Ekonometrika
Al Muizzuddin F
• The key concept underlying regression
analysis is the concept of the conditional
expectation function (CEF), or population
regression function (PRF)
• Our objective in regression analysis is to
find out how the average value of the
dependent variable (or regressand) varies
with the given value of the explanatory
variable (or regressor).
2
• This book largely deals with linear PRFs,
that is, regressions that are linear in the
parameters. They may or may not be
linear in the regressand or the regressors.
• For empirical purposes, it is the stochastic
PRF that matters. The stochastic
disturbance term ui plays a critical role in
estimating the PRF.
3
• The PRF is an idealized concept, since in
practice one rarely has access to the entire
population of interest. Usually, one has a
sample of observations from the
population. Therefore, one uses the
stochastic sample regression function
(SRF) to estimate the PRF
4
• The method of ordinary least squares is
attributed to Carl Friedrich Gauss, a
German mathematician.
• Under certain assumptions the method of
least squares has some very attractive
statistical properties that have made it one
of the most powerful and popular
methods of regression analysis.
5
FIGURE - A
6
• The Least-squares procedure obtains estimates
of the linear equation coefficients b0 and b1, in
the model.
yˆ i  b0  b1 xi
• by minimizing the sum of the squared
residuals ei.
2
ˆ
SSE   e   ( yi  yi )
2
i
7
• This results in a procedure stated as
SSE   e   ( yi  (b0  b1 xi ))
2
i
2
8
• The slope coefficient estimator is
n
b1 
 ( x  X )( y
i
i 1
i
Y )
n
 (x  X )
i 1
2
sY
 rxy
sX
i
• And the constant or intercept indicator is
b0  Y  b1 X
9
10
11
12
13
14
TUGAS KE-2
•
•
Ditulis tangan pada kertas folio garis
Dikumpulkan pada saat UTS
15
Perhatikan data berikut
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Income (x) Retail Sales (y)
9098
5492
9138
5540
9094
5305
9282
5507
9229
5418
9347
5320
9525
5538
9756
5692
10282
5871
10662
6157
11019
6342
11307
5907
11432
6124
11449
6186
11697
6224
11871
6496
12018
6718
12523
6921
12053
6471
12088
6394
12215
6555
12494
6755
Notes :
1. Hitung nilai koefisien b0 dan b1
2. Tulis persamaan regresinya
16