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<p>O erro está na definicao de Sigma, você fez os cálculos com
variâncias marginais igual a 1 e segundo o "enunciado" essas
variâncias são bem menores.<br>
</p>
<br>
<div class="moz-cite-prefix">On 17/10/2016 17:05, Adriele Giaretta
Biase via R-br wrote:<br>
</div>
<blockquote
cite="mid:CANjWqYxenQJUmVv8xL6h8c3pfYsRcgAzDO3QVTpST+uRNQS=NA@mail.gmail.com"
type="cite">
<div dir="ltr">
<p class="MsoNormal" style="text-align:justify"><font
face="times new roman, serif"><span style="font-size:16px">Olá
pessoal,</span></font></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif"><br>
</span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-family:"times new
roman",serif;font-size:12pt">tenho uma dúvida com
relação à geração de variáveis aleatórias normais
multivariadas no R.</span><br>
</p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif">Eu gostaria de gerar
duas variáveis aleatórias (x1, x2) usando distribuição
normal multivariada com
estrutura de correlação entre elas. A Estrutura da matriz de
correlação foi
estimada antes com base num banco de dados reais (com
correlação fraca de - 0.2).
Porém, essas variáveis não podem ser negativas, Ex. x1 tem
média e variância,
respectivamente, iguais a 0.0067 e 0.0017; x2 tem média e
variância,
respectivamente, iguais a 0.1374 e 0.0024. Eu gero as
variáveis da seguinte forma:</span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif"><br>
</span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif"><br>
</span></p>
<p class="MsoNormal" style="text-align:justify"><u><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif">Programa usado no R:<span></span></span></u></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">#
Simulando os parâmetros com estrutura de correlação entre
eles<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">n
<- 1000 # tamanho da amostra gerada<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">p
<- 2 # numero de variáveis a serem
geradas<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">library(MASS)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif"># construíndo a matriz de correlação para
usar nas simulações, baseadas na característica da amostra
coletada</span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">mu<-rep(0,
times = p)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">rho
<- - 0.2 # correlacao
negativa <span></span></span><span
style="font-family:"times new
roman",serif;font-size:16px">- 0.2</span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">sigma2
<- 1<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">Sigma
<- sigma2 * ((1-rho)*diag(p)+rho*matrix(1, p, p))<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">X1
<- 0.0096 # Media da variavel x1<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">X2
<- 0.1203 # <span></span></span><span
style="font-family:"times new
roman",serif;font-size:16px">Media da variavel x2</span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">media
<- c(X1,X2)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">y <- mvrnorm(n, media, Sigma)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif" lang="EN-US">cor(y)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif" lang="EN-US">apply(y, 2,
mean)<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif">y<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif"><br>
</span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[1,] 0.309910452 1.0642521083</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[2,] -0.251583312 1.8909032058</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[3,] 1.330362012 -1.1239501814</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[4,] -0.793399464 -1.5433056284</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[5,] 2.165144843 -0.2645184534</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[6,] 0.532777085 1.0910864562</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[7,] -1.612135390 2.0489354648</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">
[8,] -0.430529913 1.0312062602</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><font
face="times new roman, serif"><span style="font-size:16px">...</span></font></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span
style="font-size:12pt;font-family:"times new
roman",serif"><span> </span></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif">Quando gero as
simulações para x1 e x2 usando a função <i>mvrnorm</i>,
o resultado me retorna alguns valores negativos para as
variáveis, isso não
poderia ocorrer. Teria alguma outra função em que eu possa
fornecer a variância
de cada uma dessas variáveis, além da estrutura de
correlação? Como poderia
contornar essa situação, usando o R?<span></span></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif"><span> </span></span></p>
<p class="MsoNormal" style="text-align:justify"><b><u><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif">Obs:</span></u></b><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif">
No SAS, a seguinte programação funciona perfeitamente:<span></span></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:12pt;line-height:115%;font-family:"times
new roman",serif"><br>
</span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">proc</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
</span><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">iml</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">wrksize=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">100000</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">K=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">2</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">N=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1000</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">; </span><span
style="font-size:18pt;font-family:"courier
new";color:green;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">/*
tamanho da amostra
*/</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">M={</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"></span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">};<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">S={
</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0.5283</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">,<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0.5283</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">};<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">X=shape(</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">,K,N);<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">ME=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">;
SI=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">DO</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">I=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">TO</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
K;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">DO</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">J=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">TO</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
N;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">if</span><span
style="font-size:18pt;font-family:"courier
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lang="EN-US"> I></span><b><span
style="font-size:18pt;font-family:"courier
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lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> </span><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">then</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> do;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
ME=M[I]+(S[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">,I])`*(inv(S[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">,</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">])*(X[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">,J]-M[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">]));<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> </span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">SI=S[I,I]-(S[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">,I])`*(inv(S[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">,</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">])*(S[</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">:I-</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">,I]));<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">end</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
X[I,J]=ME+NORMAL(</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">0</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">)*SQRT(SI);<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> </span><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">END</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">END</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">Z=t(X);<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">varnames=</span><span
style="font-size:18pt;font-family:"courier
new";color:purple;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">'X1'</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">:</span><span
style="font-size:18pt;font-family:"courier
new";color:purple;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">'X2'</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">create</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
NOVO </span><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">from</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> Z[colname=varnames];<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">append</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">from</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> Z;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">quit</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">data</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
MEXT; </span><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">set</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> NOVO;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">options</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">ps</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">66</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> </span><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">ls</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">75</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> X1=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">0.0067</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">+</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">0.0017</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">*X1; </span><span
style="font-size:18pt;font-family:"courier
new";color:green;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">/* normal */</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> <span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US"> </span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">X2=</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0.1374</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">+</span><b><span
style="font-size:18pt;font-family:"courier
new";color:teal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">0.0024</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">*X2;
</span><span style="font-size:18pt;font-family:"courier
new";color:green;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">/*
normal */</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span> </span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">proc</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"></span><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">corr</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">
</span><span style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">data</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">=MEXT;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><span
style="font-size:18pt;font-family:"courier
new";color:blue;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">var</span><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">
X1 X2;<span></span></span></p>
<p class="MsoNormal"
style="margin-bottom:0.0001pt;line-height:normal"><b><span
style="font-size:18pt;font-family:"courier
new";color:navy;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">run</span></b><span
style="font-size:18pt;font-family:"courier
new";color:black;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"
lang="EN-US">;<span></span></span></p>
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<div>
<div style="font-family:times,serif;margin:0cm 0cm
0.0001pt;font-size:16px"><span style="white-space:pre"> </span>Adriele
Giaretta Biase.</div>
<div style="font-family:times,serif;margin:0cm 0cm
0.0001pt;font-size:16px"><span style="white-space:pre"> </span>Mestre
em Estatística e Experimentação Agropecuária -
UFLA. <br>
<span style="white-space:pre"> </span>Doutora em
Estatística e Experimentação Agronômica - ESALQ/ USP</div>
<div style="font-family:times,serif;margin:0cm 0cm
0.0001pt;font-size:16px"><span style="font-size:12pt;white-space:pre"> </span><span
style="font-size:12pt">Contato: (19) 98861-0619.</span></div>
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