Kajian Faktor-Faktor Yang Mempengaruhi Pertumbuhan Ekonomi Di Provinsi Sumatera Utara Berdasarkan Data Pada Tahun 2003-2012 Dengan Menggunakan Regresi Linier Berganda

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+ 6 (ܽ, ܾ_ଵ, ܾ_ଶ, ܾ_ଷ) <

6 3 6 6

9 + < + 6 < 6

ܺ ܻ1 6 (ܺ_ଵ)1 (ܺ_ଶ)1

∑ ܻ = ܽ + ܾଵ∑ ܺଵ+ ܾଶ∑ ܺଶ+ ܾଷ∑ ܺଷ #3.

∑ ܻܺଵ = ܽ ∑ ܺଵ+ ܾଵ∑ ܺଵଶ+ ܾଶ∑ ܺଵܺଶ+ ܾଷ∑ ܺଵܺଷ #37

∑ ܻܺଶ = ܽ ∑ ܺଶ + ܾଵ∑ ܺଵܺଶ+ ܾଶ∑ ܺଶଶ+ ܾଷ∑ ܺଶܺଷ #39

∑ ܻܺଷ = ܽ ∑ ܺଷ + ܾଵ∑ ܺଵܺଷ+ ܾଶ∑ ܺଶܺଷ + ܾଷ∑ ܺଷଶ #3/

L

6 1

1.040.674 = 10 ܽ + 13.580.466,74ܾଵ+ 31.753,16ܾଶ+ 127.410.206 ܾଷ

1.482.845.759.835,5 = 13.580.466,74ܽ + 44.678.340.166.573,5 ܾଵ

+ 45.296.470.704,4 ܾଶ+ 173.981.406.645.639 ܾଷ

3.596.870.326,5 = 31.753,16 ܽ + 45.296.470.704,4 ܾଵ+ 132.416.115,5 ܾଶ

+ 410.576.972.899,1 ܾଷ

13.331.446.397.896,8 = 127.410.206 ܽ + 173.981.406.645.639 ܾଵ

+ 410.576.972.899,1 ܾଶ+ 1.625.393.892.831.280ܾଷ

* + ܽ, ܾ_ଵ, ܾ_ଶ, ܾ_ଷ <

1 + L + 6

4 = −૚૜૞ૢૢ૜, ૟૝૜

૚ = ,

1 + +

ܽ, ܾଵ, ܾଶ, ܾଷ ?#3%@

Ŷ = −૚૜૞ૢૢ૜, ૟૝૜+ , '+૞, + , (

ܻ

Ŷ Ŷ, ܻ − Ŷ, ܻ − Ŷଶ 6

2&' 1

' ? ' . $( 2"%"-# $ $%"# &$(- %"$( &* ' - $ % $+ / *% , *

-"$ Ŷ ( − Ŷ) ( − Ŷ)

#$$% /838$719 /83#%$1/0 7/.18 %%$3.&$1#.70 #$$. 8%3%#810 8%39&$1# #8&1% /03&%#1#0&9& #$$7 8/380/18 8838/91.7 0/819 07/3/.018977 #$$9 0%3%./1. 0.39%71&0 &3#8/18 &39783.&&199& #$$/ 003/0#1% &$#3.771% #399%1$ /3$0&370&1.0% #$$8 &$93&/#1. &$939//1# 7$.18 #7.38$91&/00 #$$0 &&&37701# &&.3&0#10 #39%%1/ 930%93.$$19%8 #$&$ &&83/&810 &$03/8/10 830%&1$ /03/9&30##10/ #$&& &#9378/19 &#738%%1% /7.1% 798307#19/%. #$&# &%.3.9%10 &%93%/.1/ &30&$18 %397&3&%#1.8&

1 17 1 17 8 1 19 89

! .3# 1 6

?#38@

௘ = 5∑ܻ − Ŷ ଶ

− # − 1

∑ܻ − Ŷଶ C101.290.510,5

C10

௘ = 5∑ܻ − Ŷ ଶ

− # − 1

௘ = 5101.290.510,5_{10 − 3 − 1}

௘ = 5101.290.510,5₆

௘ = √16.881.752

6) = 789:, ;78

1 0&: * &$ &%&/, $ *

1

'! 1

2&' 1

' ' $( 2"%"-# $ $%"# &$(- %"$( ' 0&: * &$ &%&/, $ * -"$ Ŷ − < − < Ŷ − < − <

#$$% #738%919&%#% #73#9&18 99/37%$378% 9%83&7837%01# #$$. #$3.7/1&07%8 #$3/%817 .&83.0938.#19 .%$3$873%8#1% #$$7 &73&0$107%$. &93&9019 #%$3/973$7.1. #9&3.77309.1# #$$9 03.%#1#$99/ &$3/#$1$ 88309937##199 &&.30&83.$$1$ #$$/ &39&#1$07/// .3#/71& #3708387#1/0. &83#/93.8$1$ #$$8 #39$01/8%% #3&$71$ 938&$309818/% .3.%&3$#71$ #$$0 &$3&#717$./. /3.0&18 &$#37#738.91# 793&#/3$9/1# #$&$ 73/#$17.90&/ &.397&17 %#3/#.397/1$% #&.39993.7#1% #$&& #&3/9710&$.8 ##37#$1# ./%3/7.38701# 7$/3&703.$81$ #$&# %#3%$/1#0%98 %$3%0917 &3$.%3/9&3##7 0#%30./3#&#1%

! .3% 1 +

6 ?#30@

ଶ ₌ ∑Ŷ − ܻA ଶ

∑ܻ − ܻAଶ

ଶ ₌ 3.067.935.412

3.169.225.930

ଶ _{= 0,968039351}

_{= 9, B>:}

=1 0&: * &$ 0/&' *

1

'! 1

?#3&$@

= &ଶ

= &0,968

= 0,983889908

= 9, B:7

1 0&: * &$ 0/&' * $% / / 2&' &2 *

&3 + , ?ܺ_ଵ)

?ܺ_ଶ)3

భమ = ௡∑ _భమ ∑ భ∑ మ ௡ ∑ _భమ ∑ _భమ_{௡ ∑ మ}మ _∑ మమ భమ = *%.+,*.--.** *.ଶଶଶ.-.,+,.+.* /,.%*.*.-.+.*.+%..+-.+.% భమ = ଶଵ.-*.+-.--*,, .-...*....%+,%*-.++,.,+

_భయ = ௡∑ భయ ∑ భ∑ య ௡ ∑ _భమ _{∑ భ}మ_{௡ ∑ య}మ _{∑ య}మ

_భయ = _{/ ଵ.+-.%-.,-.+,.- *,.-+.,,-..ଷଵଶ.}ଵ.-+..*.,,.*%,.+ ଵ.-.+.,*.++.%%

భయ =

+.%*..%,..*

*....,.%.+.*..-,,-..*-%.+

_భయ = 9, 998

%3 + ?ܺ_ଶ)

?ܺ_ଷ)3

మయ =

௡∑ మయ ∑ మ∑ య

௡ ∑ _మమ _{∑ మ}మ_{௡ ∑ య}మ _∑ యమ

మయ =

*.%.-,+.-..++ *.*%.,-,.,%,.-%,+, / ..-%..*-.%*% *,.-+.,,-..ଷଵଵ.

_మమ = _{%.-,+...*.,,-,**-,,+--,+},.+.-.*,*

_మయ = 9, 99C

21 0&: * &$ 0/&' * $% / / 2&' &2 * +&$( $ / 2&' # &2 *

&3 + '!ܻ , ?ܺ_ଵ)3

భ =

௡∑ భ ∑ ∑ భ

௡ ∑ మ _∑ మ_{௡ ∑ భ}మ _∑ భమ

_భ =*....*%-.%+..%% *.ଵଷଶ....,**..,-,_{/ଷଵ.,+.%+.*,***%.-.++.+.*%+}

_భ =_{ଷ.-%..%-.-.,,.-%*%*%.-%*-*},+%.,..+%*.-,*

#3 + '!ܻ

?ܺ_ଶ)3

_మ = ௡∑ మ ∑ ∑ మ ௡ ∑ మ _∑ మ_{௡ ∑ మ}మ _{∑ మ}మ

మ =

%.+,..-.,% ଷଷ.**.,...+,.* /ଷଵ.,+.%+.*,*%..+-.+.%

మ =

ଶ.+*.%.%,,

ଷ.,*.+..-*,.,,++,++.%

_మ = 9, BC7

%3 + '!ܻ ?ܺ_ଷ)

య =

௡∑ య ∑ ∑ య

௡ ∑ మ _∑ మ_{௡ ∑ య}మ _∑ యమ

య =

ଵଷଷ.*.*,.+-..+,. ଵଷଶ.%+.*...-...** /ଷଵ.,+.%+.*,*.%-..%.%.*

_య = _{.-.%-..,+.-,,.*-%+-%+%%-%.+}-.+-%.,.*

_య = 9, :B7

1 ! ($ : # $* 0&: * &$ &(/&* /* ' 5 ! % % *% # 6

+ + ? )@ +

6 3

+ +

6 , ܺ_ଵ '!ܻ +

1 6 ܺ_ଶ

'! ܻ + 1 6

' ܾ = 0 ( = 1,2,3)" 6 +

? 1 @

? '! @3

'ଵ ܾ ≠ 0 ( = 1,2,3) ) 6 +

? 1 @

? '! @3

+ ܾ_ଵ%_ଵ1

+ ܾ_ଶ%_ଶ1 + ܾ_ଷ%_ଷ3

var − kov ܾ3Var − kov ܾ ?#3&/@

" − #$" ܾ = %௘ଶܺ′ܺ ଵ

%௘ଶ C4108,741ଶ

%௘ଶ C16.881.752,605081

ܺ′ܺ ଵ _C

ۏ ێ ێ

ۍ 162,866_2,332ݔ10 0,002 −1,341ݔ10 2,332ݔ10 3,881ݔ10 1,678ݔ10 −2,286ݔ10 0,002 1,678ݔ10 7,129ݔ10 −2,090ݔ10 −1,341ݔ10 −2,286ݔ10 −2,090ݔ10

1,107ݔ10 _ے

D4 − EFD C

2.749.471.820,316 3,937 41.085,446 −226,323 3,937 6,551ݔ10 2,832ݔ10 −3,859ݔ10 41.085,446 2,832ݔ10 1,204 −0,004 −226,323 −3,859ݔ10 −0,004 1,868ݔ10

" − #$"(ܾ) . ?

? @

" − #$"(ܾ) =

"_#$"ܾܽ

ଵ, ܽ

#$"ܾଶ, ܽ

#$"ܾଷ, ܽ

#$"ܽ, ܾଵ

"ܾଵ

#$"ܾଶ, ܾଵ

#$"ܾଷ, ܾଵ

#$"ܽ, ܾଶ

#$"ܾଵ, ܾଶ

"ܾଶ

#$"ܾଷ, ܾଶ

#$"ܽ, ܾଷ

#$"ܾଵ, ܾଷ

#$"ܾଶ, ܾଷ

"ܾଷ

+

"ܽ C%ଶ C2.749.471.820,316

"ܾଵ C%ଵଶ C6,551G10

-"ܾଶ C%ଶଶ C1,204

"ܾଷ C%ଷଶ C1,868G10 %

* _ଵ1_ଶ1 _ଷ ?#3&8@1

?#3&0@ ?#3#$@

ଵ = &6,551G10

-60' = 9, 998

ଶ = √1,204

60 = 8, 9B;

ଷ = &1,868G10 %

60( = 9, 997

(

&3 , ܺ_ଵ

;

' ܾଵ = 0 " 6 +

3

' ()*+ ,- ) < )

' ()$-# ,- ) > )

* ) * )

* )

) = ) !"#௡

) = )

.%-) = 2,36

* )

* ) ?#3#&@

)ଵ =_%ܾଵ ଵ

)ଵ =0,002_0,001

)ଵ = 2

! ) < ) 6 2 < 2,36 1

#3 ܺ_ଶ

;

' ܾଶ = 0 " 6 +

'! 3

'ଵ ܾଶ ≠ 0 ) 6 +

'! 3

' ()*+ ,- ) < )

' ()$-# ,- ) > )

* ) * )

* )

) = ) !"#௡

) = )

.%-) = 2,36

* )

* ) ?#3#&@

)ଶ =_%ܾଶ ଶ

)ଶ =5,876_1,097

! ) > ) 6 5,356 > 2,361

' ()$-# 'ଵ()*+3

%3 ܺ_ଷ

;

' ܾଷ = 0 " 6 +

'! 3

'ଵ ܾଷ ≠ 0 ) 6 +

'! 3

' ()*+ ,- ) < )

' ()$-# ,- ) > )

* ) * )

* )

) = ) !"#௡

) = )

.%-) = 2,36

* )

)ଷ =_%ܾଷ ଷ

)ଷ =0,017213114_0,004

)ଵ = 3,982

! ) > ) 6 3,982 > 2,361

' ()$-# 'ଵ()*+3

1 ! ($ : # $* &/* , $ &(/&* 5 ! % % *% # 6

+ ' ? @ +

1 6 , ܺ_ଵ1

ܺଶ1 ܺଷ <

1 6 '!ܻ + 3

(

73 ;

' ܾଵ = ܾଶ = ܾଷ = 0" 6 + <

? 1

@ ? '!

@3

'ଵ ܾଵ ≠ ܾଶ ≠ ܾଷ ≠ 0) 6 + <

? 1

@ ? '!

' ()*+ ,- 3 ≤ 3

' ()$-# ,- 3 > 3

/3 * 3 * 3

* 3

3.%&_భ,&ଶ

(*/) * ,*+-0 "ଵ = # − 1

= 3 − 1

= 2

(*/) * ,*1*2) "ଶ = − #

= 10 − 3

= 7

3.%&భ,&ଶC3.%ଶ ,- C4,74

* 3

* 3 ?#3##@

3 =

1మ ଵ 1మ

௡ ଵ

3 =

,+,. ଷ ଵ ,+,. ଷ ଵ

83

! 3 > 3 6 60,5 > 4,741

' ()$-# 'ଵ ()*+3

1 1 &$(0' - $ % &$( $

( 6 6

&3 ) + = - % /% ''

/0(/ ,1 % % *% <* % % *% <* 3

(

&3 1 / 2'& &> 6

- ? % &>@ 3

) < / 2'& &>

&3 ,& 6 1 O&1 O# O%3

#3 .)& 6 3

) * <1 > 1 1 < + < * 1 1 1

> 1 > <61 3 6

1 6 ",&/ < 3

%3 ; +%-1 6

3 8 3

.3 &< , '* 3

% 3

73 2&' 3 C

'!1 O& C , 1 O# C 1 O% C

3

93 '"&* ** $( 1

6 6 3

/3 =0'",$* 3

83 ' ($ 3 ) ( + 1

> 1 ' 3 '

3

03 & *"/& 3 )

1 * 1 2 3

< 3

6 + 6 3

,2 / 1 &$( * $ % &> ) +

%3 1 $ '.@&1

.3 < 1 ? '!@

&)&$+&$% O& ?, @1 O# ? @1 O% ? @ $+&)&$+&$%

,2 / 19 0% # '0( &(/&*

73 % % *% <* 6 *% , %&*1

0+&' : %1 &*</ )% 3&3

,2 / 1 0% # '0( &(/&* '0%*

83 6 ?

%@3

%3 6

6

: '&1 3& * + 6

1 6 3&3

1 &,2 - * $

< 1

&3 ! ?#3.@1 ?#37@1 ?#39@1 ?#3/@ +

ܽ = −135993,643

ܾଵ = 0,001539635

ܾଶ = 5,875794424

ܾଷ = 0,017213114

6

Ŷ = −135993,643 + 0,001539635ଵ+ 5,875794424ଶ+ 0,017213114

#3 ? ! @

6 1

'! 6 6 6

'! 6

* + (ଶ)6 0,9683 ) 6

96,8% '!

1 1 1 3,2%

6 + 3

.3 +

6 1

1 '!

0,9843 &1

1 1

'!

3

73 + ) A ! A " !

&3 + '!(ܻ) , (ܺ_ଵ)

* + 6 +( > 0)

6 '! 3

) 6 '! 1

3 6 1 '!

3 ; '!

1

#3 + '!(ܻ)

(ܺଶ)

* + 6 +( > 0)

6 '!

3 ) 6 '!

1 3

6 1 '!

3 ; '!

1 6 ? &@ 6

0,9243

%3 + '!(ܻ) (ܺ_ଷ)

* + 6 +( > 0)

6 '!

3 ) 6 '! 1

3 6 1 '!

3 ; '!

1

6 ? &@ 6 0,8943

93 + + ' ? )@

&3 , (ܺ_ଵ)

6 ) = 2,36

+ '! 3

#3 (ܺ_ଶ)

6 ) = 2,36

) = 5,3563 ! ) > )1

' ()$-# 'ଵ ()*+1 6

6 + '!

3

%3 (ܺ_ଷ)

6 ) = 2,36

) = 3,9823 ! ) > )1

' ()$-# 'ଵ ()*+1 6

6 + '!

3

/3 + ' ? 3@

6 3 = 4,74

3 = 60,53 ! 3 > 31

' ()$-# 'ଵ()*+1 6 6 + <

? 1

1 @ ? '!

9

91 &* ,)"' $

! 1

6 Ŷ = −135993,643 + 0,001539635_ଵ+

5,875794424ଶ+ 0,0172131143 + 6

0,968 1 - 96,8% '!

1 1

1 3,2% 6 + 3

1 1 '!

0,9843 "

1

6 &3

+ + ? @

- ܺ_ଶ ܺ_ଷ

6 + '!

ܻ3 , ܺ_ଵ 6 +

'! ܻ3 ) 6 +

< ? 1

@ ? '!

@1 +

6

< 1 1

+ +

6 3 6

) #$&%3 ! 3

! 3 &0083 " 3 6 ! 3

: 1 3 #$&%3 ) ?

6 < @3 3

4 3 #$$83 $ " # 3

! 3

" 1 < 3 #$$$3# " 3 ! ) 3

1 3 #$$93" # 3 < 3

3 &00#3! 3 3 " ! 3

) + 3 &00/3 ) ' 1 3 ! 3 6 3

) + 3 #$$$3 ) ' " 1 1 3 ! 3

6 3

1 3 #$$73 3 ! 3 ! : , 3

P Q 1 , )3 #$&%3 " >

" ) 3 , ) 1 1 3

=

! " # " $

%!# $ ! !&

! "

# " $

%!# $

! !&

" ' ""

! " # " $

%!# $ ! !&

( ) *

! " # " $

%!# $ ! !&

! " # " $

+! "

, -!

+! "

."" " / $

. #

" 0 " 1 (' * %!# $ ! !& ! "

# " $

2 3 4 " 2 1

!# / +! " / +! " 5

" ₂

!

6

3 4 " 2 1

2 " 0 " 1 (' * %!# $ ! !& ! " # " $

7 " 8 ' // 0

" 8

' // 0

."" "

(' * ) )

! " # " $

%!# $ ! !&

#!# 9 #!#

" 0 4 !

" 0 4 ! )

" ."" " / " 0

4 !

, -! " 0 4 !

! )

! )

! ! ) )

! ) )

! ! )

$ 0

' &: 0

' " ; " 4 !