regresion simple

1. = ( )
'
!
" "
# $
%
#& #&
" & & ( )
=β +β + β* * + +β +ε
=β +β + β* * + +β +ε
* =β * +β * + β* ** + +β +ε
=β +β + β* * + +β +ε
+
=β +β + β* * + +β +ε ∀ = *
+
β *
ε
β *
ε
= * β = β* = * * ** * ε = ε*
β * ε
=β +ε
, - & . // ! 0 1 ,%
2 & & 3/

2. $ 4
& = ∀ = ) 5
&
β *
ε
β *
ε
= * β = β* = * ** * ε = ε*
β * ε
6 % & & (
" &
' )
' ! "#! " ! $ % ! 2
7 5 ) 47 &
& " 8
(ε ) = /
' ( !" ! " 2 4 8
%
(ε ) = σ
) * " "+ 2 4
(ε ε ) = / ∀ ≠
9 %
, -! * " % . " : %)
&
/ " 8
0 " &
1 "2 3 " 43 !4
" &
=β +ε
;
< =β<
β< 0
8 "
8 0 8 0 "

3. 8 4
)
( −< ) = ε
= =
9 8 0 = 5 "
2 ! & = "2! = $+ β &
0 4 " > ?= @
" &
0
& 0 4 = "2!
2 & 8 = $+ β
< 8 &
β =( )
−
< ' '
*
= = = =
β
<
β
<
= =
*
= =
β = β*
< < ' = ' =
* * *
= = =
β
<
= =
: 4 ' 8 ) &
( )
−
' 8 8
0
<=β
<
< =β +β
< < + β*
<
* + +β
<
: A β )
< &
= ) 5
)
, > 5 //B " 0 $ = ?> C D

4. < =β +β
< < + β*
< + +β<
& )
0
" β
< ) 8 > ?
. " 8 &
9 4 ' '
8 4 4 4
( )
−
% & 4 % & β
< '
& :
0 = $+ β
% "
; 5 > ?= @ = "2!
& ) 0 4
&
*
" &
( β< ) = β
B
6 4 0
( β< ) = σ ( ' )
−
2 4 4 ) 4 β<
4 ) 4 ;
4( )
−
' 8 4 4 ) 4 β< 8
8 2 & 4 4 ) 4 4
) ) 5 &
4 "
σ β< σ β< β< σ β< β*
< σ β< β<
σ β< σ β< β*
< σ β< β<
( β< ) = σ ( ' )
−
= σ β<
*
σ β<
* β<
σ β<

5. +
( β< ) ( β< β< ) ( β< β< )
* ( β< β< )
( β< ) ( β< β< )
* ( β< β< )
( β< ) = σ ( ' )
−
=
( β< )
* ( β< β< )
*
( β< )
" (σ )
4 ( ) 8 (σ< ) "
4 4 ) 4 β< & #
& ()
( β< ) = ( ' )
−
# ( )
β
< 0
4
4 %
5 5 !2 "2
2 ( )
& ) "
&
! = ! + !
! ! !
( − )=( < − )+( −< )
+
( ' − ) = ( β< ' ' − )+( ' −β '
< ' )
! =( ' −
! )
(
! = β'
! < ' − )
! =(
! ' −β '
< ' )

6. 2 & &
: '
' =
=
6 6 7 1 (σ ) ( )
" 4 8 ( ) 8 σ
ε
ε 'ε
=σ =
< = =
− −
; ! =
! ε = ' −β '
< '
=
! ! ' −β '
< '
=σ =
< =
− −
: ( ) && ) &
( ) =σ
6 " 85 5 ( ) $" 85 5 9
2 ( )
" ( ) ( )
&
!! !!
= = −
!! !!
" ( )
5 /≤ ≤ 6 =
& 6 =/
" ( ) 39
2 4 4 6
( − )
= −
( − )
( − )
6 8 5 5

7. " ) 5
: 2
β
< = &
0 & &
5 &
% "/ β =
< % "# β ≠
<
0 & $ ( − ) &
β −
<
$ =
β<
9 $ $ ) $ $
α
$ ) ( − ) &
$α # α & 6 $ > $α
( − ) ( − )
%4 % β =
<
6 0
% "/ β = /
< % "# β ≠ /
<
0 & $ ( − ) &
β
<
$ =
β<
!
& $ $
α
$ ) ( − ) &
$α # α & 6 $ > $α
( − ) ( − )
%4 % β =
<
# % )
" 9
2
5
β + β + + β =
β + β + + β =
β + β + + β =

8. "
β
<
β
<
= = β=
<
β
<
6 & %
( ) (
( &
: % "/ β=
<
; 0
( )( ) ( )
−
( )
−
− β '
< ' ' − β
<
% =
! !
−
" 0 % % ( ) & )
( − ) & 6 % 8
> ) % %4 %
5 & , &
1 & % & " / β = β* =
< < =β =/
<
" & & 1 )
& # ) ( !)
! ( !&)
!
& ) ( !! ) & 8
& 0
( ! − !&)
! !
% =
!&
!
−
" 0 % % ( ) & )
( − ) & 6 % 8
> ) % %4 %
5 &
1 % 0

9. % =
( − )
−
" 0 % % ( ) & )
( − ) & 6 % 8
> ) % %4 %
5 &
6 6 3 $ 86 54
2 9:+ 9
& 8
& 66
Fuente de variación SS G de L MS
Regresión ! =β
! < − k-1 !!
−
! !
Error (Residuos) ! =
! −β n-k
−
Total − n-1
" 9:+ 9 8 =6 & )
&
: 9:+ 9 ( ) ) (% ) )
!! !!
= = −
!! !!
% =
( − )
−
'!
+ 8 % = ( )
'!
%&
6 . .2 5 $2 5
D % & ) )
" 5
&

10. & ( 4
;
$ &
β ε
= β/
" &
= β/ + β +ε
=α + β +ε *
α= β/ " α ) β
& ) ) 8 = $+
; ;
;
" β
A " 5
) β ? :
0 & A β & )
% ?
! 5 ; $ ;
= %
!
E
, 8 5 & 3
> 5 //B
= ( + )
$
$ / B
)
&
$ = / +$ ( + ) F
# β = / ) β = ( + ) ) & &
8
$ = β + β $ + ε$ G
" )
& 0 ) ;

11. " β
$
# ( =(
$ $ − $− )
$ =
( $ − $− ) =∆
$
$−
$( $ $ =
( $ − $− )H // = ∆I $
$−
∂ $
=β
∂$
−
$ $−
=β
∂$
6 //
∆ $
H // = β H //
∂$
∆I $
= β H //
∂$
" &
$ J β H //
$ " β H //
$
9% ; &
$ =β +β $ + ε$ 3
" β $
" β $
∂ $
=β
∂ $
∂ $
=β
∆ $
6 //
∂ $
H =β H
∆ $ // //
∂ $
=β H
∆I $ //

12. " & $
J β H
//
$ 5 β = 3//
I $ 3// H =3
//
& 5 5
6 &
$ =β +β + ε$ K
$
9 0 "
= $+
2 0 $
β ) $ 0 β
$
∂ $
= −β −
∂
$
$
∂ $
= −β
∂ $ $
" β & ) β
&
> 5 //B $) $ = ?> C D
) @# )# // " 0 = ) $ = ?
> C?D
- & . // $ ( * $ )+& ,( ,%

13. 2 $% % ( -$ )
L.( / 0M // /// &
-$ = β / + β $ +β $ + ε$ $=
$ & ( $ ) $
(1 ( # ) H //
1 ) 5 &
&
// // // // //
$ = B/ -$ = / $ =/ - $ = / $ = /
$= $= = = =
// // // //
$ $ =/ $
= / - $ =F ) - = F
= = = =
4$ ) 4
4" 8 = $+ "
4 ) 4 4 ) 4
5 "
4 ! &
4 $ &
4 6 5 & N#
8
4 $ ) 9:+ 9
4 O N$
4$ ) 4 '
// B/ /
= B/ / /
/ / /
4" 8 = $+
β =( )
−
# < ' '
4( )
−
4 ' ) '
/
' = F
/

14. − /
/ /
( )
−
= − /
/ B
/ /
/
2 &
− /
/ / /
β =( )
−
< ' ' = − / F
/ B
/
/ /
/
β = − *B
<
+ 8 > ?.
9 4 ' '
// B/ / / / /
B/ / / F / /
/ / / // /
6& 4 4%
( )
−
& 4 % & β
< '
− /
/ / / /
/ / −* − /
B / B
/ /
/ /
/
:
0 = $+ β
" 4 β = − *B
<
' −β '
< ' //
9% = ) ' = = -$ = F "
− = $=

15. /
F− −* F
B
' −β '
< ' /
= =
− // − *
F− G F
= = / /P
P3
4 4 ) 4
( β< ) = ( ' )
−
− / P −P /
/ / /// ///
( β< ) = P
//
−
/ B
/ = −P
///
P
B//
/
/ / / / P
/ ///
5 !
4 &
2 0
-$ = / F − / 3F
< (# ( )$ + 1$
-$ = / F − / 3F
<
$ + $
$ &
!
" β/ =
< )
∂-
& =β
∂ $
$
$
∂- β *
= " β = − = / 3F "
< I (
∆I $ // B
/ 3F
H // /// = 3F/
//
∂-$
(1 ( # ) H // " =β
∂ $
$
" β =
< "
& // ///

16. 4$ &
& 0
$
" β/
< &
" / β/ = /
<
" # β/ ≠ /
<
/F
$ = = 3 BF
P
///
α
" 0 0 ) ( − )
& " 0 $ / /F = PKB PFI 4
P3
) $/ / = G PPI 4 %4 %
P3
PPI 4 &
β
< &
"/ β = /
<
"# β ≠ /
<
−/ 3F
$ = = −F
P
B//
α
" 0 0 ) ( − )
& " 0 $ / /F = PKB PFI 4
P3
) $/ / = G PPI 4 PPI 4 %4
P3
% &
β< &
"/ β =/
<
"# β ≠/
<
$ = = / FB
P
///

17. α
" 0 0 ) ( − )
& " 0 $ / /F = PKB PFI 4
P3
) $/ / = G PPI 4 PPI 4 %4
P3
% &
4 6 5 & N#
# B 0 %
2 %
"/ β = β = /
< <
"# "/
( )( ) ( )
−
( )
−
− β '
< ' ' − β
<
% =
! !
−
" &
β/
< β/
<
/ / / / / β
< −*
= β= β
< < = β=
< β
< = = B
/ / / / / β
<
β β
* *
< <
* *
"
−
− /
/ / / /
/ −* / / / −*
− B − / / − B
/ / / / B /
/
/ /
/
% =
K 3F
P3
−
B
/ −* B / −*
−* B −* B
B / B / /
/
% = =
/ /P / /P
% = = GG GG
/ /P

18. " 0 0 &
) P3 & " 0
%( P3 )
= B 3P PPI 4 ) %( P3 )
= * /P PFI 4 " 0
) 0 PFI ) PPI %4
% 5 &
5 &
8 $
4 ) 9:+ 9
1 ) 4#
! =( ' −
! )
(
! = β'
! < ' − )
! =(
! ' −β '
< ' )
; & -$ )
& / -$ )
" ! =( ' −
! )= F − // ( / ) =
2 & #66 ! = ! − !
! ! !
! = β'
! < ( ' − ) 8 %) & !!= F
9 ) 9:+ 9
4O N"
2 & 9:+ 9 ( )
!! F
= = = / FK*
!!
" ( ) 5
" / FK* FK *I
&
: , 9:+ 9 J&
4
'! G F
% = = = G3 P
'! / /P