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Academia de Studii Economice a Moldovei

Facultatea de Cibernetică, Statistică şi Informatică Economică

Catedra: Matematică și Statistică Economică

Lucrare de laborator nr.1

Tema: ”Modelul de regresie liniar simplu”

  A efectuat: A verificat:

 Studenta gr. SPE!"! #rofesor universitar:

$%iaconu Cristina P&r țac'i Ion

Chişinău , 201

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1.!m e"tras de pe site#ul $iroului %ational de &tatistica '''.statistica.md datele cu pri(ire la  (aloarea )ib#ului in decursul anilor 1**+#2011, iar pentru anul 2012 (oi ace pre(e-iunea.

2.)entru a alcatui sistemul de ecuatii normale si a estima parametrii a si b eectuie-

calculele necesare.

(abelul !: Elemente de calcul

 )r. Anul

*aloarea PI+

lui

mii lei- t t/ t0

´̂ y

  ! / " 1 2 3

! !445 5"""3!! !" !34 !65""341" !224/7"

/!444 55!1525 !! !/!

4343"1"5 35621"7

"/666 !/25!/25 4 5!

!!"/"!"// !/62!36!

1 /66! !766""57 7 14 !!46/"764 !7/47732

2 /66/ /62"4"53 2 /2 !6/3434"6 //21"4/4

3 /66" /16145!1 " 4 7/!1411/ /774664"

7 /661 /432/273 ! ! /432/273 ""6"3/27

5 /662 "11"1367 ! ! "11"1367 "5/5/1/!

4 /663 "412""56 " 4 !!5"36!16 1"2/5252

!6 /667 13643/42 2 /2 /"615!172 15771714

!! /665 273!7!36 7 14 16""/6!/6 216/64!"

!/ /664 24!2/561 4 5! 2"/"72/"3 24/37677

!" /6!6 317!37"3 !! !/! 7!!551643 312!"/1!

!1 /6!! 73751572 !" !34 445/6""72 34724162

(otal   144/"6717 6 4!6 /"57661354 144/"6713

 y

−

8"2324""4 mii lei

2.1 a!lcatuiesc sistemul de ecuatii normale si estime- parametrii a si b.

{na+ba =¿{   14a+0 t =492307460a+910b=23877004689=¿{~a=35659339~b=2623082

Am obtinut urmatorul model de regresie liniar sim#lu :

~ y8"2324""49/3/"65/0t

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. /ntroduc datele problemei in &)&& astel am obtinut:

Coeicientsa

Model Gnstandardied Coefficients Standardied

Coefficients

t Sig. 42.6H Confidence Interval for +

+ Std. Error +eta o@er +ound G##er +ound

!

Constant- !65!7.344 157.1/! //.!41 .666 !!576.767 4731.34!

Anii 2.1!2 ./1" .457 //./7" .666 1.554 2.416

a. %e#endent *ariable: Produsul intern brut mill lei

.

!%34!a

Model Sum of S;uares df Mean S;uare F Sig.

!

>egression 5/64./15 ! 5/64./15 143.644 .666 b

>esidual /!2.!!4 !" !3.215

(otal 51/1."37 !1

a. %e#endent *ariable: Produsul intern brut mill lei

 b. Predictors: Constant-, Anii

Coeicientsa

Model Gnstandardied Coefficients Standardied

Coefficients

t Sig. 42,6H Confidence Interval for +

+ Std. Error +eta o@er +ound G##er +ound

!Constant- !65!7.344 157.1/! //.!41 .666 !!576.767 4731.34!

Anii 2.1!2 ./1" .457 //./7" .666 1.554 2.416

a. %e#endent *ariable: Produsul intern brut mill lei

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5. 4eriicam dacă estiamtorii sunt semniicati(i 6T#&tudent, calcul7nd (ariația estimatorilor si(ariația re-iduală

  Ŷ    Y −Ŷ    (Y  −Ŷ  )2 (Y  − Ý  )2 (Ŷ  − Ý  )2

!. 5,""" !.17 3.53" 17.!6677 4/1.644 !"55.127

/. 5,5!2 3.552 !.4"6 ".7/14 542.6/7 !6!1./"!

". !/,25! !/." 6./5! 6.67543! 35".572 345.3263

1. !7,66" !7.7!2 6.7!/ 6.263411 17/.!14 11!.7!1"

2. /6,2"4 /".!" /.24! 3.7!"/5! ""6.452 /1".1//1

3. /1,626 /5.212 1.142 /6./626" /!2.23! !6".772

7. /4,32" "".43 1."67 !5.226/2 5/.1/5 //.77!45

5. "1,1"2 "4."72 1.416 /1.16"3 !5.131 6.1!"1144. "4,12" 11.74 2.""7 /5.15"27 6.2/6 "3.344"3

!6. 13,643 26./62 1.!64 !3.55"55 21.//5 !"!.3/47

!!. 27,3!7 22.3/ !.447 ".455664 "23.31" /52./612

!/. 24,!2" 3!.6"2 !.55/ ".21!4/1 1!7.6!7 147.1/"5

!". 31,7!7 33.12 !.7"" ".66"/54 372.//6 735./572

!1. 73,752 7!.532 1.4/6 /1./631 !115.6"! !647.743

!2. 5!,712 77./5 1.132 !4.4"3/" !526.!!5 !152.415

(otal 25! 24! !6 //! 51/1."37 5/!3.1/2

!.   s2=∑ (Y −

^Y )

2

n−2=221

13=17

/.  var (b̂ )=s2 ∙   1

∑ x2=

 17

280=0.061

".  var (â )=s2∙( 1n+   ´ x

2

∑ x2 )=17 ∙(  1

15+4020025

280   )=17 ∙ (1.311+14357.232)=244095.23

1.  t calc â

0.05 =  |â−0|

√ var ( â)

=10817.7

494.06=21.895

2.  t 

calc b̂

0.05 =  |b̂−0|

√ var ( b̂)=

5.4147

0.247=21.922

3.  t stat =1.753

 

!lcătuesc inter(alele de 7ncredere pentru a și b

!.   b∈ [5.4147±1.753 ∙0.247 ] , b∈ [4.9817 ;5.8477 ]

/.   a∈ [−10817.7±1.753 ∙494.06 ] , a∈ [−11683.79 ;−9951.61 ]

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4eriic area 8/&9 și coeicientul de determinație r2

!.  F =

SPE

s2  =

8216,425

17

=483,32

/.  r

2=SPE

SPT  =

8216,425

8424.367=0,975

6.Concluzie generala:In fnal am determinat calculele necesare dupa modelul de regresie multipla incare am or!it despre eolutia in timp a "I#$ului%anii 1998$2011.&m o!tinut

modelul Ý =3565339+2623082∗t  %ast'el am constata ca modelul de regresie

este adecat .