Upload
uta-price
View
78
Download
4
Embed Size (px)
DESCRIPTION
Regresi linier sederhana. Kuliah #2 analisis regresi Usman Bustaman. Apa itu ?. Regresi Linier Sederhana. Regresi ( Buku 5: Kutner , Et All P. 5). Sir Francis Galton (latter part of the 19th century): studied the relation between heights of parents and children - PowerPoint PPT Presentation
Citation preview
REGRESI LINIER SEDERHANA
KULIAH #2 ANALISIS REGRESI
Usman Bustaman
APA ITU?• Regresi
• Linier
• Sederhana
REGRESI (Buku 5: Kutner, Et All P. 5)
Sir Francis Galton (latter part of the 19th century):
- studied the relation between heights of parents and children
- noted that the heights of children of both tall and short parents appeared to "revert" or "regress" to the mean of the group.
- developed a mathematical description of this regression tendency,
- today's regression models (to describe statistical relations between variables).
LINIER
Masih ingat Y=mX+B? Slope? Konstanta?
B
m
X
Y
LINIER LEBIH LANJUT…- Linier dalam paramater…
- Persamaan Linier orde 1:
- Persamaan Linier orde 2:
- Dst… (orde pangkat tertinggi yang terdapat pada variabel bebasnya)
SEDERHANA
Relasi antar 2 variabel:
1 variabel bebas (independent variable)
1 variabel tak bebas (dependent variable)
Y=mX+B?
Mana variabel bebas?
Mana variabel tak bebas?
B
m
X
Y
BAGAIMANA MEMBANGUN MODEL REGRESI LINIER SEDERHANA?
Analisis/Comment Grafik-2 Berikut:
Analisis/Comment Grafik-2 Berikut:
A B
C D
FUNGSI RATA-2 (Mean Function)
If you know something about X, this knowledge helps you predict something about Y.
PREDIKSI TERBAIK…
Bagaimana mengestimasi parameter dengan cara terbaik…
Regresi Linier
Regresi Linier
Koefisien regresi
Populasi
Sampel
Y = b0 + b1Xi
Y =𝛽0+𝛽1 𝑋
Regresi Linier Model
ie
X
Y
Y X b b0 1+=Yi
Xi
? (the actual value of Yi)
REGRESI TERBAIK = MINIMISASI ERROR- Semua residual harus nol
- Minimum Jumlah residual
- Minimum jumlah absolut residual
- Minimum versi Tshebysheff
- Minimum jumlah kuadrat residual OLS
ORDINARY LEAST SQUARE (OLS)
ASSUMPTIONS
Linear regression assumes that… • 1. The relationship between X and Y is linear• 2. Y is distributed normally at each value of X• 3. The variance of Y at every value of X is the same
(homogeneity of variances)• 4. The observations are independent
ASUMSI LEBIH LANJUT…
Alexander Von Eye & Christof Schuster (1998) Regression Analysis
for Social Sciences
ASUMSI LEBIH LANJUT…
Alexander Von Eye & Christof Schuster (1998) Regression Analysis
for Social Sciences
PROSES ESTIMASI PARAMETER (Drapper & Smith)
KOEFISIEN REGRESI
XbYb 10 21x
xy
xx
xy
S
Sb
n
XX
n
YY observasi jumlah n
1
)( 1
2
n
YYYVar
n
i
1)( 1
2
n
XXXVar
n
i
xxS
)(SSTS yy
xyS
1),(Covar 1
n
YYXXYX
n
i
SIMBOL-2 (Weisberg p. 22)
MAKNA KOEFISIEN REGRESI
b0 ≈ …..
b1 ≈ …..
?x = 0
- Tinggi vs berat badan- Nilai math vs stat
- Lama sekolah vs pendptn- Lama training vs jml produksi
…….
C A
B
A
yi
x
yyi
C
B
ii xy
y
A2 B2 C2
SST Total squared distance of observations from naïve mean of y Total variation
SSR Distance from regression line to naïve mean of y
Variability due to x (regression)
SSEVariance around the regression line Additional variability not explained by x—what least squares method aims to minimize
n
iii
n
i
n
iii yyyyyy
1
2
1 1
22 )ˆ()ˆ()(
REGRESSION PICTURE
Y
Variance to beexplained by predictors
(SST)
SST (SUM SQUARE TOTAL)
Y
X
Variance NOT explained by X
(SSE)
Variance explained by X
(SSR)
SSE & SSR
Y
X
Variance NOT explained by X
(SSE)
Variance explained by X
(SSR)
SST = SSR + SSE Variance to beexplained by predictors
(SST)
Koefisien Determinasi
orsby Predict explained be toVariance
Xby explained Variance2 SST
SSRR
Coefficient of Determinationto judge the adequacy of the regression model
Maknanya: …. ?
Koefisien Determinasi
SALAH PAHAM TTG R2
1. R2 tinggi prediksi semakin baik ….
2. R2 tinggi model regresi cocok dgn datanya …
3. R2 rendah (mendekati nol) tidak ada hubungan antara variabel X dan Y …
Korelasi
yx
xy
yyxx
xyxy
xy
SS
Sr
rRR
2
Correlationmeasures the strength of the linear association between two
variables.
Pearson Correlation…?
Buktikan…!
KORELASI & REGRESI
21x
xy
xx
xy
S
Sb
yx
xy
yyxx
xyxy
SS
Sr
𝑺𝒀=√𝑺𝒀𝒀
𝑺𝑿=√𝑺𝑿𝑿
ASSUMPTIONS
Linear regression assumes that… • 1. The relationship between X and Y is linear• 2. Y is distributed normally at each value of X• 3. The variance of Y at every value of X is the same
(homogeneity of variances)• 4. The observations are independent
UJI PARAMETER RLS
Linear regression assumes that… • 1. The relationship between X and Y is linear• 2. Y is distributed normally at each value of X• 3. The variance of Y at every value of X is the same
(homogeneity of variances)• 4. The observations are independent
DISTRIBUSI SAMPLING B1
b1 ~ Normal ~ Normal
Uji koefisien regresi
ib
iikn S
bt
)1(
0:
0:
1
0
i
i
H
H
Uji koefisien regresi
xx
eekn
SS
b
bS
bt
2
11
1
11)1( )(
0:
0:
1
10
AH
H
Selang Kepercayaan koefisien regresi
xx
ekn
xx
ekn S
Stb
S
Stb
2
)1(,2/11
2
)1(,2/1
Confidence Interval for b1
Uji koefisien regresi
xxe
ekn
SX
nS
b
bS
bt
22
00
0
00)1(
1)(
0:
0:
0
00
AH
H
xxekn
xxekn S
X
nStb
S
X
nStb
22
)1(,2/00
22
)1(,2/0
11
Confidence Interval for the intercept
Selang Kepercayaan koefisien regresi