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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 .
