CALCULOS de elaboracion de proyecto
25
CALCULO DE LA DEMANDA FUTURA AÑOS CONSUMO AÑOS X CONSUMO Y 1 4.8 1 4.8 2 5.6 2 5.6 3 6.5 3 6.5 4 7.3 4 7.3 5 8.1 5 8.1 6 8.5 6 8.5 7 9.1 7 9.1 8 9.8 8 9.8 9 10.4 9 10.4 10 11.9 10 11.9 Sumatori ∑ 55 82 I) CALCULO DE PARAMETROS Fórmulas a utilizar: DATOS CALCULADOS: X= ∑ 55 XY= ∑ 510.90 Y= ∑ 82 a= 4.20666667 X^2= ∑ 385 Y^2= ∑ 716.42 N= 10 K= 2 II) CALCULO DE r Y r^2 r= 0.99397355 (cifra que representa la certeza d siendo su error 1-r) r^2= 0.98798342 (coeficiente de determinacion) II) PRUEBA F O ANALISIS DE VARIANZ Prueba de hi α= (1-α)= m= n= Ho: β1=b=0 Ha: β2=b≠0 r=( −( ) ∑ ∑ ( ))/(√[ ( ^2)] ∑ ∑ [ ( ^2 )−( ∑ ∑ 〖 ) 〗 ^2]) = 〖 Ȳ− 〗 ^2 b=( ( ) ∑ (∑ 〖 b=(1 (82) 5)^2 r=( −( ) ∑ ∑ ( ))/(√[ ( ^2)] ∑ ∑ [ ( ^2 )−( ∑ ∑ 〖 ) 〗 ^2]) = 〖 82/10−0.72606060 ( ∗ 55/10) 〗 ^2 =( ^2/( −1))/ ((1− ^2 )/( − )) =(0.98798342/(2−1))/ ((1−0.98798342)/(10−2)) =+
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Transcript of CALCULOS de elaboracion de proyecto
CALCULO DE LA DEMANDA FUTURA
AÑOS CONSUMO AÑOS X CONSUMO Y Y^21 4.8 1 4.8 1 23.042 5.6 2 5.6 4 31.363 6.5 3 6.5 9 42.254 7.3 4 7.3 16 53.295 8.1 5 8.1 25 65.616 8.5 6 8.5 36 72.257 9.1 7 9.1 49 82.818 9.8 8 9.8 64 96.049 10.4 9 10.4 81 108.16
10 11.9 10 11.9 100 141.61∑ Sumatoria 55 82 385 716.42
I) CALCULO DE PARAMETROSFórmulas a utilizar:
DATOS CALCULADOS:
∑X= 55∑XY= 510.90
∑Y= 82 a= 4.20666667 b= 0.72606061∑X^2= 385∑Y^2= 716.42
N= 10K= 2
II) CALCULO DE r Y r^2
r= 0.99397355 (cifra que representa la certeza de la evaluacion siendo su error 1-r)
r^2= 0.98798342 (coeficiente de determinacion)
III) PRUEBA F O ANALISIS DE VARIANZAPrueba de hipotesis
α= 0.05 (mide error tipo1)(1-α)= 0.95
m= g.l. en el numerador n= g.l.en el denominador
X^2
Ho: β1=b=0Ha: β2=b≠0
r=(𝑁 ∑𝑋𝑌 −(∑𝑋)(∑𝑌))/(√[𝑁(∑𝑋^2)][𝑁(∑𝑌^2 )−(∑ 〖𝑌 )〗^2])
𝑎= 〖 Ȳ�−𝑏𝑋〗^2 b=(𝑁 ∑𝑋𝑌 −(∑𝑋)(∑𝑌))/([𝑁(∑𝑋^2 )−(∑ 〖𝑋 )〗^2])b=(10(510.9) −(55)(82))/([10(385)−(55)^2])
r=(𝑁 ∑𝑋𝑌 −(∑𝑋)(∑𝑌))/(√[𝑁(∑𝑋^2)][𝑁(∑𝑌^2 )−(∑ 〖𝑌 )〗^2])
𝑎= 〖 82/10−0.72606060∗(55/10)〗^2
𝐹=(𝑅^2/(𝐾−1))/((1−𝑅^2 )/(𝑁−𝐾))𝐹=(0.98798342/(2−1))/((1−0.98798342)/(10−2))
𝑌=𝑎+𝑏𝑥
F= 657.747021 F(1,8)(0.95)= 5.32Como:
Rechazamos la hipótesisEl parámetro b es significativo estadisticamente.
IV) CALCULO DE LA VARIANZA DE LOS PARAMETROS
Formulas matriciales que identificaremos de los parámetros:
F Є R.C.
Var (𝛽)=𝑣𝑎𝑟( ¦ (𝑎 █ 𝑏@ ))𝑐 Var (𝛽)= 〖 (𝑋𝑋)〗^(−1 ). "б" ^2)
"б" ^2=(𝑒^𝑡.𝑒)/(𝑛−𝑘)
"e" ^𝑡.e= 𝑌^𝑡 Ȳ− 𝛽^𝑡(𝑋^𝑡Y)
𝑌^𝑡 Ȳ= ∑ ^2𝑌 𝛽^𝑡= (a ,
b)
𝑋^ 𝑡Y=((∑𝑌)¦(∑𝑋𝑌))
〖 (𝑋〗^𝑡 〖𝑋 )〗^(−1)=((𝑁 ∑𝑋 )¦(∑𝑋 ∑𝑋^2 ))^−1"e" ^𝑡.e= 716.42−(4.2066667 0.7260606060) (82¦510.90)
"e" ^𝑡.e= 716.42−715.885705 "e" ^𝑡.e= 0.5314295"б" ^2=0.5314295/(10−2)
"б" ^2= 0.0664286875
〖 (𝑋〗 ^𝑡 〖𝑋 )〗^(−1)=((10 55 )¦(55 385))^−1
𝐴=(((10 55 )¦(55 385)))/825 =((0.4666667 −0.06666666 )¦(−0.066666666 0.0121212))
Var (𝛽)= ((0.4666667 −0.06666666 )¦(−0.066666666 0.0121212)) (0.0664286875)
Var (𝛽)= ((0.0310000541 −0.0044285791 )¦(−0.044285791 0.0008051962))
XY4.80 AÑOS (X) DEMANDA OFERTA
11.2019.50 1 4.8 0.8 4 229.20 2 5.6 1 4.6 2.340.50 3 6.5 1.2 5.3 2.6551.00 4 7.3 1.5 5.8 2.963.70 5 8.1 1.9 6.2 3.178.40 6 8.5 2 6.5 3.2593.60 7 9.1 2.8 6.3 3.15
119.00 8 9.8 3 6.8 3.4510.90 9 10.4 3.5 6.9 3.45
10 11.9 3.9 8 411 12.1933333 1.785 10.408333333 6.24512 12.9193939 1.829 11.090393939 6.6542363613 13.6454545 1.93790909 11.707545455 8.1952818214 14.3715152 2.04681818 12.32469697 8.6272878815 15.0975758 2.15572727 12.941848485 9.7063863616 15.8236364 2.26463636 13.559 10.1692517 16.549697 2.37354545 14.176151515 10.632113618 17.2757576 2.48245455 14.79330303 11.538776419 18.0018182 2.59136364 15.410454545 12.328363620 18.7278788 2.70027273 16.027606061 12.8220848
AÑOS (X) OFERTA
1 0.82 13 1.24 1.55 1.96 27 2.88 39 3.5
10 3.911 1.785
(mide error tipo1) 12 1.82913 1.9379090914 2.0468181815 2.15572727
DEMANDA INSATIFECHA (D-O)
DEMANDA DIRIGIDA %
DEMANDA HISTORICA
DEMANDA FUTURA
16 2.2646363617 2.3735454518 2.48245455
El parámetro b es significativo estadisticamente. 19 2.5913636420 2.70027273
n= tamaño de muestra
k= N° de variables incluidas la variable dependienteAÑOS (X) OFERTA
e= errores del modelo muestral 1 4.8 0.82 5.6 13 6.5 1.24 7.3 1.55 8.1 1.96 8.5 27 9.1 2.88 9.8 39 10.4 3.5
10 11.9 3.911 12.193333333 1.78512 12.919393939 1.82913 13.645454545 1.9379090914 14.371515152 2.0468181815 15.097575758 2.1557272716 15.823636364 2.2646363617 16.54969697 2.3735454518 17.275757576 2.4824545519 18.001818182 2.5913636420 18.727878788 2.70027273
DEMANDA-LINEAL
"e" ^𝑡.e= 0.5314295
Var (𝛽)= ((0.0310000541 −0.0044285791 )¦(−0.044285791 0.0008051962))
Var (a)= 0.0310000541
Var (b)= 0.0008051962
Se (a)= 0.1760683223
Se (b)= 0.0283759792
DEMANDA
4.85.66.57.38.18.59.19.8
10.411.9
12.193333333333312.919393939393913.645454545454514.371515151515115.0975757575757
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
2
4
6
8
10
12
14
16
18
20
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO LINEAL
15.823636363636416.549696969697
17.275757575757618.001818181818218.7278787878788
4.8 4.85.6 5.66.5 6.57.3 7.38.1 8.18.5 8.59.1 9.19.8 9.8
10.4 10.411.9 11.9
13.1720219617377 11.012308817568214.4489475518416 11.288044639892815.8496611957006 11.541697007951417.3861631871229 11.776542419546919.0716171555303 11.9951782670897
20.920462842343 12.199698443797222.948539810162 12.3918156189072
25.1732231445989 12.572948509664827.6135723113486 12.744285525967230.2904944438027 12.906832070994
DEMANDA-SEMILOGARITMICA
DEMANDA- LOGARITMICA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
2
4
6
8
10
12
14
16
18
20
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO LINEAL ,SEMILOGARITMICO Y
LOGARITMICO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
DEMANDA-LINEALOFERTA DEMANDA-SEMILOGARITMICADEMANDA- LOGARITMICA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
2
4
6
8
10
12
14
16
18
20
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO LINEAL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210
2
4
6
8
10
12
14
16
18
20
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO LINEAL ,SEMILOGARITMICO Y
LOGARITMICO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
DEMANDA-LINEALOFERTA DEMANDA-SEMILOGARITMICADEMANDA- LOGARITMICA
CALCULO DE LA DEMANDA FUTURA
AÑOS CONSUMO AÑOS X CONSUMO Y1 4.8 1 4.82 5.6 2 5.63 6.5 3 6.54 7.3 4 7.35 8.1 5 8.16 8.5 6 8.57 9.1 7 9.18 9.8 8 9.89 10.4 9 10.4
10 11.9 10 11.9
I) CALCULO DE PARAMETROSFórmulas a utilizar:
∑X= 55 a= 0.6776309927 b=∑Y= 82 a= 4.7602634933 b=
∑X^2= 385∑logY= 8.986417194
∑XlogY= 52.740455470 Entonces: Y=4.760263493(1.096942261)^x∑logY^2= 8.212641607
N= 10
II) CALCULO DE R Y R^2
r= 0.9858320498 r^2= 0.97186483
III) PRUEBA F O ANALISIS DE VARIANZA
𝑌=𝑎.𝑏^𝑥
𝑎′= 〖 Ȳ�′−𝑏〗^′X b'=(𝑁 ∑𝑋𝑌′ −(∑𝑋)(∑𝑌′))/([𝑁(∑𝑋^2 )−(∑ 〖𝑋 )〗^2])b=(10(52.74045547) −(55)(8.986417194))/([10(385)−(55)^2])
𝑎= 8.986417194/10 −0.0401837685∗55/10
r=(𝑁 ∑𝑋𝑙𝑜𝑔𝑌 −(∑𝑋)(∑𝑙𝑜𝑔𝑌))/(√[𝑁(𝑋^2 )−〖 (∑𝑋)〗^2][𝑁(∑𝑙𝑜𝑔𝑌^2 )−(∑ 〖𝑙𝑜𝑔𝑌 )〗^2])r=(10 ∗(52.740455470 −55∗(8.986417194))/(√[10(385)−( 〖 55〗^2)][10(8.212641607)−( 〖 8.986417194)〗^2])
𝐹=(𝑅^2 (𝑁−𝐾))/((1−𝑅^2 )/(𝐾−1)) 𝐹=(0.97186483/(10−2))/((1−0.97186483)/(2−1))
F= 276.34163122
Rechazamos la hipótesis
IV) CALCULO DE LA VARIANZA DE LOS PARAMETROS
Formulas matriciales que identificaremos de los parámetros:
Var( log a) =0.000224967283 Se(log a) = 0.014996899Var( log b) =0.00000564329691 Se(log b) = 0.00217229819Covar(log a, log b)= Covar(log b, log a) = -0.00003213813301
𝐹=(𝑅^2 (𝑁−𝐾))/((1−𝑅^2 )/(𝐾−1)) 𝐹=(0.97186483/(10−2))/((1−0.97186483)/(2−1))
Var (𝛽)= 〖 (𝑋^𝑇 𝑋)〗^(−1 ). "б" ^2) "б" ^2=(𝑒^𝑡.𝑒)/(𝑛−𝑘)"e" ^𝑡.e= 𝑌^𝑡 Ȳ− 𝛽^𝑡(𝑋^𝑡Y)
𝑌^𝑡 Ȳ= ∑𝑙𝑜𝑔𝑌^2 〖 (𝑋〗^𝑡 〖𝑋 )〗^(−1)=((𝑁 ∑𝑋 )¦(∑𝑋 ∑𝑋^2 ))^−1𝑋^𝑡 Ȳ=((∑𝑙𝑜𝑔𝑌)¦(∑𝑙𝑜𝑔𝑋𝑌)) 𝛽^𝑡= (a ,
b)
"e" ^𝑡.e= 8.212641697−(0.6776309927 + 0.0401837685) (8.9864¦█([email protected]@55.47))"e" ^𝑡.e= 8.212641697−(6.0894747798 + 2.110310227
"e" ^𝑡.e= 0.003856582
"б" ^2=(𝑒^𝑡.𝑒)/(𝑛−𝑘)"б" ^2=0.003856582/(10−2)
"б" ^2=0.00048207275
〖 (𝑋〗^𝑡 〖𝑋 )〗^(−1)=((0.4666666667 − 0.0666666666 )¦(−0.066666666−0.0121212121))^−1Var (β)= ((0.4666666667 −0.06666666 )¦(−0.066666666 0.0121212)) (0.00048207275)Var (log 𝑎/log 𝑏 ) )= ((0.000229967283 −0.0002113813301)¦(−0.00003213813301 0.000005843296911))" "
* El logaritmo del valor a estimado varía en 0.014998899 unidades del verdadero valor poblacional* El logaritmo del valor b estimado varía en 0.00241723unidades del verdadero valor poblacional B* La covarianza entre los logaritmos d los estimadores es de -0.00003213813301
V) PRUEBAS t LOS PARAMETROS POBLACIONES:
Ho: A=0Ha: A≠0
En la tabla:
t 0.025=2.306
Como t Є R.C.Rechazamos la Ho
Ho: B=0Ha: B≠0
En la tabla:
t 0.02518=2.306
Como t Є R.C.Rechazamos la Ho
PUEBRA t PARA EL PARAMETRO b=A
t a/2, (n-2)
PUEBRA t PARA EL PARAMETRO b=B
t a/2, (n-2)
𝑡=(𝑎−𝐴)/(𝑆𝑒(𝑎))=(0.6776309927−0)/0.014998899 𝑡=45.17871558
𝑡=±2.306
𝑡=(𝑏−𝐵)/(𝑆𝑒(𝑏))=(0.0401837685−0)/0.002417229819 𝑡=16.62389786
𝑡=±2.3060.95
0.025
2..306
0.025
2..306RARC RC
0.95
0.025
2..306
0.025
2..306RARC RC
AÑOS (X) DEMANDA
X^2 log Y X log Y log Y^2 1 4.81 0.68124124 0.68124124 0.46408962 2 5.64 0.74818803 1.49637605 0.55978532 3 6.59 0.81291336 2.43874007 0.66082813 4 7.3
16 0.86332286 3.45329144 0.74532636 5 8.125 0.90848502 4.54242509 0.82534503 6 8.536 0.92941893 5.57651355 0.86381954 7 9.149 0.95904139 6.71328975 0.91976039 8 9.864 0.99122608 7.92980861 0.98252913 9 10.481 1.01703334 9.15330005 1.03435681 10 11.9
100 1.07554696 10.7554696 1.15680127 11 13.17202212 14.448947613 15.849661214 17.386163215 19.071617216 20.920462817 22.948539818 25.173223119 27.6135723
0.0401837685 b= antilog(0.0401837685) 20 30.29049441.096942261
AÑOS (X)
123456789
101112131415161718
Prueba de hipotesis 19
DEMANDA HISTORICA
DEMANDA FUTURA
𝑌=𝑎.𝑏^𝑥
b'=(𝑁 ∑𝑋𝑌′ −(∑𝑋)(∑𝑌′))/([𝑁(∑𝑋^2 )−(∑ 〖𝑋 )〗^2])b=(10(52.74045547) −(55)(8.986417194))/([10(385)−(55)^2])
20
α= 0.05(1-α)= 0.95
F(m,n)(α)F(1,8)(0.95)=5.32
Como:Rechazamos la hipótesis
El parámetro b es significativo estadisticamente.
Ho: β1=b=0Ha: β2=b≠0
F Є R.C.
𝛽^𝑡= (a , b)
* El logaritmo del valor a estimado varía en 0.014998899 unidades del verdadero valor poblacional* El logaritmo del valor b estimado varía en 0.00241723unidades del verdadero valor poblacional B
0.95
0.025
2..306
0.025
2..306RARC RC
0.95
0.025
2..306
0.025
2..306RARC RC
OFERTA
0.8 4 21 4.6 2.3
1.2 5.3 2.651.5 5.8 2.91.9 6.2 3.12 6.5 3.25
2.8 6.3 3.153 6.8 3.4
3.5 6.9 3.453.9 8 4
1.97580329 11.19621866748 6.71773122.16734213 12.28160541907 7.368963252.37744918 13.47221201635 9.430548412.60792448 14.77823870905 10.34476712.86074257 16.2108745822 12.15815593.13806943 17.78239341599 13.33679513.44228097 19.50625883864 14.62969413.77598347 21.39723967291 16.68984694.14203585 23.47153646465 18.77722924.54357417 25.74692027723 20.5975362
OFERTA DEMANDA0.8 4.81 5.6
1.2 6.51.5 7.31.9 8.12 8.5
2.8 9.13 9.8
3.5 10.43.9 11.9
1.97580329 13.172021961742.16734213 14.448947551842.37744918 15.84966119572.60792448 17.386163187122.86074257 19.071617155533.13806943 20.920462842343.44228097 22.948539810163.77598347 25.17322314464.14203585 27.61357231135
DEMANDA INSATIFECHA (D-O)
DEMANDA DIRIGIDA %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO SEMILOGARITMICO
4.54357417 30.2904944438
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
OFERTA DEMANDA
CURVA DEMANDA-OFERTA POR EL METODO SEMILOGARITMICO
AÑOS (X) DEMANDA OFERTA
1 4.8 0.8 42 5.6 1 4.63 6.5 1.2 5.34 7.3 1.5 5.85 8.1 1.9 6.26 8.5 2 6.57 9.1 2.8 6.38 9.8 3 6.89 10.4 3.5 6.9
10 11.9 3.9 811 11.0123088175682 1.65184632 9.3604624949329312 11.2880446398928 1.6932067 9.5948379439088913 11.5416970079514 1.73125455 9.8104424567586614 11.7765424195469 1.76648136 10.010061056614815 11.9951782670897 1.79927674 10.195901527026216 12.1996984437972 1.82995477 10.369743677227617 12.3918156189072 1.85877234 10.533043276071118 12.5729485096648 1.88594228 10.687006233215119 12.7442855259672 1.91164283 10.832642697072120 12.906832070994 1.93602481 10.9708072603449
AÑOS= X DEMANDA= Y Xi Xi*Yi1 4.8 0 02 5.6 0.69314718 3.881624211135693 6.5 1.09861229 7.140979876342714 7.3 1.38629436 10.11994883617525 8.1 1.60943791 13.03644709071626 8.5 1.79175947 15.22995548843857 9.1 1.94591015 17.70778235640348 9.8 2.07944154 20.37852710846249 10.4 2.19722458 22.8511356042967
10 11.9 2.30258509 27.4007626066291- 82 15.1044126 137.7471631786
Calculo de c -1.07715612231356 Y=(Xi- c)/dcalculo de d 0.315560656051355
DEMANDA INSATIFECHA (D-O)
DEMANDA HISTORICA
DEMANDA FUTURA
22.3
2.652.93.1
3.253.153.4
3.454
5.61627749695985.75690276634536.86730971973117.00704273963047.64692614526977.77730775792077.89978245705338.33586486190778.66611415765778.7766458082759
yi^223.0431.3642.2553.2965.6172.2582.8196.04
108.16141.61716.42
DEMANDA DIRIGIDA %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
2
4
6
8
10
12
14
Column DColumn E
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
2
4
6
8
10
12
14
Column DColumn E
AÑOS (X) OFERTA
1 4.8 0.8 4.8 4.82 5.6 1 5.6 5.63 6.5 1.2 6.5 6.54 7.3 1.5 7.3 7.35 8.1 1.9 8.1 8.16 8.5 2 8.5 8.57 9.1 2.8 9.1 9.18 9.8 3 9.8 9.89 10.4 3.5 10.4 10.4
10 11.9 3.9 11.9 11.911 12.1933333 1.785 13.172022 11.012308812 12.9193939 1.829 14.4489476 11.288044613 13.6454545 1.93790909 15.8496612 11.54169714 14.3715152 2.04681818 17.3861632 11.776542415 15.0975758 2.15572727 19.0716172 11.995178316 15.8236364 2.26463636 20.9204628 12.199698417 16.549697 2.37354545 22.9485398 12.391815618 17.2757576 2.48245455 25.1732231 12.572948519 18.0018182 2.59136364 27.6135723 12.744285520 18.7278788 2.70027273 30.2904944 12.9068321
DEMANDA-LINEAL
DEMANDA-SEMILOGARI
TMICA
DEMANDA- LOGARITMI
CA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
DEMANDA-LINEALOFERTA DEMANDA-SEMILOGARITMICADEMANDA- LOGARITMICA
CURVA DEMANDA-OFERTA POR EL METODO LINEAL ,SEMILOGARITMICO Y
LOGARITMICO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
DEMANDA-LINEALOFERTA DEMANDA-SEMILOGARITMICADEMANDA- LOGARITMICA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
5
10
15
20
25
30
35
DEMANDA-LINEALOFERTA DEMANDA-SEMILOGARITMICADEMANDA- LOGARITMICA
