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Introductory
Econometrics
with APplications,
Harcourt College
Publistrers-2oo2
s6ch,
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hut
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kinh te sri dpng kinh t6 luong
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Biiln dd.Cl4p'hav, bfi5n
giei
thich
t.1*5'irtori!6
t6ng ti6u ding vir GNP
cria ViQt Nam
s53.099.984.896
526.442.004.480
2.530.537 .897 .984 2.667 .299.99s.648
13.285.535.514.624
14.33t .699.189.824
26 .849 .899 .9'l 0 .560 28.092.999.401.412
39.446.699.311.104 4t.954.997 .960.704
64.036.997 .693.440
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114.704.00s.464.064 t36.57 t.000.979.4s6 371;77 4
139.822.006.009.856 170.258.006.540.288
186.418.693.406.720
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222.439.040.614.400 258.609.007.034.368
250.394.999.521.280 313.623.008.247 .808
36r .468 .004 .401 .t52
April
2011
Ngudn : World Development Indicator CD-ROM
2000,
WorldBank.

ph6t
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ta
c6
th€ rinh
rorin
tryc
ri6p
hifp phLrong
sai nhu
sau
D6i
v6i
bitin
ngiu
nh-i6n
rdi rac
cov(X,
y)
=
II
G
-
p,
Xy
-
p,
)f(x,

ldp th5ng
k6 thi
hi6p phuo,ng
sai cria
chtng
bing
0.
cov(X,Y)
-
E(XY)
-p-pr,
?)
cov.(a
rbx,c
rdY
)
bdcov(X.Ylvbi
a,b,c,d
ld cdc
bing
so
Nhuoc
di6m
c0a hi6p phuong
sai Id
n6
phu
rhu6c
dmr
vi Ao'Iudng.

.'
_;:
rxY
J"*(x)r-(y)
-
"-",
,,qi
i 1,,
.!
._re:6
y.lqfran
tio
Iuong
-ai
quuni*iqp$lihtini.,
;iru
r,ui
bitin. p
se
nh6n
gi6
tri
nim
F.tI1 1 Il,.t ,N:,
p=-1
thi
m6i quan
ha ln
iifui, ct{rbi6n
hodn

ld hai
var(X+Y)
:
:
var(X) +
var(X-g:
2cov(X,Y)
-
2cov(X,Y)
2.f.5.
MQt
s6
phin
ph5i
x{c
su6t
quan
trgng
PhAn
phdi
chuAn
_
Bi6n
ngiu
nli6n
X
c6 lcj,vqng
li
p, phuong
sai ld

mdt
d0
Tinh chit
cria
Xiip
xi 95%
Xiip
xi 99,7Y.
diii x(mg
quanh
gi6
tri
trung binh.
(1)
Him
(2)
x6p
tich nim dudi
c
du6i
dudng
pclf nim trong
kholng
pto-,
x6p xi 95%
diQn
trong khoang
F+2o',
vi xdp xi 99,1%
di€n tich ndm

vit X,
-
N(u,,ol)
thi Y
=aXr+bXz
voi a
vi
b h
heng s5 c6
phAn phtSi
Y-N[(ap1+bp),(
a' o', + b' ol)
].
_(5)
Dlnh
$
gi6i
han trung
tim 2: Duoi
mQt s6 tli6u ki€n xic tlinh,
gi6
t{ trung binh
miu cria
c6c m6t bitin
ngiu nhi6n sE
gAn
nhu
hrAn theo
ph6n ph6i
chu6n.

l
E6 nhon(kurtosis):
f,
-
z
-'l
I/
-'L
,,\'t
K:El l"
tsl
l=j
L(
"
/l
(7)
Dga
vlo ki5t
qua
d muc
(6),
ngudi
c6 th6
ki6m dinh
xem mQt bi6n
ngSu nhi6n c6
tu6n theo phdn
phi5i
chuin
hay kh6ng bing c6ch ki6m dinh

nirn
rlt
, ffa" Xt, Xz, ,Xr
lir c6c bi5n ngiu
nhicn dQ.cgip
.O
ppan pnai
chu6n hod
k '-'-
'
thi
xi
=
iXl
tu6n
theo phdn ph6i
Chi-bintr
phuong
vdi
k bflc I: do,
i-t
Tinh
chit
cria
12
Phin
ph6i
Student
t
r;

b6c tu do.ldm hon
1

/r\ ,,
=
n.+}}
^
ta thay
phdn ph6i
t
bing
phAn phtii
chuAn
ho6.
"ri,/
Ia
doc
tdp
th5ng
k€ thi
F(Kr,r2)
=
#
ruin theo ph6n ph6i
F
/k,
voi
(kr,k)
bAc tu
do.

m6t
phAn
ph5i t
voi
k
bic
tg
do 1A
mQt
phin
ph6i F
v6i
t vA
k b4"
tu do
tl
=
F1,.ry
(a)
N6u
bdc
tu do
miu
kz kh6
lon
thi
k,F,.,,1,1
=
Ii, '
Luu f

chudn
2.z.Thdngke
m6
ta
MA
ti daiieu
th6ng
k6(Descriptive
Statistic)
c6 b5n tinh
chdt
m6
ti
phin ph6i
x6c
sudt
cia
:
C6
bi5n
tinh
chit
m6
ti
phin
su6t
cria
mOt
bi6n
ngiu

th6ng
kO
gita hai
bi6n
s6
dugc
m6
tri
blng
2.2.t.
Xtt
hn6ng
trung
tam
cria
dfr
liQu
-
DO
tr6i(skewness)
cria
phdn
ph6i
Trung
binh
ti5ng
th6
6ia
tri t"3l
vg"g)

sip
hQ s6
khi P(X<Md)
=
0,5.
Trung
vi
miu
: Niiu
s6
PhAn
tu
crira
theo
thu
tu
ting
din
hoic
giam ddn.
Trong
kinh
t6 tuqng
hiu€ohu
chgng
ta chi
trCn
trung
\4.
l3r

sai
Phuong
sai
ola
b(x-p,)'l
Phuong
sai mAul
D6
lQch
chuAn
mI, :
S,
=
1ffi
^ln
hoac:
ox
=1,16x
2.2.3.
DQ
tr6i S
D6 tr6i
t6ne
th6 , ufltLll'l
L\
o.
/l
Le Khic
Bo HUA
Bii gi.tne

ngdn di
oi
:i00.
Trung
binh
dua
tr6n
mOt m6u
e6j
.Chring
ta dirng
thO u. Hdrr"*tt6c lrr
2.2.4. DQ
nhgn K
Do
n.tron crja
ta"e *e effx
-r.,
]''l
L\
o
/l
v6i
s,,
=_Li(x,_xft_y)
2.3.
Th5ng
k6 suy di6n
- vdn tli udc Iugng
2,3.1.

phi
cho
hoc
tdp
cira m6t
hqc sinh
. Gi6 su chtng ta
bi6t
phuong
sai cria
X ld
p
ld mQt si5 chua
bitlt. Chring
ta
tim c6ch
udc lugng
p
binh miu d6 u6c luong cho
gi6
tri
trung
binh cua t6ng
1
F
He+ u.oc
luqng nhu sat
1',- i
x
=;(\

luong
dlem.
X6c su6t d6 m6t u6rX6c
sudt dE m6t
udc
luong
di€m nhu
tr6n
dfrng bing trung
bin-h
thuc
Li bao nhi€u?
Rdr
.p
hav
c6 thd n6i hiu nhu
bins
0.
th6p hay
c6 th6 n6i hAu nhu
beng
0.
I-l6c luqng
khoing
Udc lugng
khoing cung cdp mQt khoing
gi6
tri c6 th€ chua
gie
tri

April 201I
LA Khdc
B6 - HUA
Bdi
siane
Kinh
tE ltottz
girip
ich dugc
gi
cho chring
ta trong
viec
x6c dinh
p.
Nhu v{y
c6 mQt su
tl6nh d6i
trong
u6c
luqng khoang
voi
cimg mQt
phuong
ph6p
udc
luqr.g nh0t
tlfuh: khoang
cing hep
thi

sai.
Kj vgng
cria X
95%.
tl6c luqng khoAng
v6i tlQ tin
cly
95%
Luu f: Mic dir vC
u voi xic su6t 95%
nhung khong
thd p6!m6t cu
thC nhu
(103;
107) c5 xic suit
chria
p
li 95%. Khoing
(103;107) chi
p
ho[c
kh6ng
chfa
p.
dd
tin cdy 95% cho u6c
luong khoang cho
p
nhu sau: Vdi
quy

<
cr< 1
hay x6c
su6t khoing tu 0, diln 0, chria
gi6
tri that 0 li 1-cr thi l-a dugc
ggi
li dQ tin
cly ctia udc lu<rng,
cr du.c
ggi
li mric
j
nghia
cta udc luqng vA cflng ld x6c su6t mic sai
lim ioai
I.
N€u cr
=
5% thi l-cr li
95%.
Mric
f
nghia
5% hay d6 rin c$y
95Yo
thudng tlugc sti dlmg
trong th5ng k6 vi trong kinh t6 lugng.
X
x Z2 vd chring

vt6i
m6u
nh6
Kh6ng thi6n
lQch(kh6ng chQch)
M6t udc
luqng
1d kh6ng
thi6n
l6ch ni5u kj, vgng cua 0 thing
bing 0 .
E(e)
=
0
Nhu dZ chimg
minh d hin
tr6n,
X
o(0)
ld
u6c
luong kh6ng thi6n
l6ch
cria
p.
s,qi ".!h6
ig- khi
e;
ld
u6c luong thi6n 16ch

hon
01.
Phuong
sai nh6 nhit
Hdm
u6c luons 0. c6 nhuons
/A,- ,A' I r
Apnl 2011 20
Tuy6n
tinh
MQt
udc luqng
0
cta 0
tlugc
goi
ld utic
luqng
tuy6n
tinh n6u
n6 li
mQt him
s6
tuyt5n
tinh cta c6c
quan set mAu
1
Ta
c6 X
=

u6c luqng
tuyt5n
tinh, kh6qglhicn
lQch
vd c6
phutmg
sai
nh6 nh6t
trong 1op
c6c u6c
luqng
tuyi:n tinh
khong thi6n
tqcff6ha:.%
ca
th6 chimg minh
tluqc X
ta stUE.
&q*
{
Sai
sii'btnt
phudng
trung
binh
rih6 nhAt
.!
.
'{
.

l€ch cua
udc luqng.
Chring
ta mu5n
u6c lgqng
it
thiCn lQch il6ng
th
j
c6
phumrg
sai n]rd.
Ngudi ta
sri
dung inh ctr6isai
sti
binh
phurmg
trung bin} nhd
khi k:hbng
th6 chgn u6c lugng
kh6ng
thidn l€ch
t6t nh6t.
I
, \"
$,5
1 a
(
Tinh

tinh
chdt,cria
mflfi kvn hay
tin] ti6m can.
Tinh kh6ng
thi6n IQch
Udc
lucrng 0 tlugc
gqi
li
l€ch
ti€m cdn cia 0
Vi dg
2.12. X6t
t
blen
ngau
n-t en x:
f
f*,-*
minh
tluoc
ntiu limr(6")
=
o
/ r\
Et6'i1=olll-r
I
\
n,/

a}= r ,,ii
6 li mQt si5 duong
nh6 tu,
i.
April
201 1
2l
s{sl
Hinh
2.6.
Udc
luong nhdt
qurin
Quy
lu$t
chuin
tiQm
cfn
M6t
udc
lucrng
0 dugc
goi
ld ph6n phiii
tttin phdn
ph6i
"t
iA,
tt i'"01l6u
I tid" a6rr

phrit
bi6u v€
gi6
tri
cta rham
sii hoa.
m6t rap lop ttram
iti t<tr i
cdn khi phAn
ph5i
mAu
cria n6 tirin
Trong phdn
tr6n chring
ta d6. th6y
ph6i
chuin
v6i
trung
birh
p.
vd
phuong
sai
o2 thi
X c6
phan
ph6i
chuan
binh

k6 gie
thi6t
thiins
ke
2.4.1.
cie
cdc
tham
gin
thiiit
kh6ng thudng dugc
ki1' hi€u
ld Ho
vi
gii
thii5t nguoc
thulng
tinh
tlugc
Xr
=105
ngdn d6ng/hoc
sinh/th6ng.
Chring ta
xem x6t
kha neng
bec b6
ph6t
bi6u
cho

kh6ng chfa
p
:]
nhi6n
p6
cung
sl
Apil
20l l 22
La Khic 86 HuA
Bdi sianz
Kinh i
lLrcnP
thi ta b6c b6
gin
thi6t kh6ng
v6i d6 tin ciy 95o/o,
ngtgc l4i
ta kh6ng drl co sd dti
b:ic bd
gid
thi6t Ho.
d
phAn
tr6n chring
ta dd tinh
duoc u6c luqng
khoing cria
p
dua theo X, 12r(103;107).

,,(
mlen
chap nian
ouoc
g9l
ra
ml
_ '-l
to3
|
ro7
l
rvrid',
biLC
|
20
Mi6D chfp
d{n
,"
|
*;:o*
[{i6n bic ulin arhp nrin tIIaubnc
b6
Znn
Ta c6 tdt cri hii midn b6c
b6
vi do tinl chdt tltii
xung cia
phAn ph6i
chuin,

lacotatcahalII
chdp
nnan
va miBn b6c b6 theo tr cria tri thilng k6 Z
.
midn b6c
b6
vi
do
tinh ch6t a6i
xung cria
phAn phi5i
chuAn,
ni5u mric
1i
Xic suAt itii Z nim trong
hai khoing t6i h4n lA
P(2.,,
<
z
<
z,_.,
r)
=
|
-
a
(z.l)
hay
Pt Z,_,,,

121
\
/n
"''
.!n,l
Cric
mQnlr
dA
e.t)
vd
(2.2)
ld nh&ng
m6nh
ttd
xric
su6r.
f ltlh
gia
thi6t
rh6ng,k6
theo phuong
phdp
truyin
rhSng
Ph61
bi6u
mfnh
tl6 xic
suAt
r(X

Neu
xt-L,.",2
Ji
>po
hoic
X,+2,_o,,
J;=.
U,
thi ta
b6c bo
He vdi
d6
.
tin
c6y
1-cr
hay
xdc
su6t
m[c sai
lAm
ld cr.
'
''
>
N5u
X,-2,_,,,*<po3X,+2*,,,-|
tntat<trOpgrfrJia.tffi,
\i
n

IU
>
Z1-"p
thi
ta bic
bd H6
vdi
d6
tin ciy
1-cr
ha
>N
V<ii
mric
1i
t-7-d/)
-
LAi
.n/^
va
thi
ta
kh6ng thii
b6c
b6
Hs.
I05
-
106
__-t

tic quy6t
dinh
F
N6up<o:B6cb6Ho.
F
Nilu
p
>
cr : Kh6ng
the
bec b6
Ho.
Trong
vi dp tr6n p
=
0,32> ct:5%.V4y
ta
kh6ng th6
b6c
b6 Ho.
April
2al
l