<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">Sobre assunto correlato sugiro olhar na Wikipédia os dados e gráficos de <div>Anscombe ‘s quartet<br><br><div id="AppleMailSignature" dir="ltr">Enviado do meu iPhone</div><div dir="ltr"><br>Em 5 de mar de 2021, à(s) 10:01, Julio Stern <<a href="mailto:jmstern@hotmail.com">jmstern@hotmail.com</a>> escreveu:<br><br></div><blockquote type="cite"><div dir="ltr">
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<span style="margin:0px; font-size:12pt; background-color:rgb(255,255,255)"><span style="margin:0px; font-size:14pt; font-family:Arial,Helvetica,sans-serif">Caros Redistas </span></span></div>
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<span style="margin:0px; font-size:12pt; background-color:rgb(255,255,255)"><span style="margin:0px; font-size:14pt; font-family:Arial,Helvetica,sans-serif">Conversando com colegas de outras areas sobre a diferenca entre Causalidade e Correlacao, </span></span><span style="color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif; font-size:12pt"><span style="font-size:14pt; font-family:Arial,Helvetica,sans-serif">principalmente
no contexto de vacinas, tratamentos medicos para Covid, etc. </span></span><span style="color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif; font-size:12pt"><span style="font-size:14pt; font-family:Arial,Helvetica,sans-serif">acabei conhecendo o</span></span><span lang="PT-BR" style="color:rgb(0,0,0); font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> livro: </span></div>
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<span lang="PT-BR" style="color:rgb(0,0,0); font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span><span lang="PT-BR" style="color:rgb(0,0,0); font-family:Calibri,sans-serif; font-size:11pt"><span style="font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></div>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">>>></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Tyler
Vigen (2015).</span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Spurious Correlations.</span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Hachette
Books.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">que tem gráficos fantasticos, com series temporais totalmente desconexas que exibem altíssima correlacao.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Nao tenho o livro, mas alguns graficos podem ser vistos em<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">>>> <a href="https://www.tylervigen.com/spurious-correlations">https://www.tylervigen.com/spurious-correlations</a></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">>>> <a href="https://tylervigen.com/discover">https://tylervigen.com/discover</a></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Comecei a fazer umas continhas rapidas sobre a probabilidade, p</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> , </span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">de
obter, em duas series temporais, x(t) e y(t) ,<span> </span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">com dez pontos de abscissa t={1,2, ... 10}</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">e
ordenada no intervalo [0,1] , uma alta correlação, i.e.,<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">p = Pr ( corr ( x(t) , y(t) )<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">>=</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">(1-alpha)
) , para alpha= 0.1</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">ou</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">0.05<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">ou</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">0.01</span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> <span> </span></span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Assumindo nao haver estrutura alguma nas series x(t) e y(t) , o resultado eh muito baixo.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Mesmo considerando uma enorme biblioteca de graficos aleatorios, nao da...<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Parece ser necessario assumir "a priori" a existência de alguma "estrutura intrinseca de associacao" entre os pontos de cada uma das series temporais,
por exemplo, alguma estrutura de auto-correlacao.<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Antes de sair por ai tentando reinventar a roda, melhor perguntar a quem sabe...<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Alguem ja deve ter pensado neste problema!<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span><span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Alguma
ideia de como modela-lo?<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">Abraco a todos e tudo de bom,<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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<span lang="PT-BR" style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif">---Julio Stern<span> </span></span><span lang="PT-BR" style="margin:0px"><span style="margin:0px; font-size:14pt; line-height:normal; font-family:Arial,Helvetica,sans-serif"> </span></span></p>
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