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V. V d minh ha.VD

. Chobngsliuvmthng xutkhuduth trong nc:Trong

Y: snlngduth ( nghn tn).

X: Kim ngchxutkhuduth (nghn tn).

Z: Vnutkhai thc ( trntriung).

Yu cu: Hy pht hinv khcphchintngaCngTuyn. C= 5%

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< Ngun: Tng cc thng k >

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Tin hnh c lng hm hi quy mu ta c:

Ta thu hm hi quy mu: = 12.47549 + 0.228322Xi + 0.001431Zi

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I. Pht hin hintng a cng tuyn.1. R2 nhng ts t thp

T bng s liu ta c: R2= 0,990379 > 0,8

tx= 2.167852 < ()

= ,5 = 2,179 tz= 1.547751 < 2.179

=>R2 cao ts t thp

Vy nghi nghc hin tng Cng a Tuyn trong m hnh cho.

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2. H s tng quan cp gia cc bin gii thch cao .

=> r23

= r32

=0,994412 > 0,8

=> Ta c c thm c s kt lun c hin tng a Cng Tuyn tronghnh.

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3. Hi quy ph.

Ta hi quy bin X theo bin Z thu c kt qu sau:

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Ta c = 0.05. KGT 0: 1: Nhn xt

Ta thy TK F c p-value =0.000000< = 0.05

Bc b H0chp nhn H1Vy cng c c skhng nh m hnh trn c hin tng a Cng

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4. o Theil

tnh c o Theil ta phi tnh c , , , , . ADCT, = , =

( ) =,,4 ,44

(,4)(,44) 0,16636. =0,99328320,98661= +(1- ) =(0,994213)2+ (1-0,9942132)0,16636 0,99038m=-[(1- ) =0,990382(1-0,98846)0,16636=0,9865Vy chng t c hin tng a cng tuyn sy ra. V mc a cng tuyn l

0.98654

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II. Khc phc hin tng a cng tuyn.

1. B bin.Cc bc cn tin hnh:

Bc 1 : hi quy Y theo X => , .Bc 2 : hi quy Y theo Z => , .Bc 3 : so snh

trong cc hi quy trn.Bc 4 : Kt lun

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Bc 1 : HI QUY Y THEO X

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Bc 2 : HI QUY Y THEO Z.

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Bc 3 : T kt qu hi qu trn ta c:

= 0.990379 = 0.988776 = 0.988459 = 0.987571 = 0.986612 = 0.985582Bc 4: Kt lun

=> Ta loi b bin Z ra khi m hnh.

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2.

S dng sai phn cp 1.

Chng ta c s liu chui thi gian biu th lin h gia bin Y v ccthuc X,Z theo m hnh sau:

= 1 + 2X2+ 3X3+ Ut (*)Vi t l thi gian. Phng php trn ng vi t th cng ng vi t -1 n

Yt-1= 1+ 2X2t-1+ 3X3t-1+ Ut-1 (**)Tr (*) cho (**) v t yt= YtYt-1xt= XtXt-1zt= ZtZt-1

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Ta thu c bng s liu mi sau :yt xt zt

0.2442 0.264 44.8987

0.3212 0.6919 58.4573

0.3322 0.14135

100.930

0.4411 0.7004 111.021

0.2112 1.1099 139.711

0.6655 0.6171 119.831

0.5049 0.3553 95.678

0.2024 1.3563 166.840

0.2244 1.1759 139.846

0.6391 1.2848 140.934

0.7865 1.9965 143.281

0.6655 1.9613 132.673

0.5588 1.243 148.982

0.0517 1.2529 244.739

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Hi quy sai phn cp 1

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Hi quy ph ca bin sai phn xttheo ztta c:

`H s tng quan gia cc bingii thch:

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Nhn Xt:

R2= 0.318112 < 0.8

r12= r21=0.582640 < 0.8

Khi ta tin hnh hi quy ph xttheo zt, mc d vn cn hin tng a Cnhng mc cng tuyn gim v p-value = 0,28779 gn vi = 0,0dng sai phn cp 1 mc ph hp ca m hnh b suy gim.

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B bin sai phn

Hi quy Y theo Xquy Y theo Z

T kt qu hi quy ca yttheo xtv ztta s loi b bin ztra khi m hnh

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Mt khc ta c t l s quan st. Phng trnh cng ng vi t quan st thvi t-1 quan st.

Ta c MHHQ gc ban u:

= 12.47549 + 0.228322Xi + 0.001431Zi (1)Xy dng hm hi quy th 2 m khi ta b i quan st u tin

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Ta c hm hi quy mi sau khi b i quan st u tin:

= 12.53141 + 0.222474Xi + 0.001445Zi (2)Ly (2) (1) ta c m hnh sai phn cp 1:

= 0,05592 + 0.00585Xi 0,000014Zi=> M hnh ny cng cngc th lm gim a cng tuyn ca cc bin d

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Kt lun.

C nhiu cch pht hin v khc phc hin tng a cng tuyn khc nphng php c nhng hn ch nht nh. V vy, khi p dng mt phno ta cn cn nhc k lng mang li kt qu tin cy nht.