<div dir="ltr"><div class="gmail_default" style="font-family:verdana,sans-serif">Adriele, boa tarde!<br><br></div><div class="gmail_default" style="font-family:verdana,sans-serif">Tentei adaptar seu código R com base no que entendi do script em SAS. Veja se pode ser útil...<br></div><div class="gmail_default" style="font-family:verdana,sans-serif"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif">### <code r><br></div><div class="gmail_default" style="font-family:verdana,sans-serif"><span style="font-family:monospace,monospace">library(MASS)<br>{<br> set.seed(1357)<br> n <- 1000 # tamanho da amostra gerada (N)<br> p <- 2 # numero de variáveis a serem geradas (K)<br> ME <- rep(1, p)<br> rho <- -0.2 # correlacao negativa - 0.2<br> sigma2 <- 1<br> sigma <- sigma2 * ((1-rho)*diag(p)+rho*matrix(1, p, p))<br> SI <- mvrnorm(n, ME, sigma)<br>}<br>apply(SI, 2, mean) # ~ 1<br># [1] 1.037774 1.017846<br><br>cor(SI) # ~ sigma<br># [,1] [,2]<br># [1,] 1.0000000 -0.1973338<br># [2,] -0.1973338 1.0000000<br><br>mu <- c(0.0067, 0.1374)<br>mean(0.0017*SI[,1]) # ~ 0.0017<br>mean(0.0024*SI[,2]) # ~ 0.0024<br><br>RES <- data.frame(X1=0.0067+0.0017*SI[,1], X2=0.1374+0.0024*SI[,2])<br><br>round(cbind(RES=colMeans(RES), INI=mu),4)<br># RES INI<br># X1 0.0085 0.0067<br># X2 0.1398 0.1374<br><br>cor(RES)<br># X1 X2<br># X1 1.0000000 -0.1973338<br># X2 -0.1973338 1.0000000<br></span></div><div class="gmail_default" style="font-family:verdana,sans-serif"><span style="font-family:monospace,monospace">### </code><br></span></div><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><span><br>================================================<br>Éder Comunello<br>Researcher at Brazilian Agricultural Research Corporation (Embrapa)<br>DSc in Agricultural Systems Engineering (USP/Esalq)<br>MSc in Environ. Sciences (UEM), <span>Agronomist (UEM)</span><br>---<br>Embrapa Agropecuária Oeste, Dourados, MS, Brazil |<O>|<br>================================================<br>GEO, -22.2752, -54.8182, 408m<br>UTC-04:00 / DST: UTC-03:00</span><div><div><div><br></div><div><br></div></div><div style="font-size:small"><br></div></div></div></div></div></div></div></div></div></div></div></div></div>
<br><div class="gmail_quote">Em 17 de outubro de 2016 16:05, Adriele Giaretta Biase via R-br <span dir="ltr"><<a target="_blank" href="mailto:r-br@listas.c3sl.ufpr.br">r-br@listas.c3sl.ufpr.br</a>></span> escreveu:<br><blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote"><div dir="ltr"><p style="text-align:justify" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px">Olá pessoal,</span></font></p><p style="text-align:justify" class="MsoNormal"><span style="font-size:12pt;line-height:115%;font-family:"times new roman",serif"><br></span></p><p style="text-align:justify" class="MsoNormal"><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 style="text-align:justify" class="MsoNormal"><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 style="text-align:justify" class="MsoNormal"><span style="font-size:12pt;line-height:115%;font-family:"times new roman",serif"><br></span></p><p style="text-align:justify" class="MsoNormal"><span style="font-size:12pt;line-height:115%;font-family:"times new roman",serif"><br></span></p>
<p style="text-align:justify" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">n
<- 1000 # tamanho da amostra gerada<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">p
<- 2 # numero de variáveis a serem
geradas<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif"><span> </span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">library(MASS)<span></span></span></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">mu<-rep(0,
times = p)<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">sigma2
<- 1<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">X1
<- 0.0096 # Media da variavel x1<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">media
<- c(X1,X2)<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">y <- mvrnorm(n, media, Sigma)<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif" lang="EN-US">cor(y)<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif" lang="EN-US">apply(y, 2,
mean)<span></span></span></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif">y<span></span></span></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif"><br></span></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [1,] 0.309910452 1.0642521083</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [2,] -0.251583312 1.8909032058</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [3,] 1.330362012 -1.1239501814</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [4,] -0.793399464 -1.5433056284</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [5,] 2.165144843 -0.2645184534</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [6,] 0.532777085 1.0910864562</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [7,] -1.612135390 2.0489354648</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px"> [8,] -0.430529913 1.0312062602</span></font></p><p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><font face="times new roman, serif"><span style="font-size:16px">...</span></font></p>
<p style="margin-bottom:0.0001pt;text-align:justify;line-height:normal" class="MsoNormal"><span style="font-size:12pt;font-family:"times new roman",serif"><span> </span></span></p>
<p style="text-align:justify" class="MsoNormal"><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 style="text-align:justify" class="MsoNormal"><span style="font-size:12pt;line-height:115%;font-family:"times new roman",serif"><span> </span></span></p>
<p style="text-align:justify" class="MsoNormal"><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 style="text-align:justify" class="MsoNormal"><span style="font-size:12pt;line-height:115%;font-family:"times new roman",serif"><br></span></p>
<p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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"><wbr>: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">:<wbr>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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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(<wbr>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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><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 class="gmail-HOEnZb"><font color="#888888"><span></span></font></span></span></p><span class="gmail-HOEnZb"><font color="#888888"><div><br></div>-- <br><div class="gmail-m_6171262782706140291gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div style="font-family:times,serif;margin:0cm 0cm 0.0001pt;font-size:16px"><span style="white-space:pre-wrap"> </span>Adriele Giaretta Biase.</div><div style="font-family:times,serif;margin:0cm 0cm 0.0001pt;font-size:16px"><span style="white-space:pre-wrap"> </span>Mestre em Estatística e Experimentação Agropecuária - UFLA. <br><span style="white-space:pre-wrap"> </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-wrap"> </span><span style="font-size:12pt">Contato: (19) 98861-0619.</span></div></div></div></div></div></div>
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