NOMBRE: ALEJANDRA ENCINAS ENCINAS MONTAO MONTAO CURSO! 7" #A#
CÓDIGO: 6157283 FECHA: 19$03$2018
PROMEDIO SIMPLE EJERCICIO 1 Re%&'(%r e& )ron*+,'-o )%r% e& )r'er ,r'e+,re /e 1994 e/'%n,e e& ,o/o /e )roe/'o +')&e /e &%+ &% + en,%+ /e / e +'err%+ /e &% e)re+% e )re+% A-e Too& Too& Co)%n.
AÑO 1988
1989
1990
1991
1992
1993
TRIMESTRE 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
VENTAS 500 350 250 400 450 350 200 300 350 200 150 400 550 350 250 550 550 400 350 600 750 500 400 650
SOLUCIÓN
P.S.=
408.33 n'/%/e+ /e S'err%+
EJERCICIO 2 E& ren/'n'en,o /e n ono /e o&'%-'*n ener%& /e I% -'/%/ /e D%en)or, &-,% -on e& er-%/o. L%+ -o,'(%-'one+ en+%&e+ )%r% 1994 +on &%+ +''en,e+ /e& -%/ro. En-en,re &% /e%n/% )%r% e& e+ /e Enero /e 1995.
MES Enero
DEMANDA 9.29
SOLUCIÓN
erero M%r(o Ar'& M%o Jn'o J&'o Ao+,o Se),'ere O-,re No'ere D'-'ere
9.99 10.16 10.25 10.61 11.07 11.52 11.09 10 10.5 10.6 9.97
P.S.=
10.42
EJERCICIO 3 n% -o)%;<% /e+e% re%&'(%r n )ron*+,'-o )%r% e& e+ /e %r'& /e& 2017 ,en'en/o en -en,% &% +''en,e 'nor%-'*n! MES Enero erero M%r(o P.S.=
VENTAS REALES 2560 3205 2830 2865
SOLUCIÓN
PROMEDIO MÓVIL SIMPLE EJERCICIO 1 L% e)re+% %r-e& S.A. /e C.>. /e+e% e&%or%r e& )ron*+,'-o /e en,%+ ?o /e &% /e%n/%@ )%r% no /e ++ )ro/-,o+ /e %or /e%n/% en e& er-%/o +e &e -ono-e -oo -B'-B%rrone+ %r-e& e+,e )ron*+,'-o /e &% /e%n/% +' re'ere )%r% e& e+ /e o-,re /e 2003 )%r% &o -%& +e /ee -on+'/er%r e n= 2 3 4. S%'en/o e &o+ &,'o+ e+e+ e& re% /e er-%/o,e-n'% B% re'+,r%/o &% 'nor%-'*n B'+,*r'-% e +e 'n/'-% en &% +''en,e en &% +''en,e ,%&%!
MES Enero erero M%r(o Ar'& M%o Jn'o J&'o Ao+,o Se),'ere
DEMANDA 30 35 28 20 25 30 35 40 50
PMS2 32.5 31.5 24 22.5 27.5 32.5 37.5
PMS3 : : : 31.0 27.7 24.3 25.0 30.0 35.0
PMS4 : : : : 28.3 27.0 25.8 27.5 32.5
=∑24_(=1)^▒/
erero M%r(o Ar'& M%o Jn'o J&'o Ao+,o Se),'ere O-,re No'ere D'-'ere
9.99 10.16 10.25 10.61 11.07 11.52 11.09 10 10.5 10.6 9.97
P.S.=
10.42
EJERCICIO 3 n% -o)%;<% /e+e% re%&'(%r n )ron*+,'-o )%r% e& e+ /e %r'& /e& 2017 ,en'en/o en -en,% &% +''en,e 'nor%-'*n! MES Enero erero M%r(o P.S.=
VENTAS REALES 2560 3205 2830 2865
SOLUCIÓN
PROMEDIO MÓVIL SIMPLE EJERCICIO 1 L% e)re+% %r-e& S.A. /e C.>. /e+e% e&%or%r e& )ron*+,'-o /e en,%+ ?o /e &% /e%n/%@ )%r% no /e ++ )ro/-,o+ /e %or /e%n/% en e& er-%/o +e &e -ono-e -oo -B'-B%rrone+ %r-e& e+,e )ron*+,'-o /e &% /e%n/% +' re'ere )%r% e& e+ /e o-,re /e 2003 )%r% &o -%& +e /ee -on+'/er%r e n= 2 3 4. S%'en/o e &o+ &,'o+ e+e+ e& re% /e er-%/o,e-n'% B% re'+,r%/o &% 'nor%-'*n B'+,*r'-% e +e 'n/'-% en &% +''en,e en &% +''en,e ,%&%!
MES Enero erero M%r(o Ar'& M%o Jn'o J&'o Ao+,o Se),'ere
DEMANDA 30 35 28 20 25 30 35 40 50
PMS2 32.5 31.5 24 22.5 27.5 32.5 37.5
PMS3 : : : 31.0 27.7 24.3 25.0 30.0 35.0
PMS4 : : : : 28.3 27.0 25.8 27.5 32.5
=∑24_(=1)^▒/
O-,re
FG
45
41.7
38.8
EJERCICIO 2 CBo-o&%,e+ T'n &%r
MES Jn'o J&'o Ao+,o Se),'ere O-,re Se),'ere
DEMANDA 150 180 200 120 140 FG
PMS : 165 190 160 130
EJERCICIO 3 ,'&'-e e& )roe/'o *'& +')&e /e 3 e+e+ )%r% )rono+,'-%r e& )re-'o /e &% M,%& n/ )%r% enero /e 1995. PRECIO DEL MES PMS FONDO Enero 19.39 : erero 18.96 : M%r(o 18.20 : Ar'& 17.89 18.85 M%o 18.43 18.35 Jn'o 19.98 18.17 J&'o 19.51 18.77 Ao+,o 20.63 19.31 Se),'ere 19.78 20.04 O-,re 21.25 19.97 No'ere 21.18 20.55 D'-'ere 22.14 20.74 Ene! FG 21.52
NOMBRE: ALEJANDRA ENCINAS MONTAO CÓDIGO: 6157283 CURSO! 7" #A#
FECHA: 19$03$2018
PROMEDIO PONDERADO EJERCICIO 1 En n )er
Me# 2
Me# 3
Me# 4
Me# $
10 0
90
1 05
95
G
=∑24 =∑24_( _(=1) =1)^▒ ^▒ 〖 _ _ 〗
F t
PP =
w1 At 1
97.5
w A 2
t
2
.......... w
n
~
At n
98
EJERCICIO 2 C%&-&e e& )roe/'o )on/er%/o % ,re+ e+e+ -on )e+o+ /e 0.6 0.5 0.5 0.3 )%r% e& )er'o/o 7.
MES 1 2 3 4 5 6 7
EMAND 62 65 67 68 71 73
PP : : : 0.3 0.5 0.6 99.7
~
100
EJERCICIO 3 Con n )roe/'o )on/er%/o F-& e+ e& )ron*+,'-o )%r% +e),'ere -on %&ore+ re&%,'o+ /e 0.2 0.3 0.5 re+)e-,'%en,eG
MES Jn'o J&'o Ao+,o
VENTAS 140 180 170
" 1 2 3
0.2 0.3 0.5
PP 70 54 34 158
PROMEDIO MÓVIL PONDERADO EJERCICIO 1 ee/Me e+ n% -o)%;<% )ro/-,or% /e %&'en,o+ )%r% )erro re'ere -%&-&%r e& )ron*+,'-o /e /e%n/% -on e& ,o/o /e e/'% *'& )on/er%/% )%r% e& )er'o/o 19. P%r% &% e)re+% &% /e%n/% )%+%/% re-'en,e e+ &% + ')or,%n,e &e %+'n%n n )e+o /e 50. L% /e%n/% 'n,ere/'% ,'ene n )e+o /e 30 &% + &eK%n% /e 20. PERIODO EMAND 1 130 2 145 3 139 4 153 5 162 6 170 7 100 8 120 9 151 10 134 11 139 12 151 13 164 14 159 15 171 16 182 17 162 18 190 19
" 0.20 0.30 0.50
PMP : : : 139 147 155 164 133 124 132 136 140 144 155 159 166 174 170 180
FEEDME 200 180 160 140 S E 120 D A 100 D I 80 N U 60 40 20 0
2
4
6
DEMANDA 130 145 139
E& nero /e 'n,eren-'one+ 'rr'-%+ /e -or%(*n e +e re%&'(%n en e& o+)',%& ener%& /e e%r,'&&e B% %en,%/o +'n -e+%r en &o+ &,'o+ %;o+. L% %/'n'+,r%-'*n /e& Bo+)',%& e+, +-%n/o e& eKor ,o/o )%r% )rono+,'-%r &% /e%n/% /e e+%+ o)er%-'one+ en e& %;o 6. A -on,'n%-'*n +e )re+en,%n &o+ /%,o+ /e &o+ &,'o+ -'n-o %;o+. ,'&'-e Proe/'o *'& )on/er%/o /e ,re+ %;o+ +%n/o )on/er%-'one+ /e ?3$6@ ?2$6@ ?1$6@ %+'n%n/o n% %or )on/er%-'*n % &o+ /%,o+ + re-'en,e+.
EMAND " 45 0.166667 30 0.333333
PMP
10
1
PERIOD
EJERCICIO 2
AÑO 1 2
8
3 4 5 6
52 56 58
0.5 43.5 50.3 56.3
EJERCICIO 3 Lo+ /%,o+ re-o&e-,%/o+ en &%+ 'n+-r')-'one+ %n%&e+ )%r% n +e'n%r'o /e S' S'% en e& %&', Co&&%e +e e+,r% en &% +''en,e ,%&%. E+,'e &% /e%n/% /e neo )%r% &o+ %;o+ /e& 4 %& 12 -on n )roe/'o *'& )on/er%/o /on/e &% 'n+-r')-'*n /e& %;o %+ re-'en,e ,'ene n% )e+o /e 2 en &o+ o,ro+ /o+ %;o+ n )e+o /e 1.
AÑO 1 2 3 4 5 6 7 8 9 10 11 12
INSCRIPCIONES %MILES& 4 6 4 5 10 8 7 9 12 14 15
PMP : : : 18 20 29 31 32 33 40 49 56
2
14
16
PMP - - -
18
20
NOMBRE: ALEJANDRA ENCINAS MONTAO
CÓDIGO: 6157283
CURSO! 7" #A#
FECHA: 19$03$2018
SUAVI'ADO E(PONENCIAL SIMPLE EJERCICIO 1
PP e+ n% e)re+% e +e /e/'-% % &% %r'-%-'*n /e %r,<-&o+ B''n'-o+ e& eren,e /e er-%/o,e-n'% e+, 'n,ere+%/o en -ono-er e& )ron*+,'-o /e en,%+ )%r% & e+ /e o-,re + e'en-'% &e -on/-e % ,'&'(%r %-,ore+ /e )on/er%-'*n )%r% Q = 0.1 0.2 0.3. P%r% &o -en,% -on &% +''en,e 'nor%-'*n B'+,*r'-% e +e 'n/'-% % -on,'n%-'*n. E& -&-&o /e& /e+e%/o +e /eer o,ener )or SES.
MESES MAO JNIO JLIO AOSTO SEPTIEMRE OCTRE P%r% e& )ron*+,'-o /e %o ,'&'(%o+ e& +)e+,o !
DEMANDA 100 120 130 120 140 FG
SES SES A)*+,.3 SES A)*+,.1 A)*+,.2 100 100 100 100 100 100 102 104 106 104.80 109.20 113.20 106.32 111.36 115.24 109.69 117.09 122.67 110 117 123
_(−1)=_ (−1)
EJERCICIO 2 Con &o+ +''en,e+ /%,o+ -%&-&e e& )ron*+,'-o /e en,%+ o /e &% /e%n/% )%r% e& )er'o/o -on+'/ere %-,ore+ /e %K+,e 0.3 0.5 &o+ /%,o+ B'+,*r'-o+ /e en,%+ %+< -oo &o+ )er'o/ 'n/'-%n % -on,'n%-'*n! PERIODOS MENSUALES 3 4 5 6
DEMANDA 16 18 20 12
SES SES A)*+,.3 A)*+,.$ 16 16 16 16 16.60 17 17.62 18.5
7 8 9
16 20
15.93 15.95 17.17
17 P%r% e& )ron*+,'-o /e& )er'o/o 3 ,'&'(%o+ e& +)e+,o !
15.25 15.63 17.81 18
_(−1)=_ (−1)
EJERCICIO 3 Lo+ /%,o+ re-o&e-,%/o+ /e &% /e%n/% %n%& /e +%-o+ /e 50 &'r%+ /e er,'&'(%n,e en %& %r/en +e )re+en,%n en &% +''en,e ,%&%. ,'&'-e e& +%'(%'en,o e)onen-'%& -on n% /e +%'(%'en,o /e 0.3 )%r% )rono+,'-%r &% /e%n/% /e er,'&'(%n,e /%/% en e& )ro&e% e e& )ron*+,'-o /e& )er'o/o %n,er'or )%r% e& %;o 1 e+ /e 5000 +%-o+ )%r% -oen(%r e& )ro-e/''en,o. DEMANDA DE FERTILI'ANTES PRONÓSTICO SES %MILES DE SACOS& ~ 5 4 5 ~ 5 6 4.7 ~ 5 4 5.09 ~ 5 5 4.76 ~ 5 10 4.83 ~ 6 8 6.38 ~ 7 7 6.87 ~ 7 9 6.91 ~ 8 12 7.54 ~ 9 14 8.87 ~ 10 15 10.41 ~ 12 FG 11.79
AÑO 1 2 3 4 5 6 7 8 9 10 11 12 P%r% e& )ron*+,'-o /e& AO 1 -oo e& )ron*,'-o %n,er'or %& %;o 1 e+ /e 5000 +%-o+ ?5@ ,'&'(%o+ e& +)e+,o !
_(−1)=_ (−1)
SUAVI'ADO E(PONENCIAL DOBLE
EJERCICIO 1 C%&-&e e& )ron*+,'-o /e +%'(%-'*n e)onen-'%& -on -o)onen,e /e ,en/en-'% )%r% &o+ 2 % 12 -on n )ron*+,'-o /e ,en/en-'% 'n'-'%& ?T1@ /e 1.8 n )ron*+,'-o /e +%'(%-'*n e 'n'-'%& ?1@ /e 60 n% Q /e 0.30 n% /e 0.30. Yt= +
T1 (/1 0
1.8 X = (_(−1) )+((1−)(_(−1)+_(−1))) 60 = (_−_(−1) )+((1−)(_(−1) )) 0.3 0.3
Me#
De+n+
(
T
SED %5&
1 2 3 4 5 6 7 8 9 10 11 12
62 65 67 68 71 73 76 78 78 80 84 85
61.26 63.15 66.20 68.48 69.52 72.28 74.47 77.49 79.68 79.63 81.13 85.11
1.638 1.713 2.114 2.165 1.826 2.107 2.134 2.399 2.335 1.621 1.585 2.302
62.9 64.9 68.3 70.6 71.3 74.4 76.6 79.9 82.0 81.3 82.7 87.4
EJERCICIO 2 n &%or%,or'o -&
DEMANDA 28 27 44 37 35 53 38 57 61 39
( 28 30.2 35.2 38.2 40.1 45.1 46.4 50.8 55.5 55.0
T 3 2.84 3.28 3.22 2.96 3.36 2.94 3.25 3.52 2.72
PRONÓSTICO : D 33.0 38.5 0 β 41.4 43.1 48.4 X = 49.3 54.1 = ( 59.0 57.7
10 11 12 13 14 15
55 54 52 60 60 75
57.2 58.6 59.2 61.0 62.4 66.4
2.62 2.38 2.02 1.97 1.86 2.29
59.8 61.0 61.2 63.0 64.2 68.7
EJERCICIO 3 InE e+ n% e)re+% )ro/-,or% /e %&'en,o )%r% )e-e+ re'ere 7+)78)+ e) 9!n#; e+n+ -on e& <!! e #8+=;>+! e?9!nen7;+) 7!n 7!e77;n 9! enen7;+ )% )r*'o+ e+e+.E& )ron*+,'-o /e /e%n/% /e& )er
DEMANDA
Xt
Tt
PRONÓSTICO (Yt)
1132 1600 1690 1640 1765 1879 1990 2100 2210 2356 2201 2027
1500 1598.2 1719.4 1833.9 1927.6 2015.8 2099.1 2178.6 2255.4 2330.9 2409.8 2463.7
150 134.46 130.48 125.68 116.10 107.74 100.40 94.11 88.93 84.90 83.11 74.35
1650 1733 1850 1960 2044 2124 2200 2273 2344 2416 2493 2538
0 X = (
= (
/e& 2003 -%& +e ron*+,'-o
9 + +e
&%-e -on+,%n,e . S)on%
)er'o/o+ )onen-'%&
r'o re%&'(* &% +,%
27
0.2 0.2 Yt= +
+((1−)(_(−1)+_(−1))) −_(−1) )+((1−)(_(−1) ))
7! e r% &o+ &e+ 0. Pren
0.1 0.3 Yt= +
−1)+((1−)(_(−1)+_(−1))) −_(−1) )+((1−)(_(−1) ))
NOMBRE: ALEJANDRA ENCINAS MONTAO
CÓDIGO: 6157283
CURSO! 7" #A#
FECHA: 19$03$2018
SUAVI'ADO E(PONENCIAL M@LTIPLE EJERCICIO MTODO HOLT
+!="+ ! Se requieren dos valores estimados iniciales, el valor inicial estimado y el valor inicial de La tendencia. Por lo regular, el valor inicial atenuado se estima promediando unas cuantas oservaciones anteriores de !a serie. "l valor inicial de !a tendencia se estima mediante el uso de la pendiente de !a ecuaci#n de !a tendencia otenida de datos anteriores. Si no $ay disponiles datos anteriores, se usa cero como estimaci#n inicial.
Se )'/e re%&'(%r e& )rono+,'-o )%r% e& )er'o/o 25 e/'%n,e &% %,en%-'*n e)onen-'%& %K+,%/% % I% ,en/en-'% )%r% &o+ +''en,e+ /%,o+ /e A-e Too& Co)%n. Se +%e e + %&%= 0.3 e,%= 0.1 no B% /'+)on'&e+ /%,o+ %n,er'ore+ )or &o ,%n,o +e +% -ero -oo e+,'%-'*n 'n'-'%&.
PERIODO DEMANDA %& %5& 1 500 2 350 3 250 4 400 5 450 6 350 7 200 8 300 9 350 10 200 11 150 12 400 13 550 14 350 15 250
A
T
500 455 390.4 385.9 398.2 378.3 318.6 303.2 307.4 266.6 221.0 262.0 339.8 340.6 311.4
0 :4.5 :10.5 :9.9 :7.7 :8.9 :14.0 :14.1 :12.3 :15.2 :18.2 :12.3 :3.3 :2.9 :5.5
500 500.0 450.5 379.8 376.0 390.5 369.4 304.6 289.1 295.1 251.4 202.8 249.7 336.5 337.7
0 β
0.3 0.1
16 17 18 19 20 21 22 23 24 25
550 550 400 350 600 750 500 400 650
379.1 431.7 427.0 407.9 467.8 558.7 553.1 517.6 564.2
1.8 6.9 5.7 3.3 8.9 17.1 14.8 9.8 13.5
305.9 381.0 438.6 432.7 411.2 476.8 575.9 567.9 527.4 577.6
EJERCICIO MODELO "INTER "l modelo de atenuaci#n e%ponencial lineal y estacional de tres par&rnetros de 'inter, que es una e%tension del modelo de (olt, pudiera reducir el error de pron#stico. Se utili)a una ecuaci#n adicional para determinar la estacionalidad. "sta estimaci#n est* dada por un !ndice estacional, la cual muestra que la estimaci#n del !ndice estacional se multiplica por y se suma despu+s a la estimaci#n estacional anterior , multiplicada por 1-y La ra)#n /t, se divide entre t, para e%presar el valor en orma de ndice en ve) de $acerlo en t+rminos asolutos, de modo que pueda promediarse con el ndice estacional atenuado al periodo t - L.
= #_/_(−$) +(1−)("_(−1)+_(−1)) _=("_−"_(−1) )+(1−)_(−1) _=% _ / _ +(1−%)_(−$) _(+!)=( _ −&_) _(−+!) A& e%rn'n%r &o+ /%,o+ /e A-e Too& Co)%n en &% +''en,e ,%&% +e o+er% e &%+ en,%+ +on -on+'+,en,een,e %&,%+ /r%n,e e& )r'er -%r,o ,r'e+,re+ e +on enore+ /r%n,e e& ,er-ero. A)%ren,ernen,e e'+,e n )%,ron e+,%-'on%&.
AÑO 1988
1989
TRIMESTRE 1 2 3 4 1 2 3
T 1 2 3 4 5 6 7
VENTAS 500 350 250 400 450 350 200
1990
1991
1992
1993
1994
4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
300 350 200 150 400 550 350 250 550 550 400 350 600 750 500 400 650 850 600 450 700
I&+,re &% %,en%-'*n e)onen-'%& %K+,%/% % &% ,en/en-'% % &% e+,%-'on%&'/%/ )%r% &o+ /%,o+ /e A-e Too& Co)%n. P%r% -oen(%r &o+ -&-&o+ +e re'eren &%+ e+,'rn%-'one+ 'n'-'%&e+ /e %&or %,en%/o ,en/en-'% -%/% n% /e &%+ -%,ro e+,'%-'one+ /e e+,%-'on%&'/%/. E& %&or 'n'-'%& %,en%/o )e/e e+,'%r+e )roe/'%n/o no+ -%n,o+ %&ore+ %n,er'ore+ /e I% +er'e. E& %&or 'n'-'%& /e I% ,en/en-'% +e )e/e e+,'%r ,'&'(%n/o I% )en/'en,e /e I% e-%-'*n /e ,en/en-'% o,en'/% /e /%,o+ %n,er'ore+. L%+ e+,'%-'one+ /e e+,%-'on%&'/%/ +e )e/en -%&-&%r )%r% /%,o+ %n,er'ore+ e/'%n,e I% /e+-o)o+'-'*n /e &% +er'e /e ,'e)o. +e /ee+,r% I% ,-n'-% /e 'n,er )%r% %= .4 = .1 = .3. % e no B% /%,o+ %n,er'ore+ /'+)on'&e+ +e +% 500 -oo e& %&or 'n'-'%& 0 -oo e& %&or /e e+,'%-'*n 'n'-'%& /e ,en/en-'% 1.0 -oo I% e+,'%-'*n 'n'-'%& /e e+,%-'on%&'/%/. C%&-&e &o+ %&ore+ %,en%/o+ %-,%&'(%/o+ )%r% e& %;o 1994 )er'o/o+ 25 %& 28.
PERIODO DEMANDA %& %5& 1 500 2 350 3 250 4 400 5 450 6 350
A
T
S
9
500 440 360.4 368.2 394.2 381.2
0 :6 :13.4 :11.2 :7.5 :8.1
1 0.94 0.91 1.03 1.04 0.93
500 500 500 500 357 362.9
0 β
S-L
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
200 300 350 200 150 400 550 350 250 550 550 400 350 600 750 500 400 650
311.9 295.6 303.0 260.3 219.5 277.5 364.7 377.0 354.1 403.1 426.4 437.5 450.1 471.9 531.8 548.8 546.4 546.4
:14.2 :14.4 :12.2 :15.3 :17.8 :10.2 :0.5 0.8 :1.6 3.5 5.5 6.0 6.7 8.2 13.4 13.7 12.1 10.9
0.83 1.02 1.08 0.88 0.78 1.15 1.21 0.90 0.76 1.21 1.23 0.90 0.77 1.23 1.28 0.90 0.76 1.22
338.8 305.5 293.2 271.2 202.9 206.2 287.6 321.7 296.5 404.9 490.3 387.3 337.6 554.1 591.0 491.7 430.9 687.3 751.9 546.2 449.6 718.8
EJERCICIO MTODO DE BRO"N L% e)re+% Mo'e >'/eo S,ore n-'on% -on %r'o+ /'+,r''/ore+ /e ren,% /e '/eo-'n,%+ en Dener Co&or%/o. L% -o)%nI% e+, -re-'en/o re'ere %)&'%r + 'nen,%r'o )%r% /%r -%'/% % I% -re-'en,e /e%n/% /e +er'-'o+. E& )re+'/en,e /e I% -o)%;'% %+'n% % J'&& O,,enre', )%r% e )rono+,'e &%+ ren,%+ /e& )r*'o e+. Lo+ /%,o+ /e ren,% /'+)on'&e+ /e &%+ &,'%+ 15 +e%n%+ +e )re+en,%n en &% ,%&% +''en,e J'&& 'n,en,* /e+%rro&&%r n )ron*+,'-o e/'%n,e n )roe/'o *'& /e ,re+ +e%n%+ n )roe/'o *'& /o&e. De-'/e e)&e%r n% %,en%-'*n e)onen-'%& /e 0.4. % e e+ o'o e &o+ /%,o+ ,'enen n% ,en/en-'% J'&, +e en-en,r% -on e + )ron*+,'-o e+, +'e)re +e+,'%n/o &%+ ren,%+ re%&e+. Por e+,% r%(*n /e-'/e 'n,en,%r I% %,en%-'*n e)onen-'%& /o'e.
1 2 3 4 5 6
5 654 658 665 672 673 671
51 654 654 655.6 659.4 664.4 667.8
7 8 9 10 11 12 13 14 15 16
693 694 701 703 702 710 712 711 728 :
669.1 678.7 684.8 691.3 696 698.4 703 706.6 708.4 716.2
45!5 " 9:'
PERIODO VENTAS POR SEMANA 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
654 658 665 672 673 671 693 694 701 703 702 710 712 711 728 :
A
A/
VALOR DE +
654 655.6 659.4 664.4 667.8 669.1 678.7 684.8 691.3 696.0 698.4 703.0 706.6 708.4 716.2 :
654 654.6 656.5 659.7 662.9 665.4 670.7 676.3 682.3 687.8 692.0 696.4 700.5 703.6 708.7 :
654 656.6 662.2 669.1 672.7 672.8 686.6 693.3 700.2 704.2 704.7 709.6 712.7 713.1 723.8 :
VALOR PRONÓSTICO DE +9 %9,1& 0 0.6 1.9 3.2 3.3 2.5 5.3 5.6 6.0 5.5 4.2 4.4 4.1 3.1 5.0
654 654 657.2 664.1 672.3 676.0 675.3 691.9 698.9 706.2 709.6 709.0 714.0 716.8 716.2 728.8
0.; 0.1 0.3 1.0
0
0.;
"_=#_+(1−)"_(−1) _^= _+(1−)_( −1)! =2 _ − _ ! *=/(1−)( _−_ !) _(+!)=_+*_ !
NOMBRE: ALEJANDRA ENCINAS MONTAO
CÓDIGO: 6157283
CURSO! 7" #A#
FECHA: 19$03$2018 REGRESIÓN SIMPLE
EJERCICIO 1 En n% e)re+% o)er%n/o 2 %;o+ en S%n,% -r( e& eren,e /e en,%+ /e+e% re%&'(%r e& ) )%r% + &'ne% /e ,r%Ke+ /e %;o+ )%r% e& %;o 2016. E#+7;n Ve+n! O!! In=;en! P;+=e+
E#+7;n
214 150 75 45 90
Ven+#
21$ 175 80 55 120
P!e;! ene 214 21$ F+7! e 7++ e#+7;n E#+7;!n+)
>er%no
150
162.5
1.65
O,o;o In'erno Pr'%er% >er%no O,o;o In'erno Pr'%er%
75 45 90 175 80 55 120
77.5 50 105
0.78 0.51 1.06
To,%& Proe/'o
790 98.75
$%#"D&)t-,+*('01.
Ven+# #;n F+7! E#+7;!n+) 91.15 95.56 88.88 84.64 106.35 101.94 108.63 112.86
2 ) 3 # % 4 2 ) 3 # % F
EJERCICIO 2 Lo+ /%,o+ /e en,%+ /e 2 %;o+ /e n% e)re+% +on &o+ +''en,e+. Lo+ /%,o+ e+,n %-& e+e+ /e en,%+ en -%/% )er'o/o. E&%or%r n )rono+,'-o en %+e % &% rere+'*n &'ne%& +'
Me# Enero:erero M%r(o:%r'& M%o:Kn'o J&'o:%o+,o Se),'ere:o-,re No'ere:/'-'ere
S8+ P!e;!
Ven+# 2 Ven+# 2 109 115 104 112 150 159 170 182 120 126 100 106 P!e;! e Ven+# e 7++ e# 112 108 154.5 176 123 103
Me#e#
Ven+#
Enero:erero M%r(o:%r'& M%o:Kn'o J&'o:%o+,o Se),'ere:o-,re No'ere:/'-'ere Enero:erero M%r(o:%r'& M%o:Kn'o J&'o:%o+,o Se),'ere:o-,re No'ere:/'-'ere SMA PROMEDIO
109 104 150 170 120 100 115 112 159 182 126 106 1553 129.4
#;n ( %ne! e 5 %=en+# *+! 9e;!!#& e#+7;!n+)&
(5
(^2
1
125.95
126.0
1
2 3 4 5 6 7 8 9 10 11 12 78 6.5
124.62 125.65 125.00 126.26 125.65 132.88 134.21 133.19 133.83 132.57 133.19 1553.00 129.4
249.2 376.9 500.0 631.3 753.9 930.2 1073.7 1198.7 1338.3 1458.3 1598.2 10234.7
4 9 16 25 36 49 64 81 100 121 144 650
A= =
123.044 0.980
5,AB
1242
EJERCICIO 3 Lo+ /%,o+ /e &% )ro/--'*n /e ,r'o en ,one&%/%+ ?@ e& )re-'o /e& W'&o /e B%r'n% en )e+e,% /-%/% /e &o+ 80 en E+)%;% eron!
Pe;!!# 1 2 3 4 5 6 7 8 9 10 SMA PROMEDIO A= = =AU
P!877;n Pe7;! e )+ e T;! H+;n+ 30 28 32 25 25 25 22 24 35 40 286 28.6
25 30 27 40 42 40 50 45 30 25 354 35.4
(;K5;
(;2
750 840 864 1000 1050 1000 1100 1080 1050 1000 9734
900 784 1024 625 625 625 484 576 1225 1600 8468 817.96
2
74.12 :1.35 = 7412V 135
REGRESIÓN M@LTIPLE EJERCICIO 1 Tre-e e+,/'%n,e+ +e 'n+-r''eron % n )ror%% /e neo-'o+ /e &'-en-'%,r% en Ro&&'n+ Co&& +''en,e ,%&% 'n/'-% ++ )roe/'o+ /e -%&''-%-'one+ ?PA r%/e )o'n, %er%e@ /e+)+ )n,%-'*n /e& SAT ?e%en e+,n/%r /e %/'+'*n % n'er+'/%/e+ en E+,%/o+ n'/o+ -o -%n/o e+,%%n en )re)%r%,or'%. F% %&n% re&%-'*n +'n''-%,'% en,re &%+ -%&''-%-'one+ S' n e+,/'%n,e ,'ene 1200 en e& SAT F-& )'en+% e +er + PAG FC& +er<% +' B'e
EN ESTUDIANTE PUNTOS SAT %(1&
GPA%(2&
A C D E I J X L M
1263 1131 1755 2070 1824 1170 1245 1443 2187 1503 1839 2127 1098
2.9 2.93 3 3.45 3.66 2.88 2.15 2.53 3.22 1.99 2.75 3.9 1.6
E& -oe'-'en,e /e -orre&%-'on e+ enor %& 50 no +e %-er-% %& 100 &%+ %r'%&e+ 'n/e)e %r'%&e /e)en/'en,e.%/e%+ e e& 'n,er-e),o e+ %or e e& &% %r'%&e 1 en -on,r% or% ne%,'% % &% %r'%&e /e)en/'en,e.
E#+Q#;7+# e )+ Ree#;n Coe'-'en,e /e -orre&%-'*n 0.659703152 &,')&e Coe'-'en,e /e /e,er'n%-'*n 0.435208249 RY2 RY2 %K+,%/o 0.322249899 3.206120688 Error ,<)'-o 13 O+er%-'one+
In,er-e)-'*n >%r'%&e 1 >%r'%&e 2
5oeicientes 8.942333836 0.007987925 :5.13445993
ANLISIS
Rere+'*n Re+'/o+ To,%&
"rror tpico 4.3132424701 0.0032629413 1.9466366081
An);#;# e )!# e#;8+)e# :servaci#n 1 2
Pron#stico 9esiduos para / 4.141149058 :3.1411490585 2.932709187 :0.932709187
"stadstico t 2.0732277163 2.4480749165 :2.6376057605
Grados de libertad
Suma de cuadrados
2
79.207901364
10 12
102.79209864 182
Proailidad !nerior <=> 0.064931357 :0.66816929 0.034370818 0.0007176385 0.024835823 :9.471836588
Re#8)+!# e +!# e 9!+;);+ Percentil 3.846153846 11.53846154
/ 1 2
3 4 5 6 7 8 9 10 11 12 13
7.557762067 :4.557762067 7.340091396 :3.340091396 4.720185324 0.2798146763 3.500961251 2.4990387493 7.84821136 :0.8482113604 7.478725697 0.5212743029 9.831036847 :0.831036847 10.73060955 :0.730609548 9.512362733 1.4876372669 5.908256155 6.0917438453 9.497939377 3.5020606231
19.23076923 26.92307692 34.61538462 42.30769231 50 57.69230769 65.38461538 73.07692308 80.76923077 88.46153846 96.15384615
3 4 5 6 7 8 9 10 11 12 13
EJERCICIO 2 E& nero /e '%Ke+ en %,o+ e,ro ?+Z%@ en e& re% /e %+B'n,on D.C. /r%n,e er%no )%re-en e+,%r 'n-&%/o+ %& nero /e ,r'+,%+ e '+',%n &% -'/%/. Dr%n,e & %;o+ +e o,'eron &o+ +''en,e+ /%,o+. De+%rro&&e n o/e&o /e rere+'*n.
A! 1 2 3 4 5 6 7 8 9 10 11 12
N e T8;#+# 7 2 6 4 14 15 16 12 14 20 15 7
Ne V;+e# 15 10 13 15 25 27 24 20 27 44 34 17
nali)ando el coeiciente de correlaci#n m@ltiple de 0,6; es cercanos a uno, nos dice que independientes se relaciona con la variale dependiente, adem*s que los residuos estan c datos oservados.
Rere+'*n Re+'/o+ To,%&
ANLISIS DE VARIAN'A Arados de Suma de Promedio de Balor crtico ? liertad cuadrados los cuadrados de ? 2 59.460186861 29.7300934307 3.202914046 0.0890243024 9 83.539813139 9.2822014599 11 143 5oeicientes
"rror tpico
"stadstico t
Proailidad
!nerior <=>
In,er-e)-'*n 1.080382482 2.3389554784 0.4619081003 0.655109311 :4.210702407 >%r'%&e 1 :0.0196 0.4110183288 :0.0476864379 0.963007572 :0.949388056 >%r'%&e 2 0.249529927 0.2365102971 1.0550488926 0.318901086 :0.285493536
Re#8)+!# e +!# e 9!+;);+
An);#;# e )!# e#;8+)e# :servaci#n 1 2 3 4 5 6 7 8 9 10 11 12
Pron#stico para / 4.686131387 3.536481752 4.206671533 4.744931387 7.044230657 7.523690511 6.75550073 5.835781022 7.543290511 11.66769927 9.2704 5.185191241
9esiduos
Percentil
:3.686131387 :1.536481752 :1.206671533 :0.744931387 :2.044230657 :1.523690511 0.2444992701 2.1642189781 1.4567094891 :1.66769927 1.7296 6.8148087591
4.166666667 12.5 20.83333333 29.16666667 37.5 45.83333333 54.16666667 62.5 70.83333333 79.16666667 87.5 95.83333333
/ 1 2 3 4 5 6 7 8 9 10 11 12
EJERCICIO 3 Lo+ %+,o+ ,o,%&e+ /e n Bo+)',%& +e re&%-'on%n -on -Bo+ %-,ore+. Do+ /e e&&o+ +on e& n -%%+ en e& Bo+)',%& e& nero /e %/'+'one+. Se re-o&e-,%ron /%,o+ en 14 Bo+)',%&e+ en &% +''en,e ,%&%. En-en,re e& eKor o/e&o /e rere+'*n )%r% )re/e-'r &o+ %+,o+ ,o,%& Bo+)',%&. An%&'-e &% e%-,',/ /e e+,e o/e&o. FDeer<%n 'n-&'r+e %%+ %r'%&e+ en e&
HOSPITAL
N DE CAMAS
ADMISIONES %CIENTOS&
1 2 3 4 5 6 7 8 9 10 11 12 13
215 336 520 135 35 210 140 90 410 50 65 42 110
77 160 230 43 9 155 53 6 159 18 16 29 28
GASTOS TOTALES %MILLONES& 57 127 157 24 14 93 45 6 99 12 11 15 21
14
305
98
63
Bemos que las variales e%#genas no e%plican a la variale de desempeCo, por ende los de correlaci#n y determinaci#n no se acercan a uno, y los residuos empie)an a aumentar a pasa el tiempo. Estadísticas de la Regresión
Coe'-'en,e /e -orre&%-'*n 0.42945435 &,')&e Coe'-'en,e /e /e,er'n%-'*n 0.184431039 RY2 RY2 %K+,%/o 0.036145773 Error ,<)'-o 4.106999996 O+er%-'one+ 14
Rere+'*n Re+'/o+ To,%&
ANLISIS DE VARIAN'A Arados de Suma de Promedio de Balor crtico ? liertad cuadrados los cuadrados de ? 2 41.958061384 20.9790306918 1.243758362 0.325862053 11 185.54193862 16.8674489651 13 227.5
5oeicientes "rror tpico "stadstico t Proailidad !nerior <=> In,er-e)-'*n 8.902519068 1.8435424725 4.8290284604 0.000528186 4.8449094437 >%r'%&e 1 0.011381338 0.0221600543 0.5135970127 0.617692422 :0.037392613 >%r'%&e 2 :0.04620145 0.046625552 :0.9909041221 0.343029019 :0.1488236
An);#;# e )!# e#;8+)e# :servaci#n 1 2 3 4 5 6 7 8
on#stico para 9esiduos 7.791994895 :6.791994895 5.33441627 :3.33441627 4.194480791 :1.194480791 8.452337236 :4.452337236 8.885052822 :3.885052822 4.13137498 1.8686250203 8.047229408 :1.047229408 9.64963075 :1.64963075
Re#8)+!# e +!# e 9!+;);+ Percentil 3.571428571 10.71428571 17.85714286 25 32.14285714 39.28571429 46.42857143 53.57142857
/ 1 2 3 4 5 6 7 8
9 10 11 12 13 14
6.222836711 8.639959823 8.903082791 8.040693153 8.860825568 7.846084803
2.7771632893 1.3600401772 2.0969172086 3.9593068466 4.1391744322 6.1539151972
60.71428571 67.85714286 75 82.14285714 89.28571429 96.42857143
9 10 11 12 13 14
ono+,'-o
T!+) P!e;! A,
?
1
91.15
2
95.56
3 4 5 6 7 8
88.88 84.64 106.35 101.94 108.63 112.86
36 4.5
790.00 98.75
3$ 5,AB
%/o+ -on /o+ &e.
F+7! e Ven+# #;n Ven+# E#+7;!n+);+ E#+7;!n+) 0.865 126.0 0.835 124.6 1.194 125.6 1.360 125.0 0.950 126.3 0.796 125.6 132.9 134.2 133.2 133.8 132.6 133.2
PRONÓSTICO PARA EL AÑO SIGUIENTE (
MES
13 14 15 16 17 18
Enero:erero M%r(o:%r'& M%o:Kn'o J&'o:%o+,o Se),'ere:o-,re No'ere:/'-'ere
PRONÓSTICO 135.8 136.8 137.8 138.7 139.7 140.7
FACTOR ESTACIONAL 0.865 0.835 1.194 1.360 0.950 0.796
+ ? @ en &%
ee B%-e /o+ %;o+. L% /e 2 %;o+ en e& )ror%% &% n 'o /e 2400 )n,o+@ &%+ )n,%-'one+ en e& SATG r% o,en'/o 2400 )n,o+G
n/'en,e+ no e)&'-%n % &% o+'-'*n &% %r'&e 2 e)&'-% /e
E VARIAN'A Promedio de los cuadrados
F
Valor crítico de F
39.60395068
3.852820519
0.0574700698
10.27920986
Superior <=> !nerior <=,0> Superior <=,0> 18.55283696 :0.6681692896 18.5528369618 0.015258211 0.0007176385 0.0152582111 :0.79708327 :9.4718365885 :0.7970832739
&o+ e+e+ /e + 12 &,'o+
as variales rcanas a los
Superior <=> !nerior <=,0>
Superior <=,0>
6.371467371 :4.2107024072 0.910188056 :0.9493880564 0.78455339 :0.2854935356
ero /e o +e 'n/'-% e+ /e n /e&oG
6.3714673707 0.9101880564 0.7845533896
oeicinetes medida que
Superior <=> 12.96012869 0.060155288 0.056420696
!nerior <=,0> 4.8449094437 :0.037392613 :0.1488235996
Superior <=,0> 12.9601286918 0.0601552883 0.0564206963
?
?^2
91.15
1
191.13
4
(
ESTACIÓN
266.63 338.57 531.73 611.61 760.38 902.86
9 16 25 36 49 64
9 10 11 12
>er%no O,o;o In'erno Pr'%er+
3694.06
204
B,
331 1
PRONÓSTICO
PRONÓSTICO 113.65 116.96 120.27 123.58
VENTAS PRONOSTICADAS 117.5 114.1 164.4 188.7 132.8 112.0
