SAMPEL
XY
x
yx
n
i
i
n
i
ii
21
1
2
12
ˆˆˆ
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PENAKSIRAN PARAMETER
22222
1
2
1
2
1
1
2
2
1
2
1
2
2
1
1
2
1
2
ˆˆˆˆ
ˆˆ
;2
ˆ
ˆ;ˆ
22
setset
xn
X
sedan
x
se
n
u
x
yx
yu
n
i
i
n
i
i
n
i
i
n
i
i
n
i
i
n
i
iin
i
i
n
i
i
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UJI HIPOTESIS DLM REGRESI (1)
• H0: 2 = 0
H1: 2 0
atau
• H0: 2 ≤ 0
H1: 2 > 0
atau
• H0: 2 ≥ 0
H1: 2 < 0
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UJI HIPOTESIS DLM REGRESI (2)
2
02
ˆ
ˆ
set
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UKURANKEBAIKAN SUAI/GOODNESS OF FIT
n
i
i
n
i
i
y
x
TSS
RSS
TSS
ESSr
1
2
1
2
2
2
2 ˆ1
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KOEFISIEN KORELASI PEARSON
n
i
i
n
i
i
y
x
r
1
2
1
2
2
2̂
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CONTOH SOAL (1)
Bradford Electric Illuminating Co. Is studying the relationship between kilowatt-hours
(thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following
Number of Rooms KWH (thousands)
12 9
9 7
14 10
6 5
10 8
8 6
10 8
10 10
5 4
7 7
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Pertanyaan:
• Tentukan persamaan regresi sampel (SRF).
• Apakah banyaknya ruangan berpengaruh terhadap penggunaan listrik? Gunakan taraf nyata 0,05.
• Tentukan koefisien determinasi persamaan regresi yang terbentuk dan berikan makna dari koefisien tersebut.
• Tentukan koefisien korelasi antara kedua variabel tersebut.
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CONTOH SOAL (2)
Seorang pemimpin perusahaan sedang mempertimbangkan apakah diperlukan tambahan anggaran untuk biaya promosi sejenis produk agar penjualan (sales) produk itu meningkat. Untuk itu ia mengambil sampel salesdan biaya promosi pada 10 daerah pemasaran produk itu, dan diperoleh hasil sebagai berikut.
Daerah Sales Promosi
A 156.8 15.3
B 201.6 23.7
C 130.3 10.9
D 150.2 20.1
E 298.6 29.1
F 160.0 18.0
G 211.6 38.0
H 300.0 30.0
I 317.4 35.2
J 148.2 19.9
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Pertanyaan:
• Tentukan persamaan regresi sampel.
• Apakah promosi berpengaruh terhadap penjualan? Gunakan taraf nyata 0,01.