bài giảng kinh tế lượng - gv. lê khắc bộ

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29
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30
3.3 tl6c
luqni
i6c h6 s5
cria

m6
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phep
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33
3.4 Kloing
tin ciy
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ve
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h6i
quy 36
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3.7 Ds bio
bing m6 hinh
h6i

quy
trai bltigi
F
40
3.8 Y nghia
cria hdi
quy
tuyiin
tinh vd m6.ry
dqng hdm
thulng tluoc st dpng 42
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cHuoNG
4. u6 niNA
HOI auYFuvEN
riNH BQr
4.1 X6y dsng
m6 hinh.
-"Ji\"}i
4s
4.2 tl6c luqng
tham s"6 c"trg
frrfl
hifih
h6i
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4.4 Ki6m
tllnh niirc
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48
a.6
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ki6m dinh
gia
thitit thi5ng k€
cho hQ sti h6i
quy
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loai
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49
MUCLUC
CHTIONG
1. GIOI
THIE,U
1.1 Kinh
tii luqng
li
gi?
I
.2 Phuong
ph6p luin
cria
Kinh
t6 lugng
1.3 Nheng
cnu h6i
d{t ra
cho mQt
nhd kinh
t6 luqng
1.4 Dt
ligu cho
nghiEn
cr?u kinh
ti5 luqng
1.5
Vai trd oia
miy vi

tinh vi
phim
m,im
chuy6n dung
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rHlpu
l40r
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DEN
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s6 thay d6i
5.3 Tu
tuong
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5.4 Lua chgn m6 hinh
CHU0NG 6 DtlBAovol
MO HiNH
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quy
don

gian
6.2 Tinh
ch6t tr5 cta dt lieu;hu6i
thoi
gian
vi hQ
qud
cua n6 diSn m6 hinh
6.3
M6
hinl
t.u h6i
quy
6.4 M6
hinl c6 tt6 tr6
phnn
phili
6.5
t-ldc luong m6 hinh
t.u
h6i
quy
6.6 Pb6t hiQn
tu tuong
quan
trong
m6 hinh t.u h6i
quy
Trang
3

J
4
7
9
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56
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60
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62
62
62
64
64
April 2011
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pianp
kitth ti luotts
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7. cAc M0 HiNH
DU
BAo
nr.4,Nc
rirur rrl6Nc xB
^,
,:. i ,.
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mantr

pnan
cua du lrgu chuol tnfi
glan
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biio theo xu hu6ns dii han
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l ,,
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so l(y thu?t du bao don
gran
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tldnh sii m6 hinh du bdo
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s6
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m6 hinh ARIMA
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1. GI6t
rIrrEU
l.l. Kinh
ti5 luorrg
lh
gi?
iil;;
ttil,G1r 1'E"ono*"t
i"r"."6
nghia
li

do lu.onc
!hhf''
Th{t
ra.ph4m
vi
cria
Urf,^t6-f"frg
iO"i
t-,
Ao
luong
kinh
t6. Chring
ta sE
thAy
di6u t16
qua mQt dlnh
nghia
v6
kinh t6 luone
nhu
sau:
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ka kinh
# c6
nQi dung
chinh td
sd tiQu
thiing

ka'
kinh
tii trqng
h mAt
min26c"l4p
vbi sv
kA hqp
cia
lj' thuydt
kinh
#',c6ng
c4 todn
hoc
vd
phuong
phdp
lud,n- th,ins ki. N6i
r6nz hon,
kinh
ti
lwng
liin
quan ddn:
(
l) U. 6c
lttqng
cac
quan
h€
kinh'

ri,
til
XiZ*
chilms
li,
rhuyir
kinh
t0 bing
dft
liQu.thqrc
i.vd.kidm
dinh
gid
thidi'cia
t'inh
t6
hoc
vi hdnh
vi,
vi
13)
Dtr bdo
hdnh
vi
cia biin
s6
kinh
ft
"'
Sau

tlAy lir
mQt s6
vi
du v6
ung dung
kinh
t6
lucrnC'
: vi hdnh
vi,
vd
(3)
Dr bdo
hdnh
vi
cia bian
sd
hnh
te.
-
Sau
dAv lir
mOt s6
vi
du v6
ung dung
kinh
t6
lucrnC'
tl6c

luqng
quan
hf
kinh t6
.
:
,
,
(l)
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mric
d6ldc
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crla
vi6c
ha I6i su6r
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tang trutog
kig[]^g,.
.
.,
.
.
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Udc
lugng
nhu
ciu
cria m6t
mAt

heng
cp
th6. vi
du.ghu
c{{1e
hoi t4r
thl
truong
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i:t
pnan
tich
tec d6ng
ctra
qudng c6o
vi khuy6n
mii
l€n
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crla m6t
c6ng
ry'
/
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itlnh
giA
thiiit
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iuia ra
t6c dQng
cira
chuong
trinh
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n6ng
ldm
trng ndng
su6t
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KiCm
chimg
nhdn
dinh
d0 co
ddn
theo
e- __-
,qu
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.
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ciu vil
c6 basa
dang
fillet d
thi
trudng

nQi <lia.
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izi
ci,irr,
prli
au b6o
muc
13)
Dq b6o
chi s5
t+I
1.2.
Phuong
p
t6
luqng
Theo
phucrng
p!
cftu sri
dung
kinhit6
th6ng,
cdrigqi
ld
phuong
phrip tuan cO tli6n,
m6t
nghiBn
giim

c6cludc
n}u
sau3:
(1) Ph6t bi
gin
thi6t.
(z)
x4gdinh
dad
(3) Xric,.diph dac
",iu
,ia ni*,
toan
kinh
ti5 cho lli
thuyi5t hoac
gie
thiiit.
cria m6
hinh
kinh
t6
luong
cho
11i thuy6t noic
gla
titrit.
i
li6u.
tham s6

cria m6 hinh
kinh
tt5 lucrng.
dinh
gin
thii5t.
riii k6t ouA
giAi
k6t
quA
Du b6o ve sri
dpng m6
hinh d6
quy6t
dinh
chinh srich
l.A.KoutsoyiaDnis,
Theory ofEconometrics-Second
Edition,
ELBS with Macmillan-1996,
trang 3
2. Ramu
Ramanaiha4
Introductory Econometrics
with ApPlications,
Harcourt College Publish€rs_2oo2,
tang 2.
r
Theo
Ramu Ramanathan,

Introductory
Econometrics
with APplications,
Harcourt College
Publistrers-2oo2
s6ch,
tham
hut
thuong mqi,
l4m
ph6t
lo+i cd
phi6u
cu
th6
*u n-rE.
U6c
(6)
(1)
(8)
April
201I
L1i
thuyt5t
holc
gii
thirit
LAp m6 hinh
to6n
kinh ti!

L{p m6 hinh kinh ti5 iuorg
LI6c luqng th6ng
si5
-,.:
."
1
Krem Opn
gra
tnlet
Xiy
dmg lai m6 hinh
La Khdc
B6
-
HUA
Bdi
siAns Ki
h ti llrcrns
Hinh 1.1
Phucmg
ph6p
.
.
Vi dp
i: C6c bu6c ti(5n
<16 tdi nghi6n
ctu xu hugnl
tQ luqng
lduu
mQt vAn de

kinh te sri dpng kinh t6 luong
v6i
3n cria n6n kinh t6
Vi6t Nam.
(t)
Ph6t bi6u l,i
Keynes
cho
Qui
luAt tlin
6ng
(t1in
bi) mu5n, nhu m6t
qui
tic
vd vd
trung
binh,
ting
ti6u ding
ilu ntr4p cria hg ting l6n, nhung
kh6ng nhidu nhu ld
gia
tlng
xu hu6ng tieu ding bi6n(marginal propensity to
consume-MPC),
l6n khi
thu
nhfp tdng 1 d<rn v! ti6n t6 l6n h<rn
0 nhrmg nh6 hon I .

m6 hinh
todn
cho li thuyiit ho4c
gia
thi6t
don
gian
nh6t th€ hiQn
j
tudng cria Keynes ld dang
him tuy6n tinh.
+F,GNP
(1.1)
Trongtl6:0<
p, <1.
Biiiu di6n
du6i dang dd thi cta d4ng him niy nhu sau:
a
Joha Maynard
Keynes, 1936,
theo
DN.Gujarati,
Basic Economics, 3'a
,
1995, trang 3.
a"
trong
thu
vOy x
tuc ti6u d

April 201I
il ,';;6'.;fi;rO5'niiia"
u"n"
gini
thich cNr:
u6n a$'l4phav, pii5n
giei
thich
Hinh l.
2.
Him
ti6u dirng
theo thu nh{p.
.ra
M6
hinh
to6n v6i d4ng him
(1.1)
the hiQn m6i
quan
h!-
.tit
dinh(determrnistic
relationshrp)
gita
ti6u drirng
vd,thu,nhip
trong khi
quan
hQ

gria
cric bi6n s6
kinh te thuong
mang tinh kh6ng
chinh xiic. D6
bi6u dien
m6i
quan
hQ
khffig chinh x5c
gita
ti6u dirng vd
thu Jrfp chung
Ia dua vio thinh
phAn
sai
s6:
!.'.",q1*
TD
=
Br
+
prcNP
+
s
(1.2)
_,*" &"
'1
Trong d6
e ld sai sii, e ti mQt

birin
+dfu Siege
ti€n
cho c6c nhan ti5 kh6c
cflng tiic
dQng l€n
ti6u dirng mi chua
ilugc dua vio}{hilE
Phu<rng trinh
(1.2)
ln mot m6
hinh kinl tdtydhg
M6 hinh tr€n dugc
goi
li m6 hinh
h6i
qoy
ruy6n
tirt
.
H6j
Cuv
tuv6n
tinh llfQi duqt'chinh
cua hgc
phAn niy.
(4)
Thuthepsi5
lieu
' 3"-

\,." j
quy
tuy6n tinh. H6:
quy
tuyqn tjnh
llfQi
"dun$
chinh cua hgc
ph6n niy
(4)
ThuthapsSlieu
-i
1 1
i6 uOu
ud iie" au"g va trrurfiir?B-&i-'n,in
khh t6 ViQt Nam ru i986
di5n 1998 tinh
theo
tlon
vi
tiAn
te hiQn hanh;Ehu sq;'
i
.I]' ,
ro , ei6;
prri
thuQt hay bi6n
duoc
giii
thich GNP:

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
16.707 .000.22t .696
245.t8
1 10.535.001.505.792
88.203.000.283.136
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
222.839.999.299.s
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.

5
TD:
Tiing
rieu
dtng
cria
nen
kini
16 Vi6r
Nam,
d6ne
hi6n
hdni.
CN P:
Thu
nhnp
qudc
n6i
cLia Vidr
Nam. d6ne
hi6n
ian}r
.
-
D9. trong
thoi
h)
khao
srit c6
lam

ph6t
rdt cao
n6n
chring
ta
cin
chuyiin
dang
s6 li6u
ve
ti6u
dirng
vd
thu
nhnp
thuc
v6i
nIm
g6c
Li
1989.
Bingl.Z.
Ti6u
dring
vi thu
nhlp
cria
ViQt
Nam, gin
cd

dinh
1989
1\ am
Ti6u
dirng.
TD,
tlong-giri
c6
dinh
1989
Tdng
thu
nh6p
GNr,
dOng-gtd
cd ainh
1989
1986
22.868.960.3C)2.145
24.025.999.156.721
1987
23.611.903.339.s1s
24.888.000.975.950
1988
24.255.972.111.640
26.16s.999.171.92
1989
26.849.899.970.560
28.092.999:401.472
1990

27.760.775.225.362
29.526.AA0.611:153
1991
26.118.36s.11A.rc3
31.2.8s.998,882.8t
3
1992
27
.123.609.120.80r
.33
.990.:9.99
:913:67
9
1993
30.853.195
.807
.661
'
3:6,1
3 5.4
A,L,
69 2. 5
I 1
1994
32.834.660.781.138
:s.9ez.oo:.187.889
1995
36.638.7
54.378.646
43.19V

.n02.601.354
1996
41.190.217
.461.419
. :,,
47
.888.002.0
69.3 33
1991
41.349.567
.191.335,
51.790.873.128.79s
1998
43.126.144.904.439:,
'!'i:
54.794.'746.182.076
tic
luong
m6
hinlr
(-J,-
oc luonl
ng phumrg
phrip
t6ng
binh
chring
ta
thu
du<rc.t6t

qua
ti
.'
'ii
-_
.
if, ,".,.
,o,h-e.'S6'iata
m6
hinh)
'rfuS,"t6i
thi6u ttrdng
ry nhir
sau:
thudng
(or
dinary
Least
(s)
u
Xu hu6ng
(6)
Ki6m
dinh
Irl so
ll6c
luong
.6
F,
;

=0,68
r'cria
niSn
kinh t6
ViCt
Narn
la
MpC
:
0,6g.
th6ng
k6
Keynes.
chring
ta
cdn
x6c dinh
MPC tinh
to6n
nhu tr6n
c6
lon hon'0
vd
nh6 hsn
;
k6
hay
kh6ng.
Ph6p
kidm tlinh

niy
ctng
duoc
trinh
bdy rrong
chuong
1
v.9,,
j
2.
(7)
giii
kiit
qu6
5
Se duoc gi6i
thieu
trong
chuong
2.
Dua
theo
1i
nghia
kinh t6
cria
MpC
chung ta
diQn
giai

k6t
qua
h6i quy
nhu
sau:
!6u-d]Ic
tdng.0,68
ne.an ty
d6ng
n5u
GNp ting
i
ngdn
rj.d6ng.
(6)
Su dung
ker
quri
h6i
quy
.
Dga
vdo.
k6t que
h6i
quy
ChGg
ta c6
th6 du
beo

hoic
ph6n
tich
t6c
d6ng cia
chinh
s6ch.
vf
du
n€u
d,
brio
dugc
GNP cta
vi6r
Nam nim
2004
thi chrrne
ta
c6 thd
iu brio
tieu dims
clta
Vj€l
N1m.rrong
nam
20O4.
Ngorii
ra khi bi6r
MpC

chfng
ta c6
th6 udc
luong
s6 nh6i
c0a
n6n
kinfi t€
theo
lf thuy6t
kinh
t6
vi
m6
nhu sau:
M:
1(1-MPC)
-
1(1-0,68):3,125
)pril
201I
La Khdc 86
- HUA
Bdi
sidns
Kinh
ti luortg
Vay
kiit
qua

h6i
quy
niy
hfiu ich
cho
phin tich chinh srlch
tliu tu,
chinh sich
kich ciu-

1.3. Nhtng
ciu h6i il{t ra
cho mQt
nhir
kinh tA luqng
1.
M6 hinh
c6
f
nghia
kinh
tii kh6ng?
2. Dt
liPu c6 ding
tin cAY kh6ng?
3.
Phucrng
pbrip
u6c luqng
c6

phir
hqp kh6ng?
4. Kiit
qui
thu dugc so
vcri k6t
qui ttr
m6 hinh
khdc hay
phuong
phdp
khric nhu
th6
ndo?
1.4.
Dfr liQu
cho nghiGn
c.ri'u kinh
t6 luqng
cri ha danq dir li6u kinh tE crv bin: dri li6u c
C6
ba dang dt
fieu kinh
t6
co
bin: dt
li-6u ch6o, dt lieuchu6i
thdi
gian
vi dt liQu

bing
Dir ti6n ch 6o hro oAm orran s6t cho nhidu don vi kinh ti5 d m6t
thdi tliiim
cho tru6c. C6r
Dft
liQu
chlo bao
gdm quan
s6t cho nhidu
don vi kinh
ti5 d mQt
thdi tliiim
cho tru6c. CdLc
tlcrn vi kinh
t5 bao
gdm
cic c6c nhdn,
c6c hQ
gia
dinh,
c6c c6ng ty, c6c
tinh cac
quoc
9n
Dtr
lifu
chuSi thoi
gian
bao
g6m

c6c
quan
s6t h6n m6t don
vi
nhidu thoi
tlii.m. Vi du
ta
quan
s6t doanh
thu, chi
phi quang c5o,
dO
ddi
m6i
c6ng nghp
d m6t c6ng
ty trong khoing
thoi
gian
1
Dir liQu
bing li su k6t hqp
gita
dt liQu
ch6o vd dt li€u
du
v6i cing
b0 bi6n
s5 vd c6ng
ty

nhu
o vi du
trdn, chLing
ta thu thfp spfi
cdng ty trong
cirng mQt khoang
thdi
gian.
tai
ttic
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11
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)
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13
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?)
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.

If :1,'ITrnl" .,
O6
ttric ptrirc
nfruoc
di6m
cria
hi€p phuong
sai
ld
php
thyQc
vdo don
vi
do ludng,
nguoi
ta
su
dung
h6
sd trmrg quan
duo. c
dinliehia
-nhrr.ur,
.''
^
_
cov(X,
Y)
cov(X,
y)

.'
_;:
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

hio,
n6u
p:l
thi
mZi quan
hQ
td
d6ng
bi6n
horin
hdo.
Tti
ilinh
nghia
ta c6
i,
,, J
'
r u
url
ur
Hllla
Ia co
cov(X,Y)=po*o,'.,.,,,li,,i",:,".,,1
2.1.4.
Tinh
chAt
Goi
X vi
Y

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

o2. N6u
X
c6
phAn
phiii
chuAn thi
n6
duoc
h-i
hi6u
nhu
sau
X-
N(p,o'?)
Dang
hdm
mdt
dQ x6c
xu6t cira ph6n
ph5i
chuin
nhu sau
Apr
2aI
I
l4
.cqi!il.
.:1.
Hinh
2.3. Him

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

du6i
rng'i$lioang
pt3o.
2
J
6-p/o
thi ta c6 Z*N(0,1).
Z
goi
ld bi5n
chuAn ho6
vi N(0,1) duoc
ft
gidi-hsn.trung tnm 1:
MQt t6t trqp
tuy6n
tinh
cic
biiln c6,phAn
phtii
mQt sil tli6u
kign
x6c dinh cflng
ld m6t
phnn
ph6i
chuan.
Vi du
x,
-Niil,,.i)

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.

(6)
M6
men cria
ph6n ph6i
chuAn
M6 men bdc ba:
Etfi-tr)3]:0
Md
men bic btin
: f
[(X-p)41::o4
,;,. , 1
uor vor mot
phan
pnol
cnuan
DQ tr6i
(skewness):
April 2011
15
La Khdc 86
- HUA
Bdi
sians Kinh i
tuol1{
f. .il
s=nlIx-r'l l=o
lt _ I I
L\
(),i

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

xem S
c6
gAn
0 va K c6
gdn
I
hay
kh6ng. DAy
li nguyOn tic x6y dimg
kiilm dinh o3y lu6t
chudn
Jarqrie-Bera.
:e=Ils'+(K-3)'l
6L
4
)
JB tu6n theo ph6n pht5i
12
v6i hai
bac
t.u
do(df
:2).
:
.
Phen
ph6i
r('z
,iurr'""'tt ".
."

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;

phSi
Student
hay n6i
Tinh
chit
cria
(1)
Phan
p
b{c t.u do cdng
t,u,
=
-4:
ru6n theo phlur
'lx:*
tk
t vrli k bAc tu
do.
i xrmg
quanh
0 nhu
phdn ptrtii
chuin ho:i nhung thlp
hon. Khi
phdi
t ti6m
cAn d6n
phdn ph6i
chuin
hoii. Trong thrc hdnh. Klr i

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.

Tinh ch6t cria
ph6n ptr6i
f
(1)
P.han
ph6i
F lCch vC b6n tr6i, khi bAc tu do
kr vd k2 di l6n,
ph6n
ph5i
F ti6n d6n
phar
ph6i
chuan.
t2t
p
:
kzl
(L<2-z)v6i
di6u kidn k:> z ra
"'
=
ffif,flvrii
ttiiu ki6n kz>4.
Apnl
2011
.16
(3) Binh
phunng
cia

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

: Khi
bic
tu
do
dt
lon
thi
cac
pnan
pirOi
1'?'
pf'an
phi5i
t vi
phin
ph6i F
tiCn
den
rni, ,n:i;il#:Li;
pia,
prrir *v
a,iq"
eqi
u
ftan
pntii
c6 li6n
quan dtin
phdn
ph6i

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

nhi6n
nhu
sau:
i"
fr",lrg
*"g
,nmiay
"tti6m
gita" cria
phin
phiSi
tvtric
a6
ftran
tan cria
dt
liQu
quanh vi
tri
"di6m
gita"
-
EQ
nhon(kurtosis)
cria
phdn
ptf&!
M5i
quan
h6

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)

p,.
:
E[x]
I*,
Trung
binh
mdu
X
=
:=r-
Trung
vi
cira
ti5ng
th6 :
X ln
m6t
biiin
ngiu
Md
Ii
trung
vi
cria
t6ng
th6
h
s6
"d
gita" cria mlu

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

\*-*
2.2.2.DA
Phin
t6n
cria
dir
ffifP
N6u
s5
ptrAi tu
cria m6u
chin
thi
trung
vi
binh
cQng
cria ha;
s6
"a
gite'.
ta- a6n
t
r'.g binh
md
kh6ng
tinh
toan
Phuong

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

Kt,ttt te lrci;g
r
n/.
V,'
tro trolmau::j=- ) l-l
'-4l^l
,_
,=l
\
oAivApnan
pndi
chudn iIQ
trbi bing 0.
tnrong
ti6u
hoc
Y.
Chring tarmui5n
hoc
lA bao
nhibu. Goi X
ld biilir.n
hoc
lA bao
nhi€u. Goi X
ld bi
tiiiu
hoc
(X
tinh bing

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.

tiSrc
luong
Chring ta
tim
hiiiu bdn ch6t, dac
n-1i:]
drrtiLt,O"
t"qne th6ng
kd th6ng
qua
m6t
vi du don
giAn
ld u6c luong
gi6
tri hrurg
Vi du.11.
Gii sri
chfng ta
mu5n khio sel!.ll
phi
cho hgc tip cria hoc
sinh ti6u hoc tai
thii.
Sinh chi
phi
cho
hoc tAp cria
m6t hoc sinh ti6u
img v6i chi

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
=;(\

+-x, + +x")
X
=:({r
+X, + +X.)
-
n
\,
r,
X ta.o1tier-ngiu
nli6n.
Ung v6i mQt mau cu th6 thi X ffian
m6t
giri
tr! xric tlinh.
II6c'Inqinq
ali6m
Ung
v6i m6t
miu cu th6,
gid
su chfng ta tinh
duoc X
:
105
(ngin
d6ng,&qc
sinh). DAy
,
1
la mol uoc

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

chi
phi
trung
binh
cho hoc
t6p cta
m6t hoc sinh
ti6u hgc. Vi du chirng ta tim
duoc X
:
105. Chring ta c6 thti
n6i
p
c6 th6 nim
trong
klioing
Xtt0 hry 95sp<1i5.
Khoang
u6c luong cdng r6ng thi cing c6 khri nlng ch&a
gi6
tri trung
binh
thuc nhung
m6t khoang
u6c lucrng
qu6
rQng nhu khoing X+tOO hay 5 <
p<205
thi hiu nhu khdng
18

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

mric
dQ tin cfy
cang nh6.
2.3.3.
Phin
ptriii
cfia X
Theo
dinh 1f
gi6i
h4n trung tim
1 thi
X
ln
mQt
bitin ngiu
nhi6n c6
phan phiSi chuin. Vi
X
c6
ph6n
phtii
chudn n6n
chring ta
chi cAn
tim hai dflc
trung cta n6 ld
lc! vgng
vA
phuong

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

tic x?.y
m0r udc
lucrng.
Chring
ta cir l6p tli
lap lai
qu6
trinlr Hy
miu
vd urlc luong
thi
khoang 95%
khoang u6c iuqng chfng ta tim duoc sE chua
p.
fOn#{Lat
hcm,
ntiu
tri thting k6 cAn u6c
luong
li 0
vi ta tinh
duqc hai udc luong
0,
vd 0, sao cho
P(6,
<
tr<
0,)
=1-o
v6i 0

<
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

ta ti6n
hinh 15y
mOt m5u
voi
cd m6u n
vi
tinh
./n
Y nghra chu l
Apd 2al I
19
Lo Khdc
86 - HUA
Bai
qiane
Kinh fi tlrone
Cric tini ch6t
dring mong d<ri cia
m6t
u6c
luqng tluoc chia
thanh hai nh6m,
nh6m rinh
ch6t crla
uric I uong trdn
cd m6u nhd vd nh6m tinh
ch6t u6c luong tr6n
cd miu lon.
2.3.4. Citc tinh
chit rirng

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

cria 0.
khi
vdi b6t cri hdm
u6c lugng 6, ndo ta
I
MQt u6c
luqng lA hj
nhat.
;
ff.qui
1d
u6c
luong kh6ng thi6n l6ch
vi c6
phucrng
sai
nhd
,t
_ ,-
,
,rl.
,
:.
E(0r)=E(0r)=0
Hinh
2.5. U6c luqng hiQu
quA.
Him u6c lucmg 02
hi6u
qui

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
=

a(X,
+ X,
+
+
X,)
n
Viy X
lnudc luqng
tuY6n tinh
cho
P.
fI6"
t,.qrrg kh6ng
ihi6n
lQch
tuy5n
tintr t5t
nndt
(Best
Linear
Unbiasetl
Estimator-
BLUE)
MQt
u6c luong
6 duoc
gqi
li BLUE
niSu
n6 li

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
.!
.
'{
.

- '
Sai
sii binh
phuong rung binh:
MSE(O):E(A-e)'?
,"*-'u++n.
.,.i
Sau
khi bi6n
diii ch
ng ta nhan.lusc:
MSE(
6
):var(6
)+EGi(
0
feJ'?''''
MsE(e)<ar(e)+bias(e)
't{
:ry
Sai s6
tinfr
phuong
trung
binh bing
phuong
sai
cta udc
luori!:6ng
v6i thi€n

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

"r'4t
.;', rn6n t,irn
"l*&
-
3&fulL
2.3.5. Tinh
ch6t crla
m6u l6n
,"r'\*1;st 'o
MQt sti
uoc luong
kh6ng
thod min
.@g,Il;i$r
thiiig. kC mong
-u6n
khi cd
miu nh6
nhung
khi co miu
l6n d6n v6
han thi
lai c6 fihls6
tinh chat
th6ng ke mong mu6n.
C6c tinlr
chdt
tliSng k6 nny
dugc
goi.ia

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,/

Vay sl Ie
u6c luqng kh6ng
thi6n lQch
cna o], trong khi 6] h udc tuqng
kh6ng thi6n
lQch tiQm
cin cta o] .
Nh6t
qudn
MQt
u6c tuqng
6 auqc
ggi
Id nhdt
qurin
n6u
xic
sudt
ntiu n6 titln tliln
gii
tr!
ttring cna 0
khi cd m6u ngdy
cdng lon.
e t, nr,6t
qudn
thi li*l6
-
el
.

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

,
r i,(
,.
,
.,i
l\eu
-{
la blen
ngau
phdn
phi5i
chuAn
thi X
,,,.1 \
.
.
, ,i.
_
l
,,
,
al breu ve
gra
tn cua tlam
so hoac
ve
giA
tri
cUa mot tap
hqp

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

p
vd
phucrng
sai o2ln
vdi cit cd
m6u nh6
vd ldn.
p
vd
phucrng
sai o2 nhrmg
kh6ng theo phdn
khi
n
ti6n
d6n
v6 chng.
ptrtii
cfruin
v<ri trung
binh
p
vd phuong
sai o2ln
l1i
gi6i
han trung
tAm 2.
2.4.
Th5ng

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

rihg chi
phi
cho hoc tAp trung
binh crla hoc
sinh ti6u
hoc li 106
ngdn d6ng/th6ng.
Gia thi6r
Ho:p=106:p6
H1:P1106:pe
Chtng
ta da
bi6t X
-Nfu,
olt{, va aq tin cdy
95%o hay
mfc
!
nglia a
= 5d/o ching ta
tli
xdy dmg
du<yc u6c
lrrgng khoring cta
p
li
X, t 2
#
.
Neu khoing niy

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).

Khoing
niy chira
96
:
106. V{y
ta
kh6ng
th6 bic b6
tlugc
gia
thi6t
H0.
Kho"nng
tin
ciy md ta
thirit
iip
tlugc diroc
goi
ld miAn
"h5p "ha",
mi6n
gi6
tri nim
ngodi
: , ,(
.;.
i
en ahan nnan nrrryc sol ra mren oAc b6-
.:

,,(
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,

n6u muc
1i
ng},ia.le o thi iric
sudt
tt6
Z nim 6 miAn b6c b6 b6n tr6i li
q/2
vd xic su6t
dA Z nim 6 miAn
bec b6
b€n,tiei cnr,g
h
a/2. Chring ta d[t
gi6
tri toi han
bdn trtii lir Z,n
yit
giil
tti t6i hqn b6n
phiildZr.a.
Do
tiol ddi
ximg ta lqi c6 Za2:
-
21.o12.
jP.
b6
Hinh 2:S:iiffiiAn ct
^
, r,-",.t,,

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,_,,,

<
Z
<
Zr_.,
r)
=
1
-
o
Thay z=
*/
,i ui6p aai
m6t chrit chtng ta nh{n tluoc
/J;
April 2011
23
(
-
_\
plx
-
2,,,,
:?
=
p
<X
+ z,_,,,$l
=
r
_a

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

-
z, ,,
]
<
t,
< x +
2,",,
*lu
=
r,l
=,
-
o
t
./o
' r/n'
")
Nguy6n
tfc
ra
quydt
ainh
\
,,r i- _
Cf
,
-
i; _
6
'

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

r/n
V6i
mric
f
nghiatr:5yoth\
Zb2:Zgt,sy":1,96=2
1.,
-
t0
Tac6
X,
-2 ,,)i
=105-2:
=
I03
-
-
Jn
10
11,r,
('
lO
Xt +
Z,-,,r-7:
=105
+2
"-:
=107
.!:
VN

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

10,/
/.l1oo
th6
b6c b6
Ho.
tlinh gie
thi6t
thdng
k6 theo gi6
tr! p
oOi
vOi
tiem
dinh haiduoTgiA
tri
p
dugc iir],
ol,u
ruu,
p
=
zr\2,,1<
z)
YdiZtt= -1
ta
c6P(\<Z):0,t6,vQy
gi6irip
=
0,32.
Quy

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