gestão de materiais-8

Previso de DemandaMtodos QuantitativosMtodos Qualitativos (exerccios de reforo) GESTO DE MATERIAIS - 8

Previso de DemandaDefinio:

a informao bsica para a determinao das quantidades a serem produzidas, devido ao conhecimento das quantidades a serem vendidas, e os nveis de estoques indicados pela gesto de estoque.

Fontes de dados :

Fontes internas.

Fontes externas.

Como prever a demanda:

A previso da demanda pode ser obtida com a utilizao de mtodos ou modelos que podem ser:

Qualitativos.

Quantitativos.

Previso de Demanda

Sadas:Demanda estimada p/prod. em p/periodo de tempoOutras sadasPreviso para demanda estimada p/prod. em p/periodo de tempoEstrateg. Neg.Pl MktPl Prod.Pl Finan.Proc. p/ converter Prev. Vendas em Prev. Recursos ProduoPreviso de recursos de produoLongoprazoMdioprazoCurtoprazoPreviso de Demanda

Porque fazer previso de vendas:

Nvel Estratgico:

Planejamento de novas instalaes.

O projeto e construo de uma nova fbrica ou processo pode levar anos.

Para que essas atividades sejam viveis so necessrias previses de longo prazo da demanda .

Porque fazer previso de vendas: Nvel Ttico

Os ndices de produo devem ser alterados no intuito de atender as demandas de bens ou servios que variam ms a ms.

Muitas vezes so necessrios meses para mudar a capacidade dos processos de produo.

Os gerentes de operaes precisam de previses a mdio prazo para poder trabalhar com acordo com as demandas.

Porque fazer previso de vendas:

Nvel Operacional

A fora de trabalho deve ser alterada no intuito de atender as demandas de bens ou servios que variam semana a semana.

Os gerentes de operaes necessitam de previses de curto prazo a fim de que possam ter tempo de adequar a fora de trabalho.

Exemplos de Itens que devem ser previstos:Previso de Demanda

Horizonte da previsoIntervalo de tempoExemplos de itens que devem ser previstosUnidades tpicas de previsoLongo PrazoAnosNovas linhas de produtosCapacidade de fbricaFundos de capitalDlaresGales, horas, libras, unid. ou clientes por tempoDlaresMdio PrazoMesesGrupos de produtosCapacidades departamentaisMo de obraMP compradaEstoques UnidadesGales, horas, unid. ou clientes por tempoTrabalhadores, horasUnidades, libras, galesUnidades, dlaresCurto PrazoSemanasProdutos especficosHabilidade de MOCapacidade de MquinaDinheiro vivoEstoqueUnidadesTrabalhadores, horasGales, horas, unid. ou clientes por tempoDlaresUnidades, dlares

Mtodos Qualitativos de PrevisoEsses mtodos normalmente se baseiam em julgamentos a respeito dos fatores causais.

Fundamentam as vendas de produtos ou servios particulares e em opinies sobre a probabilidade relativa de esses fatores causais estarem presentes no futuro.

Podem envolver diversos nveis de sofisticao de pesquisa de opinio cientificamente conduzidas a suposies intuitivas sobre os eventos.

Tipos de Mtodos Qualitativos:

Consenso do comit executivo. Mtodo Delphi. Pesquisa da equipe de vendas. Pesquisa de clientes. Analogia histrica. Pesquisa de mercado.Mtodos Qualitativos de Previso

Consenso do comit executivo

Executivos com capacidade de discernimento, de vrios departamentos da organizao, formam um comit que tem a responsabilidade de desenvolver uma previso de vendas.

O comit pode usar informaes de todas as partes da organizao e fazer com que os analistas forneam anlises quando necessrio.

Essas previses tendem a ser previses de compromisso e o mtodo mais comum. Mtodos Qualitativos de Previso

2. Mtodo Delphi

Esse mtodo usado para se obter um consenso dentro de um comit.

Neste mtodo os executivos respondem anonimamente a uma srie de perguntas em turnos sucessivos.Mtodos Qualitativos de Previso

Mtodos Qualitativos de Previso2. Mtodo Delphi

Cada resposta repassada a todos os participantes em cada turno, e o processo ento repetido.

At seis turnos podem ser necessrios antes que se atinja o consenso sobre a previso.

Esse mtodo pode resultar em previses com as quais a maioria dos participantes concordou, apesar de ter ocorrido uma discordncia inicial.

3. Pesquisa da equipe de vendas

Estimativas de vendas regionais futuras so obtidas de membros individuais da equipe de vendas.

Essas estimativas so combinadas para formar uma nica estimativa para todas as regies.Mtodos Qualitativos de Previso

3. Pesquisa da equipe de vendas

A nica estimativa deve ento ser transformada pelos gerentes numa previso de vendas para assegurar estimativas realsticas. Esse um mtodo de previso popular para empresas que tem um bom sistema de comunicao em funcionamento e uma equipe de vendas que vende diretamente aos clientes. Mtodos Qualitativos de Previso

4. Pesquisa de clientes

Estimativas de vendas so obtidas diretamente dos clientes.

Clientes individuais so pesquisados para determinar quais quantidades dos produtos da empresa eles pretendem comprar em cada perodo de tempo futuro. Mtodos Qualitativos de Previso

4. Pesquisa de clientes

Um previso de vendas determinada combinando-se as respostas de clientes individuais.

Esse mtodo um dos preferidos das empresas que tm relativamente poucos clientes.

Exemplo: concessionrias de veculos .Mtodos Qualitativos de Previso

5. Analogia histrica

Esse mtodo une a estimativa de vendas futuras de um produto ao conhecimento das vendas de um produto similar. Mtodos Qualitativos de Previso

5. Analogia histrica

O conhecimento das vendas de um produto durante vrias etapas de seu ciclo de vida aplicado estimativa de vendas de um produto similar.

Esse mtodo pode ser especialmente til na previso de vendas de novos produtos.Mtodos Qualitativos de Previso

6. Pesquisa de Mercado

Nas pesquisas de mercado, questionrios por correspondncia, entrevistas telefnicas ou entrevistas de campo formam a base para testar hipteses sobre mercados reais.

Em teste de mercado, produtos comercializados em regies ou centros de compras tipo outlets so estatisticamente extrapolados para mercados totais. Mtodos Qualitativos de Previso

6. Pesquisa de Mercado

Esses mtodos comumente so preferidos para novos produtos ou para produtos existentes a serem introduzidos em novos segmentos de mercados. Mtodos Qualitativos de Previso

Modelos Quantitativos de PrevisoOs modelos quantitativos de previso so modelos matemticos baseados em dados histricos.

Esses modelos supem que dados passados so relevantes para o futuro.

Esses modelos so utilizados com sries temporais.

Modelos Quantitativos de Previso

Srie Temporal:

um conjunto de valores observados medidos ao longo de perodos de tempos sucessivos.

Esses modelos sero aplicados:

para preciso. previso. previses de longo prazo e de curto prazo.

Modelos Quantitativos de PrevisoTipos de modelos quantitativos:

Regresso Linear Mdia Mvel Mdia Ponderada Mvel Exponencial Mvel Exponencial Mvel com Tendncia

Modelos Quantitativos de PrevisoPreciso da Previso:

Refere-se a quo perto as previses chegam dos dados reais.

Uma vez que as previses so feitas antes que os dados reais se tornem conhecidos, a preciso das previses podem ser determinadas somente depois da passagem do tempo.

Preciso da Previso:

Quando as previses ficam muito prximas dos dados reais, dizemos que elas tm alta preciso e que o erro de previso baixo.

Determina-se a preciso dos modelos de previso mantendo uma contagem contnua do quanto as previses deixaram de atingir os pontos de dados reais ao longo do tempo. Modelos Quantitativos de Previso

Modelos Quantitativos de PrevisoPreviso de Longo Prazo:

Significa estimar condies futuras ao longo de intervalos de tempo normalmente maiores do que um ano.

Por exemplo:

Projetar um novo produto

(O volume de vendas justifica uma maquinrio de produo automatizado?)

Previso de Longo Prazo:


Por exemplo:

2. Determinar a capacidade de produo para um novo produto

( Quanta capacidade ser necessria?Quantas Fbricas?Onde?) Modelos Quantitativos de Previso



Por exemplo:

3. Planejar para o abastecimento de materiais a longo prazo.

(garantia de fornecimento de contrato de matria prima a longo prazo)Modelos Quantitativos de Previso

Modelos Quantitativos de PrevisoPreviso de Longo Prazo:

Numa anlise de longo prazo, os dados histricos de vendas so compostos de diversos componentes, entre eles: # tendncias, ciclos, sazonalidade e flutuao aleatria ou rudo.


As tendncias so ilustradas com uma linha com inclinao para cima ou para baixo

Ciclo, um padro de dados que pode cobrir diversos anos antes de se repetir

Sazonalidade, um padro de dados que se repete depois de um perodo de tempo

Flutuao aleatria ou rudo, um padro resultante da variao aleatria ou causas inexplicveis



As tendncias So ilustradas com uma linha com inclinao para cima ou para baixoModelos Quantitativos de Previso

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Ciclo

um padro de dados que pode cobrirdiversos anos antes de se repetir.


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Sazonalidade

um padro de dados que se repete depoisde um perodo de tempoModelos Quantitativos de Previso

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Flutuao aleatria ou rudo

um padro resultante da variao aleatria ou causas inexplicveis.


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Modelos Quantitativos de PrevisoRegresso Linear:

A anlise de regresso linear um modelo de previso que estabelece uma relao entre uma varivel dependente e uma ou mais variveis independentes.

Regresso Linear:

Uma regresso linear simples tambm pode ser usada quando a varivel independente x representa uma outra varivel que no seja tempo.

Nesse caso, a regresso linear representativa de uma classe de modelos de previso chamada modelos de previso causais .Modelos Quantitativos de Previso

Modelos Quantitativos de PrevisoDiversos mtodos de extrapolao so empregados,todos consistindo na projeo do futuro a partir dedados do passado.

Os mtodos mais simples utilizados so;

Mtodo dos Mnimos Quadrados:

a .1 Tendncia reta

a. 2 Tendncia parbola.

Modelos Quantitativos de PrevisoTendncia reta

Para efeito desse clculo de distribuio linear, consideremos inicialmente o par de eixos cartesianos x , y , e a reta r , que representa determinada tendncia :

y r

x

Modelos Quantitativos de PrevisoTendncia reta

No eixo dos x representamos em geral : ms, ano,semana.

No eixo dos y representamos : consumo, demanda,vendas fsicas, valores ( reais, dlares ), quantidadeem geral.

A cada valor de x , corresponde um valor y evice-versa.

Tendncia reta

Exemplo : Uma empresa de fertilizante apresentou os seguintes resultados de vendas nos ltimos anos:

ANO VENDAS ( toneladas)

2006 1002007 1502008 2002009 2502010 3002011 350 Modelos Quantitativos de Previso

Modelos Quantitativos de PrevisoANO VENDAS ( toneladas)

2006 1002007 1502008 2002009 2502010 3002011 350 A reta r ( tendncia ) obtida atravs da equao : y = a + b X06 07 08 09 10 11 x350

300

250

200

150

100Y r

Modelos Quantitativos de PrevisoPelo mtodo dos mnimos quadrados, os valores de a e b so obtidos pela resoluo de duas equaes:

Y = a n + b X ( equao 1 )

XY = a X + b X2 ( equao 2 )

Equao 1 : Y = a n + b X A letra n da primeira equao representa a posioque o dado ocupa no eixo dos x .

A cada posio do eixo dos x , atribudo um valor de representao a partir do valor zero que atribudo posio relativa ao vrtice.Assim, o dado que ocupa o vrtice recebe o valorzero relativo ao tempo.

O dado imediatamente acima recebe o valor 1 ; o seguinte o valor 2 ; assim por diante.

Vamos aplicar essas equaes para verificaoda tendncia :

Nota: observemos que o eixo dos X ser representa do por valores de ( 0 ) a ( 5 ) vamos determinar a tendncia para o ano 2012.

ANO X Y

2006 0 100 2007 1 150 2008 2 200 2009 3 250 2010 4 300 2011 5 350

Modelos Quantitativos de PrevisoPasso 1 :

Calcular X e XY elaborando a tabela da seguinteforma :

ANO X Y X XY

2006 0 100 0 ( 0 x 100 ) = 02007 1 150 1 ( 1 x 150 ) = 150 2008 2 200 4 ( 2 x 200 ) = 4002009 3 250 9 ( 3 x 250 ) = 750 4 300 16 ( 4 x 300 ) = 1200 5 350 25 ( 5 x 350 ) = 1750 X=15 Y=1350 X = 55 XY= 4250

Passo 2 :

Resolver as equaes :

Y = a n + b X

XY = a X + b X

Substituindo os valores assim obtidos nas equaesnormais , temos, lembrando que n = 6:

1350 = 6 a + 15 b ( I )4250 = 15 a + 55 b ( II )

O sistema de duas equaes a duas incgnitas resultante pode ser resolvido se multiplicarmos a equao ( I ) por ( - 2,5 ) e adicionarmos equao ( II ):

Passo 2 :

- 2,5 ( 1350 ) = - 2,5 x 6a + ( - 2,5 ) x 15b

3375 = - 15 a 37,5 b + 4250 = + 15 a + 55b + 875 = / + 17,5b

17,5 b = 875

875 b = ---------- 17,5 b = 50


Passo 2 :

Substituindo o valor de b na equao ( I ) original,temos :

1350 = 6 a + 15 ( 50 ) 1350 = 6 a + 750 6 a = 1350 750

1350 750 a = ------------------ 6 a = 100


Passo 3 :

Substituindo os valores das incgnitas relativas reta r ( y = a + b X ) pelos valores de a e b, temos o valor de y. y = a + b X y = 100 + 50 X

Passo 4 :

Como queremos a previso para 2012, o valor deX 6 ( pois 2011 tem valor 5 ) , ento :

y = 100 + 50 ( 6 ) y = 100 + 300 = 400 toneladas


Modelos Quantitativos de PrevisoPasso 5 :

Transportando este dado para os eixos , temos : Y

400

350

300

250

200

150

100

06 07 08 09 10 11 12 X ry = a + b Xy = 400 toneladas

Passo 6 :

Os Coeficientes de Correlao

A maior ou menor perfeio do relacionamento entre as variveis X e Y ( diz-se tambm perfeio do ajuste ), obtido atravs da linha reta, pode ser medido atravs do coeficiente de correlao ( r ) .

A grandeza obtida diretamente dos pares originais ( X , Y ) .

O coeficiente de correlao pode assumir qual quer valor entre +1 e 1 .Modelos Quantitativos de Previso

Passo 6 :

Os Coeficientes de Correlao O valor r = +1 indica uma correlao perfeita ( os valores Y so obtidos com exatido atravs dos valores X ) e positiva.

Por correlao positiva entendemos que as variveis X e Y variam no mesmo sentido( quando uma cresce a outra tambm o faz ) .

Semelhante, o valor r = -1 tambm indica uma correlao perfeita, mas as variveis so inversamente relacionadas, ou seja , quando uma aumenta de valor a outra diminui.

Passo 6 :

Os Coeficientes de Correlao

Por outro lado, a correlao entre Y e X tanto mais fraca quanto mais r se aproxima de zero um valor absoluto.

H mais de uma frmula para se calcular o coeficiente de correlao na regresso linear simples, embora todas elas sejam equivalentes. Adotaremos a seguinte :

n XY ( X ) ( Y ) r = ---------------------------------------------------- [n. X2 - ( X)2][n.Y2 (Y)2]

Passo 6 :

A mesma tabela auxiliar, elaborada para o clculode a e b , fornece as quantidades que aparecem naequao, exceo de, que deve ento sercalculada.

Exemplo :

Utilizando os dados do exemplo anterior, temos:

X = 15 Y = 1350 XY = 4250 X = 55 Y = 347500

Esses valores permitem o clculo do Coeficiente deCorrelao .

Passo 6 :

Coeficiente de Correlao( r ), temos :

6 ( 4250 ) 15 ( 1350 ) r = ----------------------------------------------------------- 6 ( 55) ( 15) . 6 ( 347500 ) ( 1350 )

O valor de r = 1,00 indica uma correlao direta muito alta. Como sugesto, podemos indicar os intervalos abaixo e as interpretaes respectivas para os valores absolutos de r. r CORRELAO 0 a 0,2 muito baixa 0,2 a 0,4 baixa 0,4 a 0,6 mdia 0,6 a 0,8 alta 0,8 a 1,0 muito alta

Passo 6 :

Coeficiente de determinao( r2 ), temos :

( Y y )2 r2 = ------------------------------- ( y y )2

Variao total = ( y y )2Variao explicada = ( Y y )2 Variao no explicada = ( y Y )2

Var. Total = Var. Explicada + Var. No explicada

O Coeficiente de determinao a razo da V.E pela V.T e ilustra quanto da variao dependente y explicada por x ou pela linha de tendncia

Passo 6 :

Para um r2 = 0,80 = 80% significa que:

80% das variaes so explicadas e 20 % no so explicadas.

Quanto mais forte a relao e o valor de r e r2 ,maior a probabilidade de as previses resultantesdas equaes regresso serem precisas. Linha de TendnciaYyVariao no explicada = ( y Y )2Variao explicada = ( Y- y )2Variao total= ( y- y )2y

Modelos Quantitativos de PrevisoIntervalos das Previses ( Intervalo de Confiana ):

A anlise de regresso gera previses para perodos futuros, sendo estas, estimativas e sujeitas a erros. A presena de erros de previso ou variaes ocasionais um fato real para quem faz previses.

Uma maneira de lidar com essas incertezas consiste em desenvolver intervalos de confiana para as previses.

y2 a. y b. xy n-2S yx = Intervalos das Previses( Intervalo de Confiana ):

A expresso S y x, denominada erro padro da previso, ou desvio padro da previso, e uma medida de como os pontos dos dados histricos estavam dispersos nas proximidades da linha de tendncias.


Intervalos das Previses( Intervalo de Confiana ): Se Syx for pequeno em relao a previso, significa que os pontos dos dados passados estavam estreitamente agrupados nas proximidades da linha de tendncias, e os limites superior e inferior esto bem prximos. Os intervalos permitem que os analistas lidem com a incerteza que cercam suas previses desenvolvendo previses da melhor estimativa. Modelos Quantitativos de Previso

Exerccio das Anlise de Regresso Linear Simples:

A Specific Motors produz motores eletrnicos. A fbrica da Specific opera em sua capacidade quase total h algum tempo. Jim White, o gerente da fbrica, acha que o crescimento de vendas prosseguir, e ele quer desenvolver uma previso a longo prazo a ser usada para planejar as exigncias de instalaes para os prximos trs anos : Modelos Quantitativos de Previso

Exerccio-1 Anlise de Regresso Linear Simples:

O registro de vendas dos ltimos dez anos acumularam-se:

Exercicio-Prev.Ser.Temp.Saz

Dados

AnoVendas trimestrais(milhares de unidades)Total Anual

Q1Q2Q3Q4

85207308205302600

95908109006002900

1065090010006503200

Totais17602440272017808700

Mdia Trimestral586.7813.3906.7593.3725.0

ndice de Sazonalidade(I.S)0.8091.1221.2510.818

I.S =Mdia Trimestral

Mdia Trimestral Total

Mdia Trimestral Total: Total Anos/12 =8700/12

Dessazonalizando as vendas : Dividir o valor trimestral pelo respectivo I.S

AnoVendas trimestrais(milhares de unidades)

Q1Q2Q3Q4

8642.6650.7655.7647.6

9729.1722.0719.7733.1

10803.3802.3799.6794.2

Anlise de regresso dos dados dessazonalizados

Periodo de tempoxyy2x2xy

Ano 8 -Q11642.6412952.31.0642.6

Ano 8 -Q22650.7423432.94.01301.4

Ano 8 -Q33655.7429940.69.01967.1

Ano 8 -Q44647.6419401.816.02590.4

Ano 9 -Q15729.1531615.025.03645.6

Ano 9 -Q26722.0521325.436.04332.2

Ano 9 -Q37719.7517923.649.05037.7

Ano 9 -Q48733.1537503.264.05865.2

Ano 10 -Q19803.3645237.981.07229.4

Ano 10 -Q210802.3643611.6100.08022.5

Ano 10 -Q311799.6639411.9121.08796.0

Ano 10 -Q412794.2630819.7144.09530.9

Totais788700.06353175.9650.058961.0

Calculando a equao de regresso com tendencia a uma reta

a=x2.y - x.xy615.41

n.(x2).-(x)2

b=n.xy - x.y16.86

n.(x2).-(x)2

EquaoY=615,421+16,86*X

Utilizando a Equaoxy

Ano 11 -Q113834.5915147908

Ano 11 -Q214851.4517478355

Ano 11 -Q315868.3119808803

Ano 11 -Q416885.172213925

Sazonalizando as vendas : Multiplicar o valor trimestral pelo respectivo I.S


Q1Q2Q3Q4

8643651656648

9729722720733

10803802800794

116759551086724

Exerccio-Regre. Linear simples

Dados

AnoVendas Anuais (Milhares de unidades)

11000

21300

31800

42000

52000

62000

72200x = valores da varivel independente x

82600y = valores da varivel dependente y

92900n = nmero de observaes

103200a = intercepto do eixo vertical

b = inclinao da linha de regresso

y = valore mdio da varivel dependente y

Y = valores de y que se situam na linha de tendncias: Y = a + b.X

X = valores de x que se situam na linha de tendncias

r = coeficiente de correlao

r2 = coeficiente de determinao

Contruo da Tabela

AnoVendas Anuais(milhares de unidades) (y)Perodo de Tempo (x)x2xyy2

110001110001000000

213002426001690000

318003954003240000

4200041680004000000

52000525100004000000

62000636120004000000

72200749154004840000

82600864208006760000

92900981261008410000

103200101003200010240000

Somatrios210005538513330048180000

Calculando valores de "a" e "b":

a =913.33

b =215.758

Montando a equao:

Y = 913,33 + 215,758*X

Projetando os prximos perodos:

Y11 =3286.673290milhares de unidades



Calculando o "r" :

r =0.9702037446

Plan3

MBD000701B4.unknown

MBD000701B6.unknown

MBD000701B5.unknown

MBD000701B3.unknown


O registro de vendas dos ltimos dez anos acumularam-se:


Dados


Q1Q2Q3Q4

85207308205302600

95908109006002900

1065090010006503200

Totais17602440272017808700

Mdia Trimestral586.7813.3906.7593.3725.0







Q1Q2Q3Q4

8642.6650.7655.7647.6

9729.1722.0719.7733.1

10803.3802.3799.6794.2



Ano 8 -Q11642.6412952.31.0642.6

Ano 8 -Q22650.7423432.94.01301.4

Ano 8 -Q33655.7429940.69.01967.1

Ano 8 -Q44647.6419401.816.02590.4

Ano 9 -Q15729.1531615.025.03645.6

Ano 9 -Q26722.0521325.436.04332.2

Ano 9 -Q37719.7517923.649.05037.7

Ano 9 -Q48733.1537503.264.05865.2

Ano 10 -Q19803.3645237.981.07229.4

Ano 10 -Q210802.3643611.6100.08022.5

Ano 10 -Q311799.6639411.9121.08796.0

Ano 10 -Q412794.2630819.7144.09530.9

Totais788700.06353175.9650.058961.0


a=x2.y - x.xy615.41

n.(x2).-(x)2

b=n.xy - x.y16.86

n.(x2).-(x)2

EquaoY=615,421+16,86*X


Ano 11 -Q113834.5915147908

Ano 11 -Q214851.4517478355

Ano 11 -Q315868.3119808803

Ano 11 -Q416885.172213925



Q1Q2Q3Q4

8643651656648

9729722720733

10803802800794

116759551086724


Dados


11000

21300

31800

42000

52000

62000

72200

82600

92900

103200

x = valores da varivel independente x

Y = a + b.Xy = valores da varivel dependente y

n = nmero de observaes

a = x2.y - x.xya = intercepto do eixo vertical

n.(x2).-(x)2b = inclinao da linha de regresso

b = n.xy - x.yy = valore mdio da varivel dependente y

n.(x2).-(x)2Y = valores de y que se situam na linha de tendncias: Y = a + b.X

r = n.xy - x.yX = valores de x que se situam na linha de tendncias

[n.(x2).-(x)2]*[n.(y2).-(y)2]r = coeficiente de correlao


Contruo da Tabela


110001110001000000

213002426001690000

318003954003240000

4200041680004000000

52000525100004000000

62000636120004000000

72200749154004840000

82600864208006760000

92900981261008410000

103200101003200010240000

Somatrios210005538513330048180000


a =913.33

b =215.758

Montando a equao:

Y = 913,33 + 215,758*X


3286.673290milhares de unidades



Calculando o "r" :

r =0.9702037446

Plan3


O registro de vendas dos ltimos dez anos acumularam-se:Modelos Quantitativos de Previso


Dados


Q1Q2Q3Q4

85207308205302600

95908109006002900

1065090010006503200

Totais17602440272017808700

Mdia Trimestral586.7813.3906.7593.3725.0







Q1Q2Q3Q4

8642.6650.7655.7647.6

9729.1722.0719.7733.1

10803.3802.3799.6794.2



Ano 8 -Q11642.6412952.31.0642.6

Ano 8 -Q22650.7423432.94.01301.4

Ano 8 -Q33655.7429940.69.01967.1

Ano 8 -Q44647.6419401.816.02590.4

Ano 9 -Q15729.1531615.025.03645.6

Ano 9 -Q26722.0521325.436.04332.2

Ano 9 -Q37719.7517923.649.05037.7

Ano 9 -Q48733.1537503.264.05865.2

Ano 10 -Q19803.3645237.981.07229.4

Ano 10 -Q210802.3643611.6100.08022.5

Ano 10 -Q311799.6639411.9121.08796.0

Ano 10 -Q412794.2630819.7144.09530.9

Totais788700.06353175.9650.058961.0


a=x2.y - x.xy615.41

n.(x2).-(x)2

b=n.xy - x.y16.86

n.(x2).-(x)2

EquaoY=615,421+16,86*X


Ano 11 -Q113834.5915147908

Ano 11 -Q214851.4517478355

Ano 11 -Q315868.3119808803

Ano 11 -Q416885.172213925



Q1Q2Q3Q4

8643651656648

9729722720733

10803802800794

116759551086724


Dados


11000

21300

31800

42000

52000

62000

72200

82600

92900

103200











Contruo da Tabela


110001110001000000

213002426001690000

318003954003240000

4200041680004000000

52000525100004000000

62000636120004000000

72200749154004840000

82600864208006760000

92900981261008410000

103200101003200010240000

Somatrios210005538513330048180000


a =913.33

b =215.758

Montando a equao:

Y = 913,33 + 215,758*X





Calculando o "r" :

r =0.9702037446

Plan3


O registro de vendas dos ltimos dez anosacumularam-se:


Dados


Q1Q2Q3Q4

85207308205302600

95908109006002900

1065090010006503200

Totais17602440272017808700

Mdia Trimestral586.7813.3906.7593.3725.0







Q1Q2Q3Q4

8642.6650.7655.7647.6

9729.1722.0719.7733.1

10803.3802.3799.6794.2



Ano 8 -Q11642.6412952.31.0642.6

Ano 8 -Q22650.7423432.94.01301.4

Ano 8 -Q33655.7429940.69.01967.1

Ano 8 -Q44647.6419401.816.02590.4

Ano 9 -Q15729.1531615.025.03645.6

Ano 9 -Q26722.0521325.436.04332.2

Ano 9 -Q37719.7517923.649.05037.7

Ano 9 -Q48733.1537503.264.05865.2

Ano 10 -Q19803.3645237.981.07229.4

Ano 10 -Q210802.3643611.6100.08022.5

Ano 10 -Q311799.6639411.9121.08796.0

Ano 10 -Q412794.2630819.7144.09530.9

Totais788700.06353175.9650.058961.0


a=x2.y - x.xy615.41

n.(x2).-(x)2

b=n.xy - x.y16.86

n.(x2).-(x)2

EquaoY=615,421+16,86*X


Ano 11 -Q113834.5915147908

Ano 11 -Q214851.4517478355

Ano 11 -Q315868.3119808803

Ano 11 -Q416885.172213925



Q1Q2Q3Q4

8643651656648

9729722720733

10803802800794

116759551086724


Dados


11000

21300

31800

42000

52000

62000

72200

82600

92900

103200











Contruo da Tabela


110001110001000000

213002426001690000

318003954003240000

4200041680004000000

52000525100004000000

62000636120004000000

72200749154004840000

82600864208006760000

92900981261008410000

103200101003200010240000

Somatrios210005538513330048180000


a =913.33

b =215.758

Montando a equao:

Y = 913,33 + 215,758*X





Calculando o "r" :

r =0.9702037446

Plan3

Mtodos Quantitativos em MedicinaTestes de Hipteses:Estatstica t-StudentFONTE : MEDICINA USPEntendo a Estatstica t-Student

Teste de Hipteses - Estatstica do testeA estatstica do teste de hiptese depende da distribuio da varivel na populao e das informaes disponveis.Entendo a Estatstica t-StudentFONTE : MEDICINA USP

Entendo a Estatstica t-StudentNa maioria das situaes reais, desconhecido.Neste caso, podemos substituir pelo desvio-padro amostral, S.Estaremos introduzindo mais um erro no processo de inferncia, o erro de estimao de .Inferncia quando desconhecidoFONTE : MEDICINA USP

Teste de Hiptese para DesconhecidoEntendo a Estatstica t-StudentFONTE : MEDICINA USP

Teste de Hiptese para uma AmostraEntendo a Estatstica t-StudentFONTE : MEDICINA USP

Distribuio t de StudentWilliam Gosset (1876-1937)Entendo a Estatstica t-StudentFONTE : MEDICINA USP

Distribuio t de StudentCurva de Densidade de Probabilidade Simtrica em relao mdia. Depende do grau de liberdade, gl . Quanto mais gl aumenta, mais a distribuio t tende Normal padro.Entendo a Estatstica t-StudentFONTE : MEDICINA USP

Grf1

0.00087268270.0240233876

0.00090372220.0241507945

0.00093577220.0242791895

0.00096886180.0244085827

0.00100302130.0245389841

0.00103828130.0246704039

0.00107467330.0248028524

0.00111222970.02493634

0.00115098340.0250708773

0.00119096840.0252064749

0.00123221920.0253431438

0.00127477120.0254808948

0.00131866090.0256197391

0.00136392520.0257596878

0.00141060230.0259007524

0.00145873080.0260429443

0.00150835060.0261862751

0.00155950230.0263307568

0.00161222750.0264764012

0.00166656850.0266232205

0.00172256890.0267712268

0.0017802730.0269204325

0.00183972620.0270708503

0.00190097470.0272224928

0.00196406590.0273753729

0.00202904810.0275295037

0.00209597060.0276848983

0.00216488390.02784157

0.00223583940.0279995326

0.00230888970.0281587996

0.00238408820.0283193849

0.00246148970.0284813026

0.002541150.028644567

0.0026231260.0288091924

0.00270747580.0289751935

0.00279425840.0291425851

0.00288353430.0293113822

0.00297536510.0294815999

0.00306981330.0296532537

0.00316694290.029826359

0.00326681910.0300009318

0.0033695080.0301769879

0.00347507740.0303545436

0.00358359590.0305336153

0.00369513370.0307142196

0.00380976210.0308963733

0.00392755360.0310800936

0.00404858220.0312653976

0.0041729230.0314523029

0.00430065250.0316408272

0.00443184840.0318309886

0.004566590.0320228052

0.00470495750.0322162955

0.00484703290.0324114782

0.00499289920.0326083722

0.00514264090.0328069968

0.00529634390.0330073713

0.00545409520.0332095156

0.00561598360.0334134496

0.00578209890.0336191935

0.00595253240.0338267679

0.00612737690.0340361936

0.00630672640.0342474916

0.00649067640.0344606834

0.00667932370.0346757905

0.00687276670.0348928349

0.00707110490.0351118388

0.00727443940.0353328249

0.00748287250.0355558159

0.00769650820.035780835

0.00791545160.0360079057

0.00813980920.0362370517

0.00836968920.0364682973

0.00860520060.0367016668

0.00884645440.0369371851

0.00909356250.0371748772

0.00934663840.0374147687

0.00960579680.0376568854

0.00987115380.0379012534

0.01014282690.0381478993

0.01042093480.03839685

0.01070559760.0386481328

0.01099693660.0389017753

0.01129507450.0391578056

0.01160013510.0394162522

0.01191224360.0396771438

0.01223152640.0399405097

0.01255811090.0402063795

0.01289212610.0404747834

0.01323370180.0407457516

0.01358296920.0410193152

0.01394006050.0412955055

0.0143051090.0415743543

0.01467824910.0418558937

0.01505961630.0421401565

0.01544934710.0424271758

0.0158475790.0427169851

0.01625445050.0430096186

0.01667010080.0433051108

0.01709467050.0436034967

0.01752830050.0439048119

0.0179711330.0442090924

0.01842331060.0445163748

0.01888497710.0448266961

0.01935627670.0451400939

0.01983735440.0454566064

0.02032835570.0457762722

0.0208294270.0460991305

0.02134071490.0464252211

0.02186236680.0467545844

0.02239453030.0470872613

0.02293735370.0474232932

0.02349098540.0477627223

0.02405557420.0481055912

0.02463126930.0484519432

0.02521821990.0488018223

0.02581657550.0491552731

0.02642648550.0495123406

0.02704809950.0498730707

0.02768156710.0502375099

0.02832703770.0506057053

0.02898466060.0509777047

0.02965458480.0513535568

0.03033695920.0517333105

0.03103193220.0521170159

0.03173965180.0525047235

0.03246026560.0528964847

0.03319392060.0532923515

0.03394076320.0536923767

0.0347009390.054096614

0.03547459280.0545051175

0.03626186890.0549179424

0.03706291020.0553351447

0.0378778590.0557567808

0.03870685610.0561829085

0.03955004160.0566135858

0.04040755390.057048872

0.04127953040.057488827

0.0421661070.0579335116

0.04306741790.0583829875

0.0439835960.0588373172

0.04491477230.0592965642

0.04586107630.0597607927

0.04682263530.060230068

0.04779957490.0607044561

0.04879201860.0611840243

0.04980008770.0616688403

0.05082390150.0621589733

0.05186357670.062654493

0.05291922770.0631554704

0.05399096650.0636619772

0.05507890240.0641740864

0.05618314190.0646918718

0.05730378890.0652154083

0.05844094430.0657447716

0.05959470610.0662800388

0.0607651690.0668212877

0.06195242460.0673685975

0.06315656140.0679220481

0.06437766430.0684817207

0.06561581480.0690476977

0.06687109060.0696200622

0.06814356610.0701988987

0.06943331150.0707842928

0.07074039350.0713763311

0.07206487430.0719751015

0.07340681260.0725806928

0.07476626240.0731931951

0.07614327370.0738126997

0.0775378920.0744392989

0.07895015830.0750730864

0.08038010910.0757141567

0.0818277760.0763626058

0.08329318610.0770185309

0.08477636130.07768203

0.08627731880.0783532028

0.08779607060.0790321497

0.08933262350.0797189727

0.0908869790.0804137748

0.09245913340.0811166602

0.09404907740.0818277342

0.09565679620.0825471036

0.09728226930.083274876

0.09892547070.0840111605

0.10058636840.0847560673

0.10226492460.0855097075

0.10396109530.0862721938

0.10567483080.0870436397

0.10740607510.0878241602

0.10915476590.088613871

0.11092083470.0894128894

0.11270420660.0902213333

0.11450480030.0910393222

0.11632252790.0918669763

0.11815729510.092704417

0.12000900070.0935517667

0.1218775370.0944091488

0.12376278950.0952766878

0.12566463680.0961545089

0.12758295060.0970427384

0.12951759570.0979415034

0.13146842990.098850932

0.1334353040.0997711529

0.13541806160.1007022956

0.13741653930.1016444904

0.13943056640.1025978682

0.14145996520.1035625606

0.14350455050.1045386995

0.145564130.1055264176

0.14763850410.1065258479

0.14972746560.1075371237

0.15183080040.1085603786

0.15394828680.1095957465

0.15607969560.1106433613

0.15822479040.111703357

0.16038332730.1127758676

0.16255505520.1138610267

0.16473971540.1149589679

0.16693704170.1160698243

0.16914676090.1171937286

0.1713685920.1183308127

0.1736022470.119481208

0.17584743030.1206450448

0.17810383910.1218224525

0.18037116320.1230135594

0.18264908540.1242184922

0.1849372810.1254373763

0.18723541820.1266703355

0.18954315810.1279174916

0.19186015470.1291789644

0.1941860550.1304548714

0.19652049890.1317453277

0.19886311940.1330504457

0.20121354270.1343703348

0.20357138830.1357051015

0.20593626870.1370548487

0.208307790.1384196757

0.21068555170.1397996777

0.21306914680.141194946

0.21545816180.142605567

0.2178521770.1440316227

0.22025076670.1454731896

0.22265349880.1469303389

0.22505993530.1484031359

0.22746963250.1498916398

0.22988214070.1513959031

0.23229700470.1529159715

0.23471376390.1544518832

0.2371319520.156003669

0.23955109770.157571351

0.24197072450.1591549431

0.24439035090.1607544499

0.24680949060.1623698664

0.24922765250.1640011779

0.25164434110.1656483588

0.25405905650.1673113725

0.25647129440.168990171

0.25888054670.1706846942

0.26128630120.172394869

0.26368804210.1741206095

0.26608524990.1758618156

0.26847740180.177618373

0.27086397180.1793901523

0.27324443090.1811770085

0.27561824720.1829787803

0.27798488610.1847952895

0.28034381080.1866263404

0.28269448210.188471719

0.28503635850.1903311924

0.2873688970.1922045083

0.28969155280.194091394

0.29200377950.1959915561

0.29430502980.1979046793

0.2965947550.1998304264

0.29887240580.201768437

0.30113743220.2037183272

0.30338928380.2056796887

0.305627410.2076520883

0.30785126050.2096350673

0.31006028480.2116281405

0.31225393340.2136307961

0.3144316570.2156424945

0.31659290770.2176626683

0.31873713850.2196907214

0.32086380380.2217260283

0.32297235970.223767934

0.32506226410.2258157535

0.3271329770.227868771

0.32918396080.2299262397

0.33121468020.2319873815

0.33322460290.2340513869

0.33521319950.2361174143

0.33717994380.2381845901

0.33912431320.2402520086

0.34104578860.2423187319

0.3429438550.2443837898

0.34481800140.2464461801

0.34666772130.2485048686

0.34849251280.2505587895

0.35029187860.2526068456

0.35206532680.2546479089

0.35381237050.256680821

0.35553252850.2587043938

0.35722532520.2607174103

0.3588902910.2627186251

0.36052696250.2647067661

0.36213488240.2666805347

0.36371360040.2686386076

0.36526267260.270579638

0.36678166240.2725022568

0.36827014030.2744050743

0.36972768410.2762866819

0.37115387940.2781456538

0.37254831930.279980549

0.37391060540.2817899134

0.37524034690.2835722817

0.37653716180.2853261798

0.37780067650.2870501273

0.37903052620.2887426399

0.38022635480.2904022317

0.38138781550.2920274185

0.38251457070.29361672

0.38360629220.295168663

0.38466266130.2966817841

0.38568336920.298154633

0.38666811680.2995857752

0.38761661510.3009737956

0.38852858530.302317301

0.38940375880.3036149239

0.39024187760.3048653253

0.3910426940.3060671983

0.39180597120.3072192705

0.39253148310.3083203082

0.39321901460.3093691187

0.39386836160.3103645536

0.39447933090.3113055122

0.39505174080.3121909437

0.39558542080.3130198507

0.39608021180.3137912916

0.3965359660.3145043831

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0.39732983160.3157522926

0.39766770550.316285658

0.39796606820.3167577731

0.39822483020.3171680811

0.39844391410.3175160959

0.39862325420.3178014039

0.39876279680.3180236649

0.39886249990.3181826131

0.39892233380.3182780584

0.39894228040.3183098862

0.39892233380.3182780584

0.39886249990.3181826131

0.39876279680.3180236649

0.39862325420.3178014039

0.39844391410.3175160959

0.39822483020.3171680811

0.39796606820.3167577731

0.39766770550.316285658

0.39732983160.3157522926

0.39695254750.3151583032

0.3965359660.3145043831

0.39608021180.3137912916

0.39558542080.3130198507

0.39505174080.3121909437

0.39447933090.3113055122

0.39386836160.3103645536

0.39321901460.3093691187

0.39253148310.3083203082

0.39180597120.3072192705

0.3910426940.3060671983

0.39024187760.3048653253

0.38940375880.3036149239

0.38852858530.302317301

0.38761661510.3009737956

0.38666811680.2995857752

0.38568336920.298154633

0.38466266130.2966817841

0.38360629220.295168663

0.38251457070.29361672

0.38138781550.2920274185

0.38022635480.2904022317

0.37903052620.2887426399

0.37780067650.2870501273

0.37653716180.2853261798

0.37524034690.2835722817

0.37391060540.2817899134

0.37254831930.279980549

0.37115387940.2781456538

0.36972768410.2762866819

0.36827014030.2744050743

0.36678166240.2725022568

0.36526267260.270579638

0.36371360040.2686386076

0.36213488240.2666805347

0.36052696250.2647067661

0.3588902910.2627186251

0.35722532520.2607174103

0.35553252850.2587043938

0.35381237050.256680821

0.35206532680.2546479089

0.35029187860.2526068456

0.34849251280.2505587895

0.34666772130.2485048686

0.34481800140.2464461801

0.3429438550.2443837898

0.34104578860.2423187319

0.33912431320.2402520086

0.33717994380.2381845901

0.33521319950.2361174143

0.33322460290.2340513869

0.33121468020.2319873815

0.32918396080.2299262397

0.3271329770.227868771

0.32506226410.2258157535

0.32297235970.223767934

0.32086380380.2217260283

0.31873713850.2196907214

0.31659290770.2176626683

0.3144316570.2156424945

0.31225393340.2136307961

0.31006028480.2116281405

0.30785126050.2096350673

0.305627410.2076520883

0.30338928380.2056796887

0.30113743220.2037183272

0.29887240580.201768437

0.2965947550.1998304264

0.29430502980.1979046793

0.29200377950.1959915561

0.28969155280.194091394

0.2873688970.1922045083

0.28503635850.1903311924

0.28269448210.188471719

0.28034381080.1866263404

0.27798488610.1847952895

0.27561824720.1829787803

0.27324443090.1811770085

0.27086397180.1793901523

0.26847740180.177618373

0.26608524990.1758618156

0.26368804210.1741206095

0.26128630120.172394869

0.25888054670.1706846942

0.25647129440.168990171

0.25405905650.1673113725

0.25164434110.1656483588

0.24922765250.1640011779

0.24680949060.1623698664

0.24439035090.1607544499

0.24197072450.1591549431

0.23955109770.157571351

0.2371319520.156003669

0.23471376390.1544518832

0.23229700470.1529159715

0.22988214070.1513959031

0.22746963250.1498916398

0.22505993530.1484031359

0.22265349880.1469303389

0.22025076670.1454731896

0.2178521770.1440316227

0.21545816180.142605567

0.21306914680.141194946

0.21068555170.1397996777

0.208307790.1384196757

0.20593626870.1370548487

0.20357138830.1357051015

0.20121354270.1343703348

0.19886311940.1330504457

0.19652049890.1317453277

0.1941860550.1304548714

0.19186015470.1291789644

0.18954315810.1279174916

0.18723541820.1266703355

0.1849372810.1254373763

0.18264908540.1242184922

0.18037116320.1230135594

0.17810383910.1218224525

0.17584743030.1206450448

0.1736022470.119481208

0.1713685920.1183308127

0.16914676090.1171937286

0.16693704170.1160698243

0.16473971540.1149589679

0.16255505520.1138610267

0.16038332730.1127758676

0.15822479040.111703357

0.15607969560.1106433613

0.15394828680.1095957465

0.15183080040.1085603786

0.14972746560.1075371237

0.14763850410.1065258479

0.145564130.1055264176

0.14350455050.1045386995

0.14145996520.1035625606

0.13943056640.1025978682

0.13741653930.1016444904

0.13541806160.1007022956

0.1334353040.0997711529

0.13146842990.098850932

0.12951759570.0979415034

0.12758295060.0970427384

0.12566463680.0961545089

0.12376278950.0952766878

0.1218775370.0944091488

0.12000900070.0935517667

0.11815729510.092704417

0.11632252790.0918669763

0.11450480030.0910393222

0.11270420660.0902213333

0.11092083470.0894128894

0.10915476590.088613871

0.10740607510.0878241602

0.10567483080.0870436397

0.10396109530.0862721938

0.10226492460.0855097075

0.10058636840.0847560673

0.09892547070.0840111605

0.09728226930.083274876

0.09565679620.0825471036

0.09404907740.0818277342

0.09245913340.0811166602

0.0908869790.0804137748

0.08933262350.0797189727

0.08779607060.0790321497

0.08627731880.0783532028

0.08477636130.07768203

0.08329318610.0770185309

0.0818277760.0763626058

0.08038010910.0757141567

0.07895015830.0750730864

0.0775378920.0744392989

0.07614327370.0738126997

0.07476626240.0731931951

0.07340681260.0725806928

0.07206487430.0719751015

0.07074039350.0713763311

0.06943331150.0707842928

0.06814356610.0701988987

0.06687109060.0696200622

0.06561581480.0690476977

0.06437766430.0684817207

0.06315656140.0679220481

0.06195242460.0673685975

0.0607651690.0668212877

0.05959470610.0662800388

0.05844094430.0657447716

0.05730378890.0652154083

0.05618314190.0646918718

0.05507890240.0641740864

0.05399096650.0636619772

0.05291922770.0631554704

0.05186357670.062654493

0.05082390150.0621589733

0.04980008770.0616688403

0.04879201860.0611840243

0.04779957490.0607044561

0.04682263530.060230068

0.04586107630.0597607927

0.04491477230.0592965642

0.0439835960.0588373172

0.04306741790.0583829875

0.0421661070.0579335116

0.04127953040.057488827

0.04040755390.057048872

0.03955004160.0566135858

0.03870685610.0561829085

0.0378778590.0557567808

0.03706291020.0553351447

0.03626186890.0549179424

0.03547459280.0545051175

0.0347009390.054096614

0.03394076320.0536923767

0.03319392060.0532923515

0.03246026560.0528964847

0.03173965180.0525047235

0.03103193220.0521170159

0.03033695920.0517333105

0.02965458480.0513535568

0.02898466060.0509777047

0.02832703770.0506057053

0.02768156710.0502375099

0.02704809950.0498730707

0.02642648550.0495123406

0.02581657550.0491552731

0.02521821990.0488018223

0.02463126930.0484519432

0.02405557420.0481055912

0.02349098540.0477627223

0.02293735370.0474232932

0.02239453030.0470872613

0.02186236680.0467545844

0.02134071490.0464252211

0.0208294270.0460991305

0.02032835570.0457762722

0.01983735440.0454566064

0.01935627670.0451400939

0.01888497710.0448266961

0.01842331060.0445163748

0.0179711330.0442090924

0.01752830050.0439048119

0.01709467050.0436034967

0.01667010080.0433051108

0.01625445050.0430096186

0.0158475790.0427169851

0.01544934710.0424271758

0.01505961630.0421401565

0.01467824910.0418558937

0.0143051090.0415743543

0.01394006050.0412955055

0.01358296920.0410193152

0.01323370180.0407457516

0.01289212610.0404747834

0.01255811090.0402063795

0.01223152640.0399405097

0.01191224360.0396771438

0.01160013510.0394162522

0.01129507450.0391578056

0.01099693660.0389017753

0.01070559760.0386481328

0.01042093480.03839685

0.01014282690.0381478993

0.00987115380.0379012534

0.00960579680.0376568854

0.00934663840.0374147687

0.00909356250.0371748772

0.00884645440.0369371851

0.00860520060.0367016668

0.00836968920.0364682973

0.00813980920.0362370517

0.00791545160.0360079057

0.00769650820.035780835

0.00748287250.0355558159

0.00727443940.0353328249

0.00707110490.0351118388

0.00687276670.0348928349

0.00667932370.0346757905

0.00649067640.0344606834

0.00630672640.0342474916

0.00612737690.0340361936

0.00595253240.0338267679

0.00578209890.0336191935

0.00561598360.0334134496

0.00545409520.0332095156

0.00529634390.0330073713

0.00514264090.0328069968

0.00499289920.0326083722

0.00484703290.0324114782

0.00470495750.0322162955

0.004566590.0320228052

0.00443184840.0318309886

0.00430065250.0316408272

0.0041729230.0314523029

0.00404858220.0312653976

0.00392755360.0310800936

0.00380976210.0308963733

0.00369513370.0307142196

0.00358359590.0305336153

0.00347507740.0303545436

0.0033695080.0301769879

0.00326681910.0300009318

0.00316694290.029826359

0.00306981330.0296532537

0.00297536510.0294815999

0.00288353430.0293113822

0.00279425840.0291425851

0.00270747580.0289751935

0.0026231260.0288091924

0.002541150.028644567

0.00246148970.0284813026

0.00238408820.0283193849

0.00230888970.0281587996

0.00223583940.0279995326

0.00216488390.02784157

0.00209597060.0276848983

0.00202904810.0275295037

0.00196406590.0273753729

0.00190097470.0272224928

0.00183972620.0270708503

0.0017802730.0269204325

0.00172256890.0267712268

0.00166656850.0266232205

0.00161222750.0264764012

0.00155950230.0263307568

0.00150835060.0261862751

0.00145873080.0260429443

0.00141060230.0259007524

0.00136392520.0257596878

0.00131866090.0256197391

0.00127477120.0254808948

0.00123221920.0253431438

0.00119096840.0252064749

0.00115098340.0250708773

0.00111222970.02493634

0.00107467330.0248028524

0.00103828130.0246704039

0.00100302130.0245389841

0.00096886180.0244085827

0.00093577220.0242791895

0.00090372220.0241507945

0.00087268270.0240233876

Normal

T1gl

Grf2

0.00087268270.02402338760.00924435410.0019604556

0.00090372220.02415079450.00935765020.0020114219

0.00093577220.02427918950.00947247320.0020636492

0.00096886180.02440858270.00958884470.0021171664

0.00100302130.02453898410.00970678720.002172003

0.00103828130.02467040390.0098263230.0022281892

0.00107467330.02480285240.00994747510.0022857559

0.00111222970.024936340.01007026660.0023447344

0.00115098340.02507087730.01019472110.0024051567

0.00119096840.02520647490.01032086240.0024670556

0.00123221920.02534314380.01044871470.0025304643

0.00127477120.02548089480.01057830270.0025954168

0.00131866090.02561973910.01070965130.0026619479

0.00136392520.02575968780.01084278570.0027300928

0.00141060230.02590075240.01097773160.0027998876

0.00145873080.02604294430.01111451510.0028713689

0.00150835060.02618627510.01125316260.0029445744

0.00155950230.02633075680.01139370090.0030195421

0.00161222750.02647640120.01153615710.0030963109

0.00166656850.02662322050.01168055890.0031749204

0.00172256890.02677122680.01182693420.0032554112

0.0017802730.02692043250.01197531140.0033378243

0.00183972620.02707085030.01212571930.0034222016

0.00190097470.02722249280.01227818710.003508586

0.00196406590.02737537290.01243274460.0035970209

0.00202904810.02752950370.01258942160.0036875506

0.00209597060.02768489830.01274824870.0037802204

0.00216488390.027841570.01290925690.0038750762

0.00223583940.02799953260.01307247750.0039721647

0.00230888970.02815879960.01323794240.0040715337

0.00238408820.02831938490.01340568370.0041732317

0.00246148970.02848130260.01357573440.0042773081

0.002541150.0286445670.01374812750.0043838131

0.0026231260.02880919240.01392289670.0044927979

0.00270747580.02897519350.01410007630.0046043147

0.00279425840.02914258510.01427970080.0047184163

0.00288353430.02931138220.01446180540.0048351567

0.00297536510.02948159990.01464642570.0049545907

0.00306981330.02965325370.01483359790.0050767741

0.00316694290.0298263590.01502335870.0052017637

0.00326681910.03000093180.0152157450.0053296171

0.0033695080.03017698790.01541079480.0054603929

0.00347507740.03035454360.01560854610.005594151

0.00358359590.03053361530.01580903780.0057309518

0.00369513370.03071421960.0160123090.0058708571

0.00380976210.03089637330.01621839980.0060139294

0.00392755360.03108009360.01642735030.0061602326

0.00404858220.03126539760.01663920170.0063098312

0.0041729230.03145230290.01685399540.0064627911

0.00430065250.03164082720.01707177360.006619179

0.00443184840.03183098860.01729257880.0067790627

0.004566590.03202280520.01751645440.0069425113

0.00470495750.03221629550.01774344420.0071095946

0.00484703290.03241147820.01797359270.0072803837

0.00499289920.03260837220.0182069450.0074549508

0.00514264090.03280699680.01844354660.0076333691

0.00529634390.03300737130.0186834440.007815713

0.00545409520.03320951560.01892668410.0080020579

0.00561598360.03341344960.01917331430.0081924803

0.00578209890.03361919350.0194233830.0083870581

0.00595253240.03382676790.01967693890.0085858699

0.00612737690.03403619360.01993403160.0087889957

0.00630672640.03424749160.02019471110.0089965166

0.00649067640.03446068340.02045902850.0092085149

0.00667932370.03467579050.0207270350.0094250739

0.00687276670.03489283490.0209987830.0096462781

0.00707110490.03511183880.02127432530.0098722133

0.00727443940.03533282490.02155371540.0101029661

0.00748287250.03555581590.02183700770.0103386247

0.00769650820.0357808350.0221242570.0105792782

0.00791545160.03600790570.0224155190.0108250169

0.00813980920.03623705170.02271085020.0110759323

0.00836968920.03646829730.02301030770.011332117

0.00860520060.03670166680.02331394920.0115936649

0.00884645440.03693718510.02362183350.011860671

0.00909356250.03717487720.02393401980.0121332313

0.00934663840.03741476870.02425056820.0124114433

0.00960579680.03765688540.02457153960.0126954053

0.00987115380.03790125340.02489699540.0129852171

0.01014282690.03814789930.02522699820.0132809794

0.01042093480.038396850.0255616110.0135827942

0.01070559760.03864813280.02590089780.0138907645

0.01099693660.03890177530.02624492310.0142049946

0.01129507450.03915780560.02659375260.0145255899

0.01160013510.03941625220.02694745240.0148526569

0.01191224360.03967714380.02730608970.0151863031

0.01223152640.03994050970.02766973240.0155266374

0.01255811090.04020637950.0280384490.0158737696

0.01289212610.04047478340.0284123090.0162278106

0.01323370180.04074575160.02879138290.0165888725

0.01358296920.04101931520.02917574170.0169570683

0.01394006050.04129550550.02956545730.0173325123

0.0143051090.04157435430.02996060260.0177153196

0.01467824910.04185589370.03036125110.0181056066

0.01505961630.04214015650.03076747720.0185034904

0.01544934710.04242717580.03117935630.0189090893

0.0158475790.04271698510.03159696440.0193225227

0.01625445050.04300961860.03202037850.0197439107

0.01667010080.04330511080.03244967640.0201733746

0.01709467050.04360349670.03288493670.0206110364

0.01752830050.04390481190.03332623890.0210570192

0.0179711330.04420909240.03377366330.021511447

0.01842331060.04451637480.03422729110.0219744444

0.01888497710.04482669610.03468720440.0224461372

0.01935627670.04514009390.03515348590.0229266517

0.01983735440.04545660640.03562621940.0234161153

0.02032835570.04577627220.03610548960.0239146559

0.0208294270.04609913050.03659138170.0244224022

0.02134071490.04642522110.0370839820.0249394838

0.02186236680.04675458440.03758337760.0254660307

0.02239453030.04708726130.03808965650.0260021737

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